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Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]
H.G.Muller wrote on Mon, Apr 28, 2008 06:59 PM UTC:
Hans Aberg:
| Perhaps the statistical method is only successful because it is 
| possible by a brute-force search to seek out positions not covered 
| by the classical theory.

I am not sure what 'brute force' you are referring to. Do you consider
Monte-Carlo sampling of a quantity you want to measure a 'brute force'
approach? I would associate that more with exhaustive search. Playing a
few thousand games can hardly be called 'exhaustive', considering the
size of the game tree for Chess.

What do you mean by 'classical theory'? Are you referring to the piece
value system 1,3,3,5,9, or some more elaborate point system including
positional advantages, or very complex methods of proving a certain
position can be won against any play?

What does it matter anyway how the piece-value system for normal Chess was
historically constructed anyway? Don't you agree that the best way to play
the game through a piece-value heuristic is to make sure that positions
with better piece values (in your favor, i.e. yours minus those of the
opponent) will have a better probability to be won? (It will be understood
that the heuristic will only be applied to 'quiet positions': the players
are supposed to be smart enough to search low-depth tactical trees that
makes them recognize that the are not a Pawn ahead but a Queen behind when
the opponent has a passer that they cannot stop, or has the move and can
capture their hanging Queen.)

💡📝Hans Aberg wrote on Mon, Apr 28, 2008 05:27 PM UTC:
H.G.Muller:
| It seems to me that in the end this would produce exactly the same
| results, at the expense of hundred times as much work. You would still
| have to play the games to see which piece combinations dominantly win.

Perhaps the statistical method is only successful because it is possible by a brute-force search to seek out positions not covered by the classical theory.

H.G.Muller wrote on Mon, Apr 28, 2008 07:06 AM UTC:
Hans Aberg:
| I describe how a piece value theory might be developed without 
| statistics. Since one P or R ahead generically wins, set them to 
| the same value. Now this does not work in P against R; so set the 
| value higher than P. Then continue this process in order to refine 
| it, comparing different endings that may appear in play, taking away 
| special cases, always with respect to tournament practice, using 
| postmortem game analysis.

It seems to me that in the end this would produce exactly the same
results, at the expense of hundred times as much work. You would still
have to play the games to see which piece combinations dominantly win. But
now you would throw away the information on how much, making the outcome of
65% equivalent to one of 95%.

While in fact there is very much information in this, as tsmall advantages
turmn out to be additive to a high degree of accuracy. If Pawn odds is 62%,
and Q vs A is 59%, I can be pretty sure that A+P vs Q will be 53%. In the
system you propose, you would have to actually play A+P vs Q before you
would know if A is worthe more or less than Q minus P.

This in particular applies to the fractional advantages. If a B-pair wins
56% from a B anti-pair, and you would only interpret that as 'B-pair is
good', you would have to explicitly test the B-pair against any other
fractional advantage (e.g. Q+BB(unpaired) vs C+BB(paired), Q+BB(unpaired)
vs A+BB(paired), etc to know that the pair advantage was half a Pawn,
rather than 3/4 or 1/4.

Why do you think this is an attractive method, and why would you expect it
to give different results in the first place? Can you construct a
hypothetical example (of score percentages) where your analysis method
would produce different results from mine?

💡📝Hans Aberg wrote on Sun, Apr 27, 2008 10:33 PM UTC:
H.G.Muller:
| Why would you want to set the values the same? Because both a Pawn and
| a Rook advantage in the end-game is 100% won?

I describe how a piece value theory might be developed without statistics. Since one P or R ahead generically wins, set them to the same value. Now this does not work in P against R; so set the value higher than P. Then continue this process in order to refine it, comparing different endings that may appear in play, taking away special cases, always with respect to tournament practice, using postmortem game analysis.

💡📝Hans Aberg wrote on Sun, Apr 27, 2008 08:25 PM UTC:
H.G.Muller:
| You seem to attach a variable meaning to the phrase 'a pawn ahead', so
| that I no longer know if you are referring to KPK, or just any position.

I tried to explain how explain the idea of a general, or 'generic' situation by restricting to this example. In a general case, one could not classify the games as exactly.

| The rule of thump amongst Chess players is that in Pawn endings that
| you cannot recognize as obvious theoretical wins/draws/losses (like all
| KPK positons, positions with passers outside the King's square etc.) a
| Pawn advantage makes it 90% likely that you will win.

It haven't seen anything like that in end-game books, or players from the time whan I was active, before the days of computer chess. I think that nowadays, people learn much by playing against strong computer programs, rather than learning classical theory. So I do no think such percentages relate to any classical chess theory, and possibly no formal mathematical statistics. Such a statistical approach, even if formalized, may still work well in a computer that by brute force can do a deeper lookahead than a human, but may fail otherwise.

H.G.Muller wrote on Sun, Apr 27, 2008 07:27 PM UTC:
I missed this one:

Hans Aberg:
| You say that a pawn ahead is always a win with only some 
| exceptions. So is a rook. So set values of these the same - 
| does not work to predict generic rook against pawn end-games.

Why would you want to set the values the same? Because both a Pawn and a
Rook advantage in the end-game is 100% won?

In the first place they aren't. An extra Pawn will win 90%, an extra Rook
99.9-100%. But, for the sake of argument, change the example to an extra
Rook or an extra Queen, and say that both now win 100%. Does that prove
the piece value of a Rook and a Queen are the same?

Of course NOT. 100% is far outside the linear regime, and obviously the
score becomes meaningless there. I never take into account the results of
thest that are more than 70% biased. I don't have to, as a full Pawn
advantage in the opening in the linear range only adds 12%, (so I get a
62% score for pure Pawn odds), and in principle I can always balance the
material such that I get scores below that by adding a Pawn.

So what would NOT work, and what I thus do NOT do, is first giving full
Archbishop odds, and then giving Chancellor odds. Because both these odds
would lead to ~95% scores, and trying to peel a piece value out of the
fact if they are 95% or 96% falls far below the resolution (determined by
statistical noise), and would be extremely sensitive to the exact initial
position (as the 5% non-wins would be due to tactical freak accidents like
quick mates or perpetuals).

What I do is play C vs A or CC vs AA (nearly equal) to see who wins. Or Q
vs A+P and Q vs C+P (to see who does better). Or A vs R+R or A vs R+B or A
vs R+N+P, to see if A typically beats those combinations (which it does,
but never by more than 60% or so, or I would give stronger material to the
weak side).

But if Q beats A by a larger score (say 59%) than A+P beats Q (say 53%), I
consider it evidence that Q-A > 0.5 Pawn. Because I know (from observation)
that adding another 50cP advantage to the imbalance in favor of the weak
side (like replacing an unpaired Bishop by a Knight) will in general
simply adjust the existing score by 6% at the expense of the side who you
give the weakness. And that duplicating a weakness (like giving one side
two unpaired Bishops in stead of the other's two Knights) will simply
double the score excess to 12%, the same as for Pawn ods, and can be
exactly compensated by giving the Knight-side an extra Pawn. So Q+N will
still beat A+B(unpaired), consistent with Q-A in the point system being
more poinst than the B-N difference of 0.5 Pawn, and A+P-Q being less.

H.G.Muller wrote on Sun, Apr 27, 2008 06:34 PM UTC:
Hans Aberg:
| You say that a pawn ahead is always a win with only some 
| exceptions. So is a rook. So set values of these the same - 
| does not work to predict generic rook against pawn end-games.
You seem to attach a variable meaning to the phrase 'a pawn ahead', so
that I no longer know if you are referring to KPK, or just any position.
The rule of thump amongst Chess players is that in Pawn endings that you
cannot recognize as obvious theoretical wins/draws/losses (like all KPK
positons, positions with passers outside the King's square etc.) a Pawn
advantage makes it 90% likely that you will win. In a Rook ending, OTOH, a
single Pawn advantage will be a draw in 90% of the cases.
| 90 % with respect to what: all games, those that GMs, newbies, or a 
| certain computer program play?
You will always be able to find players that will bungle any advantage,
amongst Humans as well as computers. 90% is the limit to which you
converge with increasing quality play. And you converge to it rather
quickly, because Pawn endings aren't that complicated. Players at a level
where 'opposition' and the 'square rule' are familiar concepts will
probably achieve close to this percentage.
| The traditional piece value system does not refer to a statement 
| like: 'this material advantage leads to a win in 90 % of the cases'.
This is because even the weakest players get to learn the piece-value
system, and the weaker they are, the more faithfully they usually adhere
to it. Even 6 year olds get to learn this before they know about castling
and e.p. capture. And to people that can only look 2 ply ahead a Pawn
advantage obviously means a lot less (in terms of score benifit they will
achieve because of this) than to 1900-rated players.

So the win percentage derived from a certain advantage according to the
piece-value system is not fixed. But that is not the same as saying that
for a given level of play, a larger advantage does not result in a higher
score. In fact it does. At any level of play, giving Knight odds between
equal players leads to a much larger win percentage than giving Pawn odds,
while Rook odds would give even more (if by then it would not already be
100%).

But if a certain position (or set of positions characterized by the same
material imbalance, as I use in my test matches) would be won in 90% of
the cases between equal players at any level above 1800 Elo by white (but
tail off below that, when you get into the regions of the real patzers),
would it, according to your definition, still be possible that black
actually had the better 'winning chances'? And that a piece-value system
that would predict these better 'winning chances' for black thus was a
correct and viable system?

I would prefer (and advice anyone else) to use a piece-value system that
would actually predict that white had better winning chances in that
position! As, by the time you will have gone through the trouble of
forcing the opponent to this position, selected on basis of the system,
you will be subjected to these very same winning chances.

💡📝Hans Aberg wrote on Sun, Apr 27, 2008 05:09 PM UTC:
H.G.Muller:
|| Change the values radically, and see what happens...
| What do you mean? Nothing happens, of course.

You say that a pawn ahead is always a win with only some exceptions. So is a rook. So set values of these the same - does not work to predict generic rook against pawn end-games.

| If they would occur 90% of the time, I would call them common, not special.

90 % with respect to what: all games, those that GMs, newbies, or a certain computer program play?

| So in your believe system, if a certain position, when played by expert
| players to the best of their ability, is won in 90% of the cases by white,
| it might still be that black has 'the better chances' in this position?

The traditional piece value system does not refer to a statement like: 'this material advantage leads to a win in 90 % of the cases'.

H.G.Muller wrote on Sun, Apr 27, 2008 11:22 AM UTC:
Hans Aberg:
| Change the values radically, and see what happens...
What do you mean? Nothing happens, of course. KPK positions that are won,
will remain won. What did you expect? That they become draws when I reduce
the Pawn value, or become lost positions when I say that a Pawn has a
negative value???
| It is true of all chess positions, not only end-game.
Except for the unfortunate detail that threredo not exist anyChess
positions other than some late end-games and a few mate-in-N problems that
are known to be won...
| But the point system will say that KQ will win over KP unless there 
| are some special circumstances, not that it will win in a certain 
| percentage if players of the same strength are making some random 
| changes in their play.
Only a quantitative measure can establish if the circumstances are
special, or not. If they would occur 90% of the time, I would call them
common, not special.
| Only that the 'winning chances' does not refer to a percentage of 
| won games of equal strength players making random variations, which 
| is what you are testing. It refers to something else, which can be 
| hard to capture giving its development history.
So in your believe system, if a certain position, when played by expert
players to the best of their ability, is won in 90% of the cases by white,
it might still be that black has 'the better chances' in this position?
If it is, this would be a very good conclusion to end this discussion
with. I don't see how going for such positions with 'better chances'
(guided by piece values) in play would win you many games, though...

💡📝Hans Aberg wrote on Sun, Apr 27, 2008 10:23 AM UTC:
Me:
| So in general, one P ahead does not win, but in special circumstances 
| it can be,  ...
H.G.Muller:
| This is already not true. In general, one Pawn ahead does win in a Pawn ending. KPK
| is an exception (or at least some positions in it are).

My statement referred to this particular ending. For other endings, I indicated it depends on the playing strength, noting that a GM would make sure to win whenever possible, but a weaker player may prefer more material. It is classification for developing playing strategies, not the theoretically best one.

| But is is still completely unclear to me how this has any bearing on piece values.

Change the values radically, and see what happens...

| KPK is a solved end-game (i.e. tablebases exist), so the concept of piece value is
| completely useless there. In solved end-games it only matters if the position is
| won, ...

It is true of all chess positions, not only end-game.

| ...and having KPK in a won position is better than having KQK in a drawn position.

So here one the point-system would be useless, if one faces the possibility of having to choose between those two cases. But the point system will say that KQ will win over KP unless there are some special circumstances, not that it will win in a certain percentage if players of the same strength are making some random changes in their play.

| I don't see how you could draw a conclusion from that that a Pawn has a higher value
| than a Queen.

I have no idea what this refers to.

| Piece values is a heuristic to be used in unsolved positions, to determine who has
| likely the better winning chances.

Only that the 'winning chances' does not refer to a percentage of won games of equal strength players making random variations, which is what you are testing. It refers to something else, which can be hard to capture giving its development history.

H.G.Muller wrote on Sat, Apr 26, 2008 09:36 AM UTC:
Hans Aberg:
| So in general, one P ahead does not win, but in special circumstances 
| it can be,  ...
This is already not true. In general, one Pawn ahead does win in a Pawn ending. KPK is an exception (or at least some positions in it are).

But is is still completely unclear to me how this has any bearing on piece values. KPK is a solved end-game (i.e. tablebases exist), so the concept of piece value is completely useless there. In solved end-games it only matters if the position is won, and having KPK in a won position is better than having KQK in a drawn position. I don't see how you could draw a conclusion from that that a Pawn has a higher value than a Queen.

Piece values is a heuristic to be used in unsolved positions, to determine who has likely the better winning chances. Like in an early middle-game position, where you just lost the exchange, and it will make you feel like you are losing the game because of that fact...

H.G.Muller wrote on Sat, Apr 26, 2008 09:24 AM UTC:
Reinhard: Within the boundary condition that the game should be played wth a strategy belonging to a sub-class of all possible strategies, (in this case a strategy with an evaluation based on additive piece values that are constant throughout the game), there is a best strategy. And the strategy will not lead to deterministic play, as there is often choice between moves that are evaluated equal, and the choice between them is based on random factors outside the strategy. So the outcome of a position under such a strategy is not fixed, but probabilistic.

That the strategy is not globally optimal, and that there exist strategies (not based on piece value but, for example, material tables), is not a problem if the playing strength of the piece-value-based strategy is not very much below the global optimum. And, considering the success that current engines hae in being the best Chess entities on the planet, I would say the piece-value-based strategies are doing a pretty good job. In particular, Joker80 is doing a pretty good job for 10x8 Chess. The strategies of our best engines are such that the variability of the result obtained from the set of positions with a certain material composition is not dominated by errors that the engines make in playing out such positions, but by the W/D/L statistics within the set. At that point, there would be very little change on improving the quality of play any further.

To give ane example: without knowledge of other details, it is better to have two minors than a Rook in a position which otherwise contains only equal numbers of Pawns (plus Kings). This despite the fact that zillions of KRPPPBNPPP positions are won for the Rook side. It is just that there are far more that are won for the B+N side. That the engines you use to decide which positions are won and which are lost (for a sample of the positions) now and then bungle a won game that was close to the limit, on the average cancels out, provided it is only the games close to the win/loss boundaries that can be bungled by the average playing inaccuracy. Because the narrow strips on either side of the boundary have equal area. Only if the accuracy gets very low, so that games very far from the boundary can still be bungled, the exact shape of the boundary (e.g. its curvature) becomes important.

Reinhard Scharnagl wrote on Sat, Apr 26, 2008 06:07 AM UTC:
Harm: If there is a best strategy (i.e. best set of piece values) it must be shared by both sides. The theoretically best play is amongst the set of self-play games. And it is only the score that results from theoretically best play that determines the piece value.

First there is no 'best play' without having complete information. But such is far away from human experiences. Nevertheless supposing to be in such a hypothetic well informed situation, indeed participating optimal players would behave related to the way you stated - beside of the fact, that then there would be no longer a need for any piece value at all, because then all nodes merely will be valued as +1, 0 or -1.

So the question is, whether your approach would be convergent to any claimed ideal value model. Living within a world without such a perfect information and using engines, which all are wearing blinkers then hiding tabooed piece trades, I intensively doubt on that. You will have to try a lot of different models implemented into engines of equal maturity to find out after a lot of experiments.

Rich Hutnik wrote on Sat, Apr 26, 2008 02:37 AM UTC:
I have been following this discussion a bit, am pretty confused, but think I have a few things down.  I had a few questions here regarding this entire discussion:
1. I know when they try to evaluate American football for fantasy league play, and are evaluating players, they will tend to treat the defense as a single entity.  The reason for this is that it is next to impossible to be able to tell the value of a single player in defense.  Can one argue that chess is similar?  Pieces work with one another.
2. Similar to this last question, are the value of pieces in Chess960 the same as they are in FIDE Chess?  Also, if players had free set up in the back row with their pieces, would they have the same value then?  Are rooks worth more if they start out in the middle, instead of the outside?

I ask this question, because of some things I am interested in doing here.  First, I would be interested in pitting Chess against Shogi or XiangQi in some way that would have the sides roughly equal to one another, by either point handicapping or something else.  

Secondarily, if you take a look at Near Chess, I have found that the game takes on entirely different dynamics if you move the rooks back or not.  This also relates to doing Near Chess vs Normal (FIDE Chess).  Playing the Near Chess side is a different animal than Normal Chess, and I found, even without castling, Near Chess holds its own.  For FYI, Near Chess is here:
http://www.chessvariants.org/index/msdisplay.php?itemid=MSnearchess

(I just bring up Near Chess now, because it fits a concern I have, and it seems like the conversation).

So, in a nutshell, would anyone want to focus on the value of a set of chess variant RULES vs another one, rather than single pieces without a context they fit into?  How about a test, for example of the value of a Queen in Chess960 depending on where it starts, and which pieces are next to it?  Maybe even work out a bidding system for configurations. 

I hold out hope that this may be a reality one day, to effectively balance a range of chess variants, so a player could play with their favorite set up, against another player's set up, and it be reasonably close.

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 10:37 PM UTC:
H.G.Muller:
| It is too vague for me. Could you give a specific example?

Take K+P against K. Then it can only be won if the king is well positioned against the pawn and the pawn isn't on the sides if the opponent king is in good position. So in general, one P ahead does not win, but in special circumstances it can be, So a player that isn't very good at end-games will probably try to get more material, but a better one will know, and an even better player will be able trying to play for the most favored end-game. A weak player may loose big in the middle game because they don't know how to keep the pieces together, but a GM might do that because knowing that the alternatives will lead to a lost end-game, so trying something wilder may be a better try. But a GM may not have much use of such long-range strategic skills against a computer that can search all positions deeper, becoming reduced, relative the computer, not being to keep the pieces together.

H.G.Muller wrote on Fri, Apr 25, 2008 09:29 PM UTC:
It is too vague for me. Could you give a specific example?

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 09:20 PM UTC:
Me:
| By experience, certain generic types of endgames will empirically 
| classified by this system. Those that aspiring becoming GMs study 
| hard to refine it, so that exceptions are covered. Once learned, 
| it can be used to instantly evaluate a position.
Someone:
| What do you mean by this? The result of end-games is not determinedby
| the material present. There are KRKBPP end games that are won for the
| Rook, and that are won for the Bishop. Similar for KRKBP and KRKBPPP.
| So how would you derive a piece-value system of this?

It hangs on the word 'generic', meaning some general empiric cases. Then the cases you cover would be special cases studied separately as a refinement. These are excepted when defining the piece value system.

Anonymous wrote on Fri, Apr 25, 2008 07:42 PM UTC:
Hans Aberg:
| By experience, certain generic types of endgames will empirically 
| classified by this system. Those that aspiring becoming GMs study 
| hard to refine it, so that exceptions are covered. Once learned, 
| it can be used to instantly evaluate a position.
What do you mean by this? The result of end-games is not determinedby the
material present. There are KRKBPP end games that are won for the Rook,
and that are won for the Bishop. Similar for KRKBP and KRKBPPP. So how
would you derive a piece-value system of this?

H.G.Muller wrote on Fri, Apr 25, 2008 07:37 PM UTC:
Reinhard:
| Thus there are no trades caused by different views of pieces values, 
| which could make a trade attractive for BOTH sides. Thus your model 
| is never verified at such critical moments. 
If there is a best strategy (i.e. best set of piece values) it must be
shared by both sides. The theoretically best play is amongst the set of
self-play games. And it is only the score that results from theoretically
best play that determines the piece value.

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 05:47 PM UTC:
Me:
| As I said, the outcome is decided by the best playing from both sides. 
| So if one starts to play poorly in the face of a material advantage, 
| that is inviting a loss.
Someone:
| We still don't seem to connect. What gave you the impression I
| advocated to play poorly? Problem is that even with your best play, it
| might be a loss. And as it is an end leaf of your search tree, which
| is limited by the time control, you have no time to analyze it until
| checkmate, or in fact analyze it at all. You have to judge in under a
| second if you are prepared to take your chances in this position,

The original context was what how I think that the classical piece value system is constructed:

By experience, certain generic types of endgames will empirically classified by this system. Those that aspiring becoming GMs study hard to refine it, so that exceptions are covered. Once learned, it can be used to instantly evaluate a position.

This is then not a statistical system.

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 05:38 PM UTC:
H.G.Muller:
| But it is still not clear to me that a Human would not suffer as bad
| from [increasing the average number of moves].

This is clearly the difficulty.

| Furthermore, computers are not really totally ignorant on strategical
| matters either. But they cannot found by search, and must be programmed
| in the evaluation.

The strength in orthodox chess derives much from implementing human heuristics. So if the game is changeable or rich in this respect, it will be more difficult for computers.

| So it would also depend on the difficulty to recgnize the
| strategical patterns for a computer as opposed to a Human.

Computers have difficulty in understanding that certain positions are generally toast. They make up by being very good at defending themselves, so a good program can hold up positions that to humans may look undefendable. So a either a variant should have better convergence between empirical reasoning and practice, or one should let the humans have access to a cmoputer that do combinatorial checking.

| And until the game strongly simplifies, the main strategic goal is
| usually to gain material, using piece values as an objective.

That seems optimistic :-). A GM advice for becoming good in learning end-games.

| Unless the opponent really ignores his King safety. Then the 
| strategic goal will become to start a mating attack.

There are all sorts of tactics possible.

One thing one can try against a computer program is giving it material in exchange for initiative. Then, the human may need some assistance on the combinatorial side.

If the game is highly combinatorial the computer is favored. So one can try to close it.

So a chess variant should admit stalling. If it is always possible to break into highly combinatorial positions, then the computer will be favored.

Reinhard Scharnagl wrote on Fri, Apr 25, 2008 02:45 PM UTC:
I wrote: Then your engine will throw away underestimated pieces too cheap and keep overestimated too dear. Thus it will start and avoid a lot of trades in unjustified manner.

This hardly occurs, because this is SELF-PLAY.

Probably you have not understood my intention. On games between our engines you commented to some trades, that your program would never do such. And this I suppose is true. Thus your engine vs. engine games are avoiding such type of trades, and never experiencing, whether such trades would be beneficial or not.

Trades in your type of engine vs. engine games will happen only, if both engines agree in the equality of that trades, or if one engine has already come into an inferior situation and could not avoid a bad trade. But then the game might allready be decided.

Thus there are no trades caused by different views of pieces values, which could make a trade attractive for BOTH sides. Thus your model is never verified at such critical moments.

H.G.Muller wrote on Fri, Apr 25, 2008 01:30 PM UTC:
Hans Aberg:
| If it is doubled, then in a 7-ply search, if the positions are 
| independent, a search for all would require 2^7 = 128 more positions 
| to search for. If there are 10 times more average moves, then 10^7 
| more positions need to be searched.
Well, actually alpha-beta pruning makes it such that in a 7-ply search you
would only need 2^4 = 16 times as many positions, or 10^4 times. (And, as
the number of transpositions would likely go up, you would save a lot of
that with a hash table.) But these are still respectable numbers, so you
would perhaps only be able to do a 5-ply or a 4-ply search. 

But it is still not clear to me that a Human would not suffer as bad from
this. The game of Arimaa was a deliberate attempt to defeat computers
through this strategy, by creating branchin ratios of thousands. But I am
not sure if this has been succesful. The prevailing opinion under Chess
programmers is that computers are poor at Arimaa not because it is too
challenging, but mainly because no serious programmer cares...

Furthermore, computers are not really totally ignorant on strategical
matters either. But they cannot found by search, and must be programmed in
the evaluation. So it would also depend on the difficulty to recgnize the
strategical patterns for a computer as opposed to a Human. And until the
game strongly simplifies, the main strategic goal is usually to gain
material, using piece values as an objective. Unless the opponent really
ignores his King safety. Then the strategic goal will become to start a
mating attack.

Anonymous wrote on Fri, Apr 25, 2008 01:10 PM UTC:
Hans Aberg:
| As I said, the outcome is decided by the best playing from both sides. 
| So if one starts to play poorly in the face of a material advantage, 
| that is inviting a loss.
We still don't seem to connect. What gave you the impression I advocated
to play poorly? Problem is that even with your best play, it might be a
loss. And as it is an end leaf of your search tree, which is limited by
the time control, you have no time to analyze it until checkmate, or in
fact analyze it at all. You have to judge in under a second if you are
prepared to take your chances in this position, as the opponent can play
other moves from the position actually on the board than those leading to
this one, so you have 200 positions that are just as likely you will end
up in. So if you want to spend more than a second of thought on each of
those 200 positions, your flag will be down even before you move.

So you will have a serious problem: 3 minutes to judge 200 positions, 198
of them not being checkmates, so you cannot be 100% sure that they are
won, and each of them needing about 100 hours of analysis to make 90% sure
what the outcome will be...

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 01:00 PM UTC:
H.G.Muller:
| Why do you think the bigger board and the stronge piece make the game
| more strategical?

I said: if one increases the average number of moves in each position, then a full search may fail, as there will be too many of them. Then a different strategy is needed for success. If it is doubled, then in a 7-ply search, if the positions are independent, a search for all would require 2^7 = 128 more positions to search for. If there are 10 times more average moves, then 10^7 more positions need to be searched.

Strategic positions is another matter: indeed, in orthodox chess, trying to settle for positions were advantage depends on long term development is a good choice against computers, the latter which tend to be good in what humans find 'chaotic' positions.

The design of a variant must be so that it admits what humans find strategic, and so it is possible to play towards them from the initial position. I am not sure exactly what factors should be there. Just putting in more material may indeed favor the computer. In orthodox chess, one can stall by building a pawn chain, and then use the minor pieces for sacrifices to create breakthrough. The chess variant must contains some such factors as well.

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 08:57 AM UTC:
H.G.Muller:
| It never happened to you that early in the game you had to step out of
| check, and because of the choice you made the opponent now promotes with
| check, being able to stop your passer on the 7th?

Early in the game, most things happen by opening theory. And if one is getting an advantage like a passer, one should be careful to not let down the defense of the king, including computing checks.

With those computer programs, a tactic that may work is to let down the defenses of the king enough that the opponent thinks it is worth going after it, and then exploit that in a counterattack.

| I think that if you are not willing to consider arguments like 'here I
| have a Knight against two Pawns (in addition to the Queen, Rook,
| Bishop and 3 Pawns for each), so it is likely, although not certain, that
| I will win from there', the number of positions that remains acceptable
| to you is so small that the opponent (not suffering from such scruples) will
| quickly drive you into positions where you indeed have 100% certainty....
| That you have lost!

As I said, the outcome is decided by the best playing from both sides. So if one starts to play poorly in the face of a material advantage, that is inviting a loss. So a material advantage of one pawn must happen in circumstances of where one can keep the initiative, otherwise, it might be better to returning that material for getting the initiative hopefully.

| What is your rating, if I may ask?

I have not been active since the 1970s, just playing computers sometimes. About expert, I think.

H.G.Muller wrote on Fri, Apr 25, 2008 08:55 AM UTC:
Why do you think the bigger board and the stronge piece make the game more
strategical? The game stage that computers usually have most difficulty
coping with it the end-game, where they fail to recognize strategic
patterns such as a defended passer tying the King forever, the Pawns on
their other wing being doomed once the opponent's King will get there, as
it eventually (far behind the horizon) unavoidably will. Or W:Ra1;
B:Bb1,Pa2, with a full Rook that will sooner or later fall victim to an
attack by the King.

End-games with slow pieces (Kings, Knights, Pawns) are usually the most
strategic of all.

💡📝Hans Aberg wrote on Fri, Apr 25, 2008 08:27 AM UTC:
H.G.Muller:
| Computers have no insight what to prune, and most attempts to make
| them do so have weakened their play. But now hardware is so fast that
| they can afford to search everything, and this bypasses the problem.

So it seems one should design chess variants where the average number of moves per position is so large that one has to prune.

| Making the branching ratio of a game larger merely means the search
| depth gets lower. If this helps the Human or the computer entirely
| depends on if the fraction of PLAUSIBLE moves, that even a Human
| cannot avoid considering, increases less than proportional. Otherwise
| the search depth of the Human might suffer even more than that of the
| computer. So it is not as simple as you make it appear below.

I already said that: the variant must be designed so that it is still very strategic to human. - It is exactly as complicated as I already indicated :-).

Therefore, I tend to think that perhaps a 12x8 board might be better, with a Q+N piece, and perhaps an extra R+N piece added.

H.G.Muller wrote on Fri, Apr 25, 2008 07:26 AM UTC:
Reinhard: | I am convinced - so please correct me if need be - that your engine | has implemented just that value scheme, you are talking about. ...' Well, initially, of course NOT. How could it? I am not clairvoyant. I started by 'common-sense logic' like 'Q = R + N + 1.5, and B << N probably means A << Q, and the synergy bonus probably scales proportional to piece value, so let me take A = B + N + 1'. Which translated to A = 7.5 with my 8x8 values B = N = 3.25 (taken from Kaufman's work). And with the setting A=7.5, C=9.0, I played the 'Chancellor army' against the 'Archbishop army', expecting the latter to be crushed, because of the 300 cP inferiority. (Which corresponds to piece odds, and should give 85%-90% scores.) But to my surprise, although the two Chancellors won, it was by less than the Pawn-odds score. | Then your engine will throw away underestimated pieces too cheap and | keep overestimated too dear. Thus it will start and avoid a lot of | trades in unjustified manner. This hardly occurs, because this is SELF-PLAY. The opponent has the same misconception. If I tell the engine A < R, there the engines wil NOT throw away their A for R, because the opponent will not let them, and 'save' its Rook when it comes under A attack. Trades of unlike material occur only rarely, unless the material is considered exactly equal (which I therefore avoid). So putting A=R is dangerous, and would suppress the measured A value because of bad A vs R trades. But not completely, as it would not always happen, and a fair fraction of the games would still be able to cash in on the higher power of A by using it to gain material or inflict checkmate before the trade was made. So even when you do set A=R, or A=R+P, the A will score significantly better than 50% in an A vs R (or AA vs RR) match. And when I discover that, I increase the A value accordingly, until self-consistency is reached. So my initial tests of CC vs AA, with the engine set to A=750, C=900 suggested that C-A ~< 50 cP. Then I repeated the match with A=850, and this eliminated the few bad trades that could not be avoided by the opponent. So CC beat AA now by an even smaller margin, of less than half the Pawn-odds score (in fact more like a quarter). So I set A=875. I did not repeat the test with A=875 yet, but I don't expect this 25cP different setting to cause a significant change in the result (compared to the statistical error with the number of games I play), if changing a full 100 cP only benifited the AA army 6%. The extra 25cP will not reverse the sign of any trade. So in practice, you are highly insensitive to what values you program into the engine, and iterating to consistency converges extremely fast. You should not make it too extreme, though: if you set Q < P, the side with the Queen will always squander it on a Pawn, as there is no way the opponent could prevent that, the Queen being so powerful and the Pawns being abundant, exposed and powerless. Similarly, setting A < N would probably not work even in an A vs B+N ending (with Pawns), as the A is sufficiently powerfol compared to individual B and N that the latter cannot escape being captured by a suicidal A. But if you are off 'merely' 2-3 Pawns, the observed scores will already be very close to what they should be based on the true piece values.

Reinhard Scharnagl wrote on Fri, Apr 25, 2008 05:16 AM UTC:
Harm, let me then focus on your method to have one engine play itself other using different armies: I am convinced - so please correct me if need be - that your engine has implemented just that value scheme, you are talking about. Suppose, that true values probably are somehow different from the built in figures. Then your engine will throw away underestimated pieces too cheap and keep overestimated too dear. Thus it will start and avoid a lot of trades in unjustified manner. And the bad payload for this is, that you are not able to detect it, because equal engines are blind to penalize each other for such mistakes. And in the end therefore such tests tend to become a self fulfilling prophecy.

Joe Joyce wrote on Fri, Apr 25, 2008 12:08 AM UTC:
This is an interesting and thought-provoking conversation. I've got a couple questions.

If the game has a large-enough branching ratio that computers can't adequately search in 'reasonable' [however it's defined] time, then wouldn't the different values that a human and a computer might assign to the same pieces *possibly* contribute to or result from the person's 'intuition'/superior playing ability? 

Following is a quote from a recent HG Muller post:
'Making the branching ratio of a game larger merely means the search depth gets lower. If this helps the Human or the computer entirely depends on if the fraction of PLAUSIBLE moves, that even a Human cannot avoid considering, increases less than proportional. Otherwise the search depth if the Human might suffer even more than that of the computer.'

If each side gets multiple moves per turn, this would increase the branching ratio. But without changing other things about chess, the human would probably be even more at a disadvantage; in Marseilles Chess, for example, with its 2 moves/side/turn, because the computer would calculate that out easily, correct? 

Consider a larger game, with several kings and several moves per turn. Let each side have as many moves per turn as they have kings. Restrict movable pieces on each side to only those friendly pieces within close proximity of the kings. This begins to shift the advantage to the human, I suspect, especially when there are maybe 6 - 8 kings or more per side, the pieces are reasonably simple, easy to understand and use, work well in groups, and number few in variety, with fairly high numbers of each type of piece. This should shift the game more toward pattern recognition and away from pure brute-force calculations, which would seemingly take rather long. Opinions?
 
Btw, I really haven't played FIDE seriously in 4 decades and I never got a rating, but my ratings at CV are 1550ish lifetime and bouncing around in the 1600's for the past 18 months, and I'd really love to get a chance to play against a program in games like the kind described above.

H.G.Muller wrote on Thu, Apr 24, 2008 08:45 PM UTC:
'This is only true if positions are viewed out of context. ...'

It never happened to you that early in the game you had to step out of
check, and because of the choice you made the opponent now promotes with
check, being able to stop your passer on the 7th?

I think that if you are not willing to consider arguments like 'here I
have a Knight against two Pawns (in addition to the Queen, Rook, Bishop
and 3 Pawns for each), so it is likely, although not certain, that I will
win from there', the number of positions that remains acceptable to you
is so small that the opponent (not suffering from such scruples) will
quickly drive you into positions where you indeed have 100% certainty....
That you have lost!

What is your rating, if I may ask?

H.G.Muller wrote on Thu, Apr 24, 2008 08:36 PM UTC:
The main difference between computers and GMs is that the latter search
selectively, and have very efficient unconscious heuristics for what to
select and what to ignore (prune). Computers have no insight what t prune,
and most attempts to make them do so have weakened their play. But now
hardware is so fast that they can afford to search everything, and this
bypasses the problem.

Also for the evaluation, Human pattern-recognition abilities are much
superior to computer evaluation functions. But it turns out extra search
depth can substitute for evaluation. It has been shown that even an
evaluation that is a totally random number unrelated to the position,
combined with a fairly deep search, will lead to reasonable play. (This
because the best of a large number of randoms is in general larger than
the best of a small number. So the search seeks out those nodes that have
many moves, and that usually are the positions where the most valuable
pieces are still on the board. So it will try to preserve those pieces.)

Making the branching ratio of a game larger merely means the search depth
gets lower. If this helps the Human or the computer entirely depends on if
the fraction of PLAUSIBLE moves, that even a Humancannot avoid considering,
increases less than proportional. Otherwise the search depth of the Human
might suffer even more than that of the computer. So it is not as simple
as you make it appear below.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 08:21 PM UTC:
H.G.Muller:
| Chess is a chaotic system, and a innocuous difference between two
| apparently completely similar positions [...] can make the difference
| between win and loss.

This is only true if positions are viewed out of context.

Humans overcome this by assigning a plan to the game. Not all position may be analyzable by such a method. The human analyzing method does not apply to all positions: only some. For effective human playing, one needs to link into the positions to which the theory applies, and avoid the others. If one does not succeed in that, a loss is likely.

The subset of positions where such a theory applies may not be chaotic, then.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 08:13 PM UTC:
GMs only search 6-8 ply deep, looking through at most a few hundred searches per position. That is feasible for a brute force computer (with pruning and noting that position evaluation still is needed), give the rather low average number of moves per position in orthodox chess.

But suppose that the average number of moves per position is made a couple of times larger. If the game is still such that humans can play it strategically, then that might improve for humans in the competition with computers.

H.G.Muller wrote on Thu, Apr 24, 2008 08:11 PM UTC:
Reinhard,

Apparently my point is not yet clear. My conclusion on piece values has
nothing to do with the fact that Joker80 ends consistently above Smirf in
10x8 Chess tourneys, and that Joker values pieces in one way, and Smirf
values them in another. This indeed is not proof for anything.

The result is 100% based on the fact that if I let engines play positions
with material imbalance, certain combinations of pieces systematically
beat other combinations, if the players are equally strong (e.g. because
they are identical). This is independent of the engine used, provided it
is not completely silly. No matter how you PROGRAMMED Smirf to value the
Archbishop, you cannot prevent that Smirf that plays a complex position
with where it has A will systematically beat the Smirf that has B+N+P in
stead. Because A is much stronger than B+N+P, and Smirf's search will
discover that, because it can use the A to gobble up Pawns which the B+N
will not be able to defend. And even if it could trade the A for B+N, and
wuld think it is an equal trade, it will most of the time prefer to win a
Pawn. And by the time it has captured the Pawn, the win of the other Pawn
will be within the horizon, and then another. And when the opponent is out
of Pawns, its own passers will get the promotion within the horizon. Most
of the time you will not be able to fool the search by giving it faulty
piece values.

H.G.Muller wrote on Thu, Apr 24, 2008 07:55 PM UTC:
Hans,

Indeed, your argument fails to take account of this gap between theory and
reality. People have not explored a significant fraction of the game tree
of Chess from the opening, or even from late middle-game psitions. And
computers cannot do it either. Nor will they ever, for the lifetime of our
Universe.

Outcomes that are in principle determined, but by factors that we cannot
control or cannot know, are logically equivalent to random quantities.
That holds for throwing dice, generating pseudo-random numbers through the
Mersenne Twister algorithm, and Chess alike. So Chess players, be they
Humans or Computers, will have to base their decisions on GUESSED
evaluations of teh positions that are in their search tree. And the nature
of guessing is that there is a finite PROBABILITY that you can be wrong.

Chess is a chaotic system, and a innocuous difference between two
apparently completely similar positions, like displacing a Pawn ofr a King
by one square, ort even who has the move, can make the difference between
win and loss. The art of evaluation of game positions is to make the
guesses as educated as possible. 

By introducing game concepts you can pay attention to ('evaluation
terms') one can classify positions, but the number of positions will
always be astronomical compared to the number of classes we have: even if
we would consider the collection of all positions that have the same
material, the same Pawn structure, the same King safety, the same
mobility, etc., we are still dealing with zillions of positions. And
unless material is very extreme (like KQQK), some of these will be won,
some drawn, some lost. The moment this would change (e.g. because we can
play from 32-men tablebases) Chess would cease to become an interesting
game. But until then, any evaluation of a position is probabilistic. The
game will most often be won for the player that goes for the positions
that offer the best prospects. The player that only moves to positions
that are 100% certain wins, will forfeit all games on time...

Now piece values are the largest explaining factor of evaluation scores,
if you would do a mathematical 'principal component anlysis' of the game
result as a function of the individual evaluation terms. That is a property
of the game, and independent of the nature of the player. Humans and
computers have to use the same piece values if they want to play
optimally. Only when the search would extend to checkmate in every branch,
(possibly via a two-directional search, starting from opening and
checkmate, meeting in the middle as tablebase hits) evaluation would no
longer be necessary, and piece values would no longer be needed.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 06:57 PM UTC:
Reinhard Scharnagl:
| It is pure luck, that chess computer program strengths accompanied our masters for a time.
| Nobody will try to win a sprint against a Porsche, because the difference is even more obvious. So 
| it does not tell anything about how to handle a subject, when different species are competing.

The computer programs for orthodox chess succeeds in part because the number of positions required for achieving a good lookahead is fairly small relative to the capacity of the most powerful computers.

If one designs a chess variant with more material in a way that it is still very strategic to humans, then it will be harder for computers to be good on that variant, as the number of positions that must be searched for will be much larger.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 06:36 PM UTC:
H.G.Muller:
| Well, let us take one particular position then: the opening position of
| FIDE Chess. You maintain that the outcome of any game starting from this
| position is fixed?

Since there is only a finite number of positions, there is theoretically an optimal strategy.

| A quick peek in the FIDE database of Grand Master games
| should be sufficient to convince you that you are very, very wrong about
| this. Games starting from this position are lost, won and drawn in
| enormous numbers. There is no pre-determined outcome at all.

They probably haven't searched through all positions to find the optimal strategy.

| Computers that use the statistical approach, such as Rybka, are
| incomparably strong. Humans, using the way you describe, simply cannot
| compete. These are the facts of life.

I suspect that humans are not allowed to search through zillions of positions like computers do. Specifically, if strong human players are allowed to experiment to search out of the weaknesses of the computer programs and using other computer programs to check against computational mistakes, I think that these computer programs will not be as strong.

But as for the question of piece values, humans and computers may prefer different values - it depends on how they should be used.

Reinhard Scharnagl wrote on Thu, Apr 24, 2008 06:33 PM UTC:
HGM: It is pure luck, that chess computer program strengths accompanied our masters for a time. Nobody will try to win a sprint against a Porsche, because the difference is even more obvious. So it does not tell anything about how to handle a subject, when different species are competing. As for our both chess programs, which are obviously of different maturity, you can find out, which is currently more successful, but that does not mean, that the winning one is based on 'more correct' ideas. Ideas are rarely implemented in equal quality. Maybe it needs a lot of approaches of different people to have a decision on such a question after a long time period.

H.G.Muller wrote on Thu, Apr 24, 2008 05:39 PM UTC:
Well, let us take one particular position then: the opening position of
FIDE Chess. You maintain that the outcome of any game starting from this
position is fixed? A quick peek in the FIDE database of Grand Master games
should be sufficient to convince you that you are very, very wrong about
this. Games starting from this position are lost, won and drawn in
enormous numbers. There is no pre-determined outcome at all.

Computers that use the statistical approach, such as Rybka, are
incomparably strong. Humans, using the way you describe, simply cannot
compete. These are the facts of life.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 05:14 PM UTC:
H.G.Muller:
| I suspect you misunderstand what quantity is analyzed. In any case not how players handle | the position. But the very question you do ask, 'what are my chances for a draw with 1, 2 | or 3 Pawns in compensation', can only be answered in a statistical sense. The answer will | never be 'with 1 Pawn I will lose, with 2 Pawns I will draw, and with 3 Pawns, I will
| win'. It will be something like: 'With one Pawn I will have 5% chance on a win and 10% on | a draw, (and thus 85% for a loss) with 2 Pawns this will be 20-30-50, and with 3 Pawns 50-| 30-20. And I can count a Passer as 1.5, so if my 2 Pawns include a passer it will be 35-
| 30-35).'

No, this is the flaw of your method (but try to refine it): 

Chess is not played against probabilities, as in say poker. There is really thought to be a determined outcome in practical playing, just as the theory says. I can have a look at my opponent and ask 'what are the chances my opponent will not see my faked position' - but that would lead to poor playing. Much better is trying to play in positions that your opponent for some reason is not so good at, but it does not mean that one takes a statistical approach to playing.

Playing strength is dependent roughly on how deep on can look - the one that looks the furthest. There are two methods of looking deeper - compute more positions. Or to find a method by which positions need not be computed, because they are unlikely to win. 'Unlikely' here does not refer to a probability of position, but past experience, including analysis. With a good theory in hand, one can try to play into positions where it applies -- this is called a plan.

If I have an when the position values applies, I can try to play into such situation, and try to avoid the others.

When I looked at your statistical values, I realized I could not use them for playing, because they do not tell me what I want to know. A computer that does not care about such position evaluations may be able to use them. But I think the program will not be very strong against an experienced human.

But in the end, it is the method that produce the wins that is the best.

H.G.Muller wrote on Thu, Apr 24, 2008 04:29 PM UTC:
'The statistical system does not say anything - I am not interested in how players on the average would handle this position.' I suspect you misunderstand what quantity is analyzed. In any case not how players handle the position. But the very question you do ask, 'what are my chances for a draw with 1, 2 or 3 Pawns in compensation', can only be answered in a statistical sense. The answer will never be 'with 1 Pawn I will lose, with 2 Pawns I will draw, and with 3 Pawns, I will win'. It will be something like: 'With one Pawn I will have 5% chance on a win and 10% on a draw, (and thus 85% for a loss) with 2 Pawns this will be 20-30-50, and with 3 Pawns 50-30-20. And I can count a Passer as 1.5, so if my 2 Pawns include a passer it will be 35-30-35).' This is all you could ever hope for. But to get that answer, you must know that the W-D-L statistics wfor the quiet situation after the opponent has defused the mate threat with so-and-so-many Pawns are x%-y%-z%. You will never be able to say if the position is won or not, unless your final position is a tablebase hit (and you have the tablebase).

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 03:46 PM UTC:
H.G.Muller:
| It seems to me that the example you sketch is exactly what the piece-value
| system cannot solve and is not intended to solve. You want to have an
| estimate of how much material it wil cost the opponent to solve a certain
| mobility or King-safety advantage. Those are questions about the
| corresponding positional evaluation, not about piece values.

The situation I depicted is the other way around: I see a good queen for rook exchange that looks promising. Can I at least ensure a draw? How much additional material would I need to get to ensure. Next, have a look at the likely pawn development. So the traditional system will tell me whether I need 1, 2 or 3 pawns.

The statistical system does not say anything - I am not interested in how players on the average would handle this position.

H.G.Muller wrote on Thu, Apr 24, 2008 02:24 PM UTC:
It seems to me that the example you sketch is exactly what the piece-value
system cannot solve and is not intended to solve. You want to have an
estimate of how much material it wil cost the opponent to solve a certain
mobility or King-safety advantage. Those are questions about the
corresponding positional evaluation, not about piece values.

Mind you, I am not saying that these positional values are not important.
They can be worth many Pawns. But a system of piece values cannot be any
good unless it is also able to (statistically) predict the outcome of a
game from a given position if these positional terms are negligibly small,
or exactly cancel for the two sides. This is why I only use symmetric
positions, without blocked Pawns (to avoid positions where the differences
needed to create the material imbalance could include trapped pieces).

First you have to know piece values, to be able to handle quiet positions
without extreme positional characteristics. Once you have those, you are
in a position to quantitatively express the equivalent material value of
positional characteristics like King safety and piece trapping.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 12:13 PM UTC:
|| So the approach I suggested is to find a set of end-game positions
|| where the outcome is always a draw or always a win, with extreme
|| positions excepted. This might produce different values.'
H.G.Muller:
| The problem is that such positions do not exist, except for some very
| sterile end-games.

There is a difference between finding formally proved positions, and those that have such an outcome by human experience. If one in middle game exchanges ones queen for a rook and temporary very strong initiative, suppose this initiative does not lead to an immediate mate combination - it might be very effective to threaten a mate, which the opponent can only avoid by giving back some extra material - how much more material is needed in order to ensure a draw? A bishop perhaps, if the pawns are otherwise favorable, otherwise at least some more material, a pawn or two. This is a different judgement than a statistical one: a purely statistical judgment can probably be quite easily beaten by a human. It goes into a difficult AI problem: computers are not very good at recognizing patterns and contexts. But the classical piece value system probably builds on some such information.

H.G.Muller wrote on Thu, Apr 24, 2008 09:18 AM UTC:
'So the approach I suggested is to find a set of end-game positions where
the outcome is always a draw or always a win, with extreme positions
excepted. This might produce different values.'

The problem is that such positions do not exist, except for some very
sterile end-games. In theory every position is either a draw or has a
well-defined 'Distance To Mate' for black or white, assuming perfect
play from both sides. But this is only helpful for end-games with little
enough material that tablebases can be constructed (currently upto 6 men
on 8x8). And even there it would not be very helpful, as the outcome
usually depends more on exact position than on the material present, and
thus cannot be translated to piece values. For a given end-game with
multiple pieces, there usually are both non-trivial wins for black as well
as white. (Look for instance at the King + Man vs King + Man end-game,
which should be balanced by symmetry from a material point of view. Yet, a
large fraction of the non-tactical initial positions, i.e. where neither
side can gain the other's Man within 10 moves, are won for one side or
the other.)

And for positions with 7 men or more, we don't even know the theoretical
game result for any of the positions. This is why Chess is more
interesting than Tic Tac Toe. It is impossible to determine if the
position is won or lost, and if you have engines play the same position
many times, they will sometimes win, sometimes lose, and sometimes draw.
So the only way to define a balanced position is that it should be won as
often as it is lost, in a statistical sense (i.e. the probability to win
or lose it should be equal). Positions that are certain draws simply do
not exist, unless you have things like KBK or take an initial setup where
a side with extreme material disadvantage has a perpetual.

💡📝Hans Aberg wrote on Thu, Apr 24, 2008 08:23 AM UTC:
H.G.Muller:
| Well, this is basically how I got the empirical values I quoted. Except
| that so far I only did it for opening positions, so the values are all
| opening values. But, like I said, they don't seem to change a lot during
| the game. For the complete list of exchanges that I tried, see
| http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1

There might be some problems here: For the classical piece value system, basically, what one gets is determining balance when the position is positionally equal and when both players play 'correctly'. By contrast, you take a statistical approach, and as you say for opening positions. The classical piece value system depends on a deeper analysis; perhaps the statistical approach can serve as a first approximation.

So the approach I suggested is to find a set of end-game positions where the outcome is always a draw or always a win, with extreme positions excepted. This might produce different values. In this setup, it is not possible to set values as exactly, as equal material means 'always result in draw for the positions considered'; perhaps it leads to only integral values, as a fraction pawn value cannot be used to decide the outcome of games. The fractions might be introduced as position compensations, like in orthodox chess reasoning, for example 'the sacrificed pawn is compensated by positional development'.

H.G.Muller wrote on Wed, Apr 23, 2008 09:38 PM UTC:
Well, this is basically how I got the empirical values I quoted. Except
that so far I only did it for opening positions, so the values are all
opening values. But, like I said, they don't seem to change a lot during
the game. For the complete list of exchanges that I tried, see
http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1
.

Compensating with Pawns is kind of difficult, though. The Pawn value is
the most variable of all pieces, and the most non-additive. You have
passers, defended passers, edge Pawns, backward Pawns isolated Pawns,
Pawns of the King's Pawn shield. One can be worth more than twice as much
as the other. And the problem is that deleting a Pawn in the opening, you
don't know where it is going to end up on the average. In addition, in
the opening you have all kinds of compensation for deleting a Pawn, in
terms of acceleration of development. In the end-game position I gave, at
least you know which type of Pawn the extra Pawn (c5) is. I would be
inclined to count that as the 'average Pawn', and deleting it does not
significantly weaken your Pawn structure.

But in general, it is much more reliable to try Queen vs 3 minors or vs 2
Rooks. That way you get relative piece values that are not very sensitive
to the value of the Pawns that you used to 'equalize'.

💡📝Hans Aberg wrote on Wed, Apr 23, 2008 06:57 PM UTC:
H.G.Muller:
| I set up a tactically dead A+5P vs R+N+6P position (
| http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it
| play a couple of hundred times to see who had the advantage. Turns out
| the position was well balanced.

This might be the way to go, because the standard exchange is equal pieces. The next step is a refinement: 'if I exchanged my R for a B, what do I need to keep a balance?' - something like 2 Pawns. The piece value system probably cannot predict well the balance in more complicated unequal exchange positions, but humans would probably try to avoid them, and they do not arise naturally, at least in human play.

So if an A is exchanged for a C, what is needed to keep the generic end game balance? And so forth. With a list of balanced combination, perhaps a reliable piece value system can be constructed. It would then only apply to the examined exchange combinations.

💡📝Hans Aberg wrote on Wed, Apr 23, 2008 06:03 PM UTC:
H.G.Muller:
| I think the following array would be more logical:
|    C H A M K A H C
|  where M=Amazon and H=Nightrider.

Yes. I was thinking about putting a Q+N piece besides the K, too. The nightrider may be too powerful though, and may be hard to learn for humans.

| ...but my guess is that it would make the
| game too tactical, without quiet positions, almost reversi-like...

One function that the minor pieces have in orthodox chess, is being suitable
for sacrifice. So having only powerful pieces could loose out on the tactical side too.

| Only the poor King has no enhancement. You could replace it by a Centaur,
| but this might make checkmating it too difficult.

The king, as piece for becoming mated, is just fine. I thought about the K+N piece a bit too.

One variation I am thinking about is 'Spartan kings': two kings, just as the Spartans, where 
When two kings remains, one can be taken; game ends when the last remaining king has become mated.

But one must think carefully about the design objectives: orthodox chess has a particularly good blend of strategy and tactics. With the Capa variation I gave, the idea is to preserve as much as possible of that, while lessening the amount of draws by adding some material.

H.G.Muller wrote on Wed, Apr 23, 2008 04:44 PM UTC:
If you like super-strong pieces (but my guess is that it would make the
game too tactical, without quiet positions, almost reversi-like), I think
the following array would be more logical:

C H A M K A H C

where M=Amazon and H=Nightrider. Pieces are the same as orthodox Chess,
but enhanced by a Knight move. In the Knight this enhancement is added
'serially', i.e. it becomes a Nightrider.

Only the poor King has no enhancement. You could replace it by a Centaur,
but this might make checkmating it too difficult.

💡📝Hans Aberg wrote on Wed, Apr 23, 2008 03:56 PM UTC:
The intent of the chess variants I posted is to design playable variations, where the pieces are used. It would be interesting to know which ones generate more exiting (including with respect to opening developments) or shorter games.

Here is yet another one: Enhanced 8x8 Orthodox chess:
  G C A Q K A C G
i.e., gotten form Orthodox chess by the piece replacements R -> G, N -> C, B -> A. So there are no minor pieces here.

H.G.Muller wrote on Wed, Apr 23, 2008 11:49 AM UTC:
As to the Amazon value: I guess you are right worrying about undefended
Pawns when designing a variant that is more fun to play. For the
determination of piece values, however, this is hardly important. In the
first place, I have to delete pieces from the nominal opening setup to
create a difference, sometimes multiple pieces (such as Q+N to balance the
Amazon), and this usually this leaves some undefended Pawns anyway. It is
more important to shuffle the pieces, to create as many different initial
positions as possible. That some of them have extra weaknesses is not so
important, as both sides have that same weakness, and I play it twice with
different sides starting.

I was never able to see a clear effect of the opening array anyway. Not
even when starting one side with Knights or Bishops in the corner, against
a normal setup. I guess this would only show up by really making opening
theory for the specific position. It is just too difficult to find ways to
exploit such weaknesses 'behind the board' at any reasonable time
control.

BTW, I terminitad the initial experiment with the Amazon after 441 games.
The Amazon was leading 52.6% over Queen + Knight, while the standard error
is about 2%, and Pawn-odds advantage 12%. This suggests Amazon to be about
20 cP stronger than Queen + Knight. But it is very possible that on this
slow laptop at this TC the Knight is underestimated by 10 cP.

Anyway, there seems to be very little to no synergy between the Queen and
Knight moves. I guess most synergy in compound pieces results from
crossing a certain threshold, needed for qualifying as 'super-piece'.
Rooks, Knights and Bishops on an empty board can all go to a given target
square along two paths (if it is reachable at all). A Queen can do that in
general in 12 ways (if the board is large enough). This huge jump in
manoeuvrability is what makes the super-pieces so much more valuable. A
superpiece can attack a Pawn chain in several places at once from several
positions, so that normal pieces cannot defend all attacked Pawns, and in
stead have to worry about their own survival. So a super-piece is much
more than just a stronger piece. It is used in in an essentially different
way. E.g. in the early end-game, chasing the King with checks while having
enough freedom to at the same time manoeuvre to get a clear shot at some
other undefended piece.

H.G.Muller wrote on Wed, Apr 23, 2008 11:16 AM UTC:
All very true. But in practice, I never have seen piece values that were
extremely different in the opening from what the are in the end-game. The
rason is probably that in the beginning there are so many pieces that even
being one or two behind does not immediately decided the game by checkmate.
The opponent can almost always fight it off for a long time by trading
material. And by the time the board is half empty, most pieces start
approaching their end-game values. So if the disadvantage of two pieces
was only transient, the pieces being present, but merely useless on the
full board, he would effectively have earned them back.

In addition, pieces are seldomly totally useless. The Rook, which is the
most notorious example of a piece that is difficult to develop early,
still make itself very useful as a defender behind the Pawn line,
preventing your position to collapse under the attack of quickly developed
pieces of the enemy. It would perhaps be different if a CV had pieces that
by rule were not allowed to move at all before 75% of the Pawns had been
captured, but than suddenly became very powerful. For such pieces it would
be very questionable if you could survive long enough for them to be of
use. But with Rooks as defenders, you can realistically expect to survive
to the point where the Rooks live up to their full potential at least 90%
of the cases. R for N or B gambits are almost non-existent. It is very
questionable if the instantaneous advantage of having N in stead of R
would allow you to win a single Pawn before the advantage evaporates.

I did make an early end-game test on the Archbishop, though, because it
was the compound of two 'early' pieces, and some players suggested that
it had its main use in the early middle-game. So I set up a tactically
dead A+5P vs R+N+6P position (
http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it play
a couple of hundred times to see who had the advantage. Turns out the
position was well balanced. This could be considered as a direct
measurement of the end-game value of the involved pieces.

💡📝Hans Aberg wrote on Wed, Apr 23, 2008 11:08 AM UTC:
In initial position setups, impose the condition that in the start position the pawns are protected by a piece. Then in N B and B N setups, the B pawn is unprotected, unless next to the B, there is a piece that can move diagonally.

Keeping the notation G = Q + N for 'general' (as 'amazon' abbreviated to 'A' would cause confusion with the 'archbishop' - and there is little convergence of names between variants), I get the following 10x8 board combinations (for white):
  R N B A Q K G B N R
and
  R C N B Q K B N G R
Here, I have required: N and B next to each other, the two B on different square colors, the two new pieces different and the more powerful piece on the kings side.

💡📝Hans Aberg wrote on Wed, Apr 23, 2008 07:59 AM UTC:
I think one needs defining the context of the piece values: the traditional orthodox piece values are mostly used by humans to predict the end-game relative strength, excepting certain types end-games: if there are pawns left that may promoted, one pawn value down will normally draw, two may loose, three is a more certain defeat, but if there is no pawn to be promoted, at least five pawns ahead (rook plus king against king) are needed for a win. In middle game, one can add empirical reasoning, like 'knights strengthen (resp. weaken) in closed (resp. open positions)'.

So here there are usage several factors that need to be indicated: empiric for use by human reasoning, end game prediction, excluding certain types of end games, whether pawns can be promoted or not. The last factor does not traditionally alter the piece values, but their interpretation. 

For piece values used by computers, these can be more exact, but under what circumstances should the values apply? - To determine a local middle game fight, or determine overall material pressure, determine open development, or predict potential end-game capabilities? Perhaps different values should be given for different chess strategic positions. With that in hand, a computer might do more human like decisions, like 'in this situation, the sacrifice of this pawn is well compensated in the long term by position, but not the short one, so the best strategy here is to take it and give it back later'.

In Capa chess variations, one idea is to add material as to make end games less likely (though this may a change if the variation is learned thoroughly). Therefore, if position values are based upon games that rarely result in end games, perhaps that should considered 'middle game piece values'. And so on.

H.G.Muller wrote on Wed, Apr 23, 2008 06:39 AM UTC:
No, I cannot: unlike this thread, it refuses my posts unless I fill in the ID field, and I do not have an ID...

Joe Joyce wrote on Tue, Apr 22, 2008 10:07 PM UTC:
HG Muller, you are certainly allowed, and encouraged, to post on piece values in the Piece Values thread. Joe

H.G. Muller wrote on Tue, Apr 22, 2008 08:58 PM UTC:
Well, too bad. I am not allowed to post in the piece values thread.

Anyway, it seems that virtually all the pieces in the games you mention
are within the capability of Fairy-Max to represent. So it should be quite
easy to determine their values to an accuracy of, say 10 centi-Pawn. It
would take perhaps just a few weeks of time. It would be preferable if
software specifically tailored to these games could be used, as Fairy-Max
cannot cope with games that are won in other ways than checkmate, and does
not support promotion rules as cumbersome as the ones needed here. (In fact
it only promotes to Queen, but a 'Queen' can be defined to be any piece
you like.)

On the other hand, I don't think modifying the rules of the games in
these respects will have virtually zero effect on the piece values, or
indeed the entire game strategy, so that Fairy-Max still might be the
strongest AI in existence that can play these games. (I would have to
expand the board vertically for some of them, though, but that is easy.)

H.G.Muller wrote on Tue, Apr 22, 2008 07:21 AM UTC:
To Joe: Well, I already applied for member status a week ago, so that I
could edit my own posts, and others would not have to wait 24 hours to see
mine. But, quite frankly, I am not aware having said anything that requires
editing. I do not consider remarking that a theory that doesn't explain
the observations is 'nonsense', or that program A beats program B by a
large margin 'ad hominems'. Theories and programs are not people. It is
a pity that some people take such remarks as a personal offense.

I would applaud a piece-value item. Therefore I will defer directly
addressing your questions below until I know where to post the answers, as
they certainly would be off topic w.r.t. the Aberg variant. So I will only
say now that my aim is to get good EMPIRICAL piece values for all common
fairy pieces in the context of (approximately) normal Chess (i.e. in a
game with an orthodox King as royal piece, and orthodox, or at least
Shatranj-type Pawns that promote to a piece as powerful as a Queen). I
especially developed the Fairy-Max engine for this project. So if you
create an item about piece value, I will be able to provide a lot of hard
facts in the coming year. (And faster if other people would be prepared to
participate and donate their computer time to the project.)

Reinhard Scharnagl wrote on Mon, Apr 21, 2008 10:28 PM UTC:
Maybe it could be interesting to read some ideas of mine at 
http://www.10x8.net/Compu/schachwert1_e.html .

Joe Joyce wrote on Mon, Apr 21, 2008 09:13 PM UTC:
Gentlemen, I'd like to put an oar into these murky waters. Let me say that, as a designer, I am very interested in piece values, and ways to derive them. I have had some thoughts and previous conversations on the subject, and my poor thoughts have led me to ask questions and make the odd observation on piece values, and I am truly interested in this topic, but... 

First, this is a page on a particular Capa variant. As such, and especially given the author's inclusion of a piece value chart and discussion, it is a fine place to argue piece values. It is not, however, a good place to stage ad hominem attacks on those who disagree with your position. [As an editor, I frown upon this practice... hint, hint!] But I am also a designer, and would like to ask some questions, so I ask you to play nice, and not drive people away with flame.

Second, I would like you to consider the piece values of pieces similar to Capa pieces, but not quite them. I offer you my games only, because other people have privately expressed to me their strong desire not to get dragged into arguments. As I respect their wishes, we are stuck with my games, and my pieces, for now. Others may suggest other pieces.

The games are:
 Great Shatranj [10x8]
 Grand Shatranj [10x10]
 Atlantean Barroom Shatranj [10x10]
 Lemurian Shatranj [8x8]
 Chieftain Chess [12x16]

Great Shatranj in particular is a shortrange version of Capa Chess, with no piece moving more than 2 squares and most pieces having a leaping ability. This should not be too difficult, I would hope, as all the pieces are exact analogs of the Capablanca pieces. 
Grand Shatranj is similarly a shortrange version of Freeling's Grand Chess, using a somewhat more powerful piece set than Great Shatranj, and Atlantean Barroom is a twisted version of Grand. No piece moves more than 4 squares in either game, and if 10x10 is too big for any reason, I'd be happy to see values for 10x8.
Lemurian is just 8x8, and thus 'easy', or at least easier, to figure piece values for, I would imagine. It is, in a very real way, a 'cut-down' version of Atlantean Barroom, with even piece moves being literally cut in half, to produce inclusive compound pieces that leap and move up to 3 squares, but may change directions.  
This takes us to Chieftain, a rather large game at 12x16, but with only 5 kinds of pieces, and no piece moves over 3 squares/turn. It also replaces pawns with non-promoting guards, simplifying that part of the evaluation. It does play with the role of kings and movement rules, though. 

Can you give me piece values for any of the pieces in these games, in a reasonable amount of time: say a week to a month? If this is pushing it, how much time is reasonable?

There are many other pieces and kinds of pieces that could be used, but these must suffice to make my arguments, unless someone else wishes to throw their piece[s] into the ring. 

I would particularly like to hear your values for the minister and high priestess for the three games they're in, and how it changes relative to the other pieces in the games. 

The shortrange Capa piece pair make interesting test pieces. Is their value constant or does it change over the three games? What about the relative values of the other pieces - can they be made 'absolute' over the 3 games, or do their values change from game to game, by how much, and why?

For those who design variants, these are fundamental questions I'm asking. Is there a system, or combination of systems, that can predict a piece's value reasonably accurately? And how close is 'reasonable'? 

I am very interested in these questions, and I know from personal communications that others are also interested, for their own games and pieces. Some would ask these questions if they weren't afraid of being insulted. 

I would like to leave Mr Aberg's page and any sense of animosity and start a piece value topic. It might be nice if the participants edited their previous remarks appropriately. Those who are not members may email me for any changes they may wish. 

Joe Joyce

H.G.Muller wrote on Mon, Apr 21, 2008 02:37 PM UTC:
At the risk of being accused of serial posting: I happened to stumble on
the exact source of Larry Kaufman's piece values. They game from a
13-line posting he made off-hand in the Rybka forum, (
http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=1986;pg=3 ,
near the bottom) when the topic of piece value of the Capablanca pieces
came up. So basically just educated guessing, done without any experience
in the game itself, just experience borrowed from normal Chess, without
any experimental input.

Does that make him 'incurably stupid'? Most certainly not! In fact,
given the virtual absense of any data to go on, and that he spend only a
few minutes on it, he did a magnificent job, displaying excellent
intuition. The fact that the result of an educated guess is off does not
make someone stupid. It is in the nature of guessing. Stupid would be to
claim that such a guess represents a 100% certain truth. As to the
'incurable', that is really an uncalled for reproach. Such an
accusation
could only be made to stick on a person that would persist in a guess
when
faced with EVIDENCE to the contrary. Larry Kaufman was never faced with
any evidence whatsoever, and I am pretty sure he would applaud it
enthousiastically if he was. I even put it to the test, by posting my
empirical piece values there. Let's hope he sees them and comments! 8-)

H.G.Muller wrote on Mon, Apr 21, 2008 08:08 AM UTC:
Oh, sorry, I mis-read. Kaufman does have Q and C unusually high, not at
900-950, like most of us. So his difference C-A is actually 150 cP, not
50cP.

So let me correct my earlier statement: Yes, then I would consider Larry
Kaufman's Archbishop value way too low. No idea what made him decide on
these values, and as they appear to be very wrong, not very interesting to
figure it out by doing any 'homework' on it.

But in stead of this fruitless discussion, let us try a more entertaining
approach. You seem convinced that A-C > 200cP (correct me if I am wrong).
So the position 
rnabqkbanr/pppppppp/10/10/10/10/PPPPPPPP/R1CBQKBCNR w KQkq - 0 1
(imbalance 2A+N vs 2C) should be biased in favor of the Chancellors. So
you should have little trouble winning it, when playing white.

So how about a 10-game free-style match, playing from this position? I
would use Joker, playing it at 1 hour per move on a 1.3GHz Pentium M. You
could play yourself, or consult any Chess program you like, to decide on
your moves. We could do this in the Gothic Chess blog, so that people can
follow the match in public.

Are you up to such a challange?

H.G.Muller wrote on Mon, Apr 21, 2008 07:10 AM UTC:
Why would I have to add Larry Kaufman to your list of 'insufferably stupid
people'? In the page you quote he has C-A only 50cP, very close to my
25cP, while having R-B at the usual value of 200cP.

Let me remind you that I was not originally discussing your theoretical
model at all, but the piece values given by Hans Aberg in this
Chessvariants item, and how they violate empirical observation. It was
YOUR claim that the empirical observations were at odds with the
predictions of your model, and by inference thus falsified the latter.

If you now want to retract that claim, and replace it by one that says
that the piece values I observed (P=85, N=300, B=350(+40 for pair), R=475,
A=875, C=900, Q=950) are exactly what your model predicts, it _might_ be
useful to look at your model. But not before. I wonder why you expect
anyone to read 58 pages of low-density information that you yourself claim
to give wrong results. Of course I have not done such 'homework'. Why
would I have the slightest interest in wrong piece values, if I already
have a quite accurate set of good piece values? It is your brain child,
and if you claim it to be at odds with the facts, I believe you on your
word!

You have been a bit ambivalent in your claims, to say the least, first
fiving a list of piece values where A~B+N, and later claiming there was no
discrepancy with A>>B+N in the opening setup. This is why I asked you to
take a clear stance on some very specific positions involving A vs C and A
vs B+N imbalances. And of course you could not do it...

But to conclude this discussion:
people that want to play Capablanca-type Chess games, or have their
computer programs play such games, guided by piece values, had better use
the values I give, if they want to win any games. If the values given by
your model are the same, OK, then they could use those too. If not, by
using the latter as guidance, they will have to get used to playing losing
Chess. Such are the facts of life, no matter how 'flawed',
'inconsistent' and 'illogical' you consider them to be. Life sucks, so
better get used to it!

Derek Nalls wrote on Mon, Apr 21, 2008 05:32 AM UTC:
'So the ply depth depends only logarithmically on search time,
which is VERY WEAKLY.

So if you had wanted to show any understanding of the matter at hand, you
should have written RIGHT! instead of WRONG! above it...'
______________________________________________________

'... it is well known and amply tested that the quality of computer play only is a very weak function of time control.'
____________________________________

I disagreed with your previous remark only because it was misleadingly,
poorly expressed.  You made it sound as if you barely realized at all that
the quality of computer play is a function of search time.  Obviously, you do.  So, here is the correction you demand and deserve ....

RIGHT!
_______

'Absolute nonsense. Most Capablanca Chess games are won by annihilation of
the opponents Piece army, after which the winning side can easily push as
many Pawns to promotion as he needs to perform a quick mate.
Closely-matched end-games are relatively rare, and mating power almost
plays no role at all. As long as the Pawns can promote to pieces with
mating power, like Queens.'

Very well.  I spoke incorrectly when I creditted you with foolishly assigning the archbishop nearly equal value to the chancellor due mainly to its decent mating power, relevant mainly in endgames ... sometimes.
You are even more foolish than that.  You actually think the archbishop 
has nearly equal value to the chancellor throughout the game- in the opening game and mid-game as well.  Wow!

By the way, please add IM Larry Kaufmann to your dubious list of 
'insufferably stupid people' who disagree with your relative piece values
in CRC:

http://en.wikipedia.org/wiki/Gothic_Chess
___________________________________________________

'... But let's cut the beating around the bush ...'

Good idea!

I have now completely run out of patience with your endless inept, 
amateurish attempts to discredit my work.  Not because you disagree.
Not even because you are unnecessarily rude and disrespectful.  Instead, 
strictly because you have NOT done your homework!  You refuse to 
read the same 58-page paper you are confidently grading with an 'F'.  

Consequently, virtually all of your criticisms to date about my model 
for calculating relative piece values have been incorrect, irrelevant
and/or irrational.  When/If you ever address concerns about my method
that I can identify as making sense and knowing at least what you are
talking about, then I will politely answer them.  Until then, my side of 
this conversation is closed.

H.G.Muller wrote on Sun, Apr 20, 2008 10:21 PM UTC:
'The quality of computer play correlates strongly as a function of ply
depth completion which, in turn, is a function of time where exponentially
greater time is generally required to complete each successive ply.'

Exactly. So the ply depth depends only logarithmically on search time,
which is VERY WEAKLY.

So if you had wanted to show any understanding of the matter at hand, you
should have written RIGHT! in stead of WRONG! above it...

'When you speak of what is needed to 'win the game' you are fixating
upon the mating power of pieces which translates to endgame relative piece
values- NOT opening game or midgame relative piece values.  '

Absolute nonsense. Most Capablanca Chess games are won by annihilation of
the opponents Piece army, after which the winning side can easily push as
many Pawns to promotion as he needs to perform a quick mate.
Closely-matched end-games are relatively rare, and mating power almost
plays no role at all. As long as the Pawns can promote to pieces with
mating power, like Queens.

Your gobbledygook about 'suppreme piece enhancements' seems to
completely undermine your own theory. What are you saying? That the values
you gave below should _never_ be used, because they will unavoidably get
bonuses as the other pieces are traded, so that one should include the
bonuses beforehand? That would be an admission that I correctly recognized
the numbers you gave as useless nonsense, as they apparently do not include
these always-present bonuses. In fact it would mean the table you give are
not piece values at all. Piece values are by definition additive
quantities, the difference of which for both sides tell you who is likely
winning (all positional factors being equal). Non-linear corrections to
that should average out to zero over all piece combinations, or you would
be hiding part of the piece values in these bonuses.

But lets cut the beating around the bush, and give us a clear statement
about the following:
1) If I delete, from the Capablanca opening setup, Ac8, Nb1 and Bc3. You
are now claiming that this gives a winning advantage to white, and that
apparently the values of A, B and N you give below do not apply (as they
would sum up to approximate equality)? So what are the total piece values
of A, B and N in that position (including all bonuses)?
2) Give us a position where the values given below (without any bonuses)
would apply, in a situation where they do not automatically cancel because
both sides have equal material of that type.

As to the alleged similarity of your model to worthless nonsense, the
litmus test is if that model can (statistically) predict results of games
(like the Elo system can for having different players, rather than
different material). So it is really very simple:

Take the position:
rncbqkbcnr/pppppp1ppp/10/10/10/10/PPPPPPPPPP/RNABQKBANR w KQkq - 0 1
Now which side does your piece-value model predict has the advantage here,
and how big is it, compared to an advantage consisting only of Pawns (and,
just to be sure, does that 'advantage' mean he will win more often, like
the advantage of the first move will make white win more often than black,
or do you consider it an 'advantage' that he loses more often?) Then
play that position between equally strong opponents of your own choice
(i.e. opponents that score 50-50 from the normal Capablanca opening
setup), with a time control of your choice, for as many games as needed to
get a statistically significant measure for the deviation of the score
percentage from 50%, and see if this matches the prediction of your
theory.

You see, that is the nice thing about science. People don't have to take
my or your word for it, to know if your theory is any good. Even if you
avoid doing such tests out of fear for being utterly falsified, anyone
else can do it too. And when your theory predicts that the Chancellors
have the advantage here, because it is 'ridiculous' to assume A and C
are approximately equally strong, they will all discover soon enough that
it is actually your theory which is ridiculous nonsense.

I have done that test. So I know the answer. You, apparently, have not...

Derek Nalls wrote on Sun, Apr 20, 2008 06:20 PM UTC:
'... the Battle-of-the-Goths tournament was played at 1 hour per game per side (55'+5'/move, the time on the clocks is displayed in the viewer). And
you call it speed Chess. Poof, there goes half your argument up in smoke.'

Sorry, I could not find the time per move on your crude web page.

Nonetheless, less than 1 minute per move is much too short to yield quality moves ... at least by anything better than low standards.
_________________________________________________________

'Not that it was any good to begin with: it is well known and amply tested
that the quality of computer play only is a very weak function of time
control.'

WRONG!

The quality of computer play correlates strongly as a function of ply depth completion which, in turn, is a function of time where exponentially greater time is generally required to complete each successive ply.
___________________________________________________________________

'The fact that you ask how 'my theory was constructed' is shocking.
Didn't you notice I did not present any theory at all?'

In fact, I have noticed that you have failed to present a theory to date.
I apologize for politely yet incorrectly giving you the benefit of the doubt that you had developed any theory at all unpublished but somewhere within your mind.  Do you actually prefer for me to state or imply that you are clueless even as you claim to be the world's foremost authority on the subject and claim the rest of us are stupid?  Fine then.
____________________________________________________________

'I just reported my OBSERVATION that quiet positions with C instead of A 
do not have a larger probability to win the game, and that in my opinion 
thus any concept of 'piece value' that does not ascribe nearly equal value to A and C is worse than useless.'

When you speak of what is needed to 'win the game' you are fixating upon the mating power of pieces which translates to endgame relative piece values- NOT opening game or midgame relative piece values.  Incidentally, relative piece values during the opening game are more important than during the midgame which, in turn, are more important than during the endgame.  Furthermore, I am particularly wary about the use of relative piece values at all during the endgame since any theoretically deep possibility to achieve checkmate (regardless of material sacrifices), discovered or undiscovered, renders relative piece values an absolutely non-applicable and false concept.

I strongly recommend that you shift your attention oppositely to the supremely-important opening game to derive more useful relative piece values.
_______

'So what have I think I proved by the battle-of-the-Goths long TC tourney
about the value of A and C? Nothing of course! Did I claim I did? No, 
that was just a figment of your imagination!'

I did not claim that I knew exactly how your ridiculous idea that an
archbishop is appr. equally valuable to a chancellor originated.  This 'tournament' of yours that I criticized just seems to be a part of your 'delusion maintenance' belief system.
__________________________________________

'It might be of interest to know that prof. Hyatt develops Crafty 
(one of the best open-source Chess engines) based on 40/1' games, 
as he has found that this is as accurate as using longer TC for relative 
performance measurement, and that Rybka (the best engine in the World)
is tuned through games of 40 moves per second.'

Now, you are completely confusing a method for QUICKLY and easily testing a computer hardware and software system to make sure it is operating properly with a method for achieving AI games consisting of highest quality moves of theoretical value to expert analysts of a given chess variant.

I have already explained some of this to you.  Gawd!
____________________________________________________

'The method you used (testing the effect of changing the piece values,
rather than the effect of changing the pieces) is highly inferior, and
needs about 100 times as many games to get the statistical noise down to
the same level as my method. (Because in most games, the mis-evaluated
pieces would still be traded against each other.)'

First, you are falsely inventing stats out of thin air!

If you really were competent with statistics, then you would know the
difference between their proper and improper application within your 
own work attempting to derive accurate relative piece values.

Second, you do not recognize (due to having no experience) the surprisingly great frequency with which a typical game between two otherwise-identical versions running a quality program with contrasting relative piece values will play into each other's most significant differences in the values of a piece.

Here is a hypothetical example ...

If white (incorrectly) values a rook significantly higher than an archbishop

AND

If black (correctly) values an archbishop significantly higher than a rook,

then the trade of white archbishop for a black rook will be readily
permitted by both programs and is very likely to actually occur at some point during a single game or a couple-few games at most.

Consequently, all things otherwise equal, white will probably lose most 
games which is indicative of a problem somewhere within its set of
relative piece values (compared to black).
__________________________________________

'If you are not prepared to face the facts, this discussion is pointless.'

When I reflect your remark back to you, I agree completely.
___________________________________________________________

'Play a few dozen games with Smirf, at any time control you feel
trustworthy, where one side lacks A and the other B+N, and see who is
crushed.'

relative piece values
opening game
(bishop pairs intact)

Muller

pawn  10.00
knight  35.29
bishop  45.88
rook  55.88
archbishop  102.94
chancellor  105.88
queen  111.76

Nalls

pawn  10.00
knight  30.77
bishop  37.56 
rook  59.43
archbishop  70.61
chancellor  94.18
queen  101.60

So, what is your problem?  Both of our models are in basic agreement on this issue.  There is no dispute between us.  [I hate to disappoint you.]

What you failed to take into account (since you refuse to educate yourself via my paper) is the 'supreme piece(s) enhancement' within my model.  My published start-of-the-game relative piece values are not the final word for a simplistic model.  My model is more sophisticated and adaptable with some adjustments required during the game.

For CRC, the 3 most powerful pieces in the game (i.e., archbishop, 
chancellor, queen) share, by a weighted formula, a 12.5% bonus which
contributes to 'practical attack values' (a component of material values 
under my model).  Moreover, the shares for each piece of the 12.5% bonus 
typically increase, by a weighted formula, during the game as some of the 
3 most powerful pieces are captured and their share(s) is inherited by the
remaining piece(s).  Thus, if the archbishop becomes the only remaining, 
most powerful piece, then it becomes much more valuable than the 
combined values of the bishop and knight.

Notwithstanding, I'll bet you still think my model is 'worthless nonsense'.
Right?

In the future, please do the minimal fact finding prerequisite to making 
sense in what you are arguing about?
____________________________________

'... the rest of the World beware that your theory of piece values 
sucks in the extreme!'

No, it does not.  Your self-described 'far less than a theory, only an 
observation' comes close, though.

H.G.Muller wrote on Sun, Apr 20, 2008 06:10 PM UTC:
BTW, Derek, the remark in your monologue that a side lacking 8 Pawns would
have difficulty winning against one lacking a Queen also qualifies for the
joke-of-th-year awards! So you didn't bother to try that either, eh? It
was just some thought that popped up in your mind, and therefore must be
true? Man, the Pawns are toast. At 40/10' they lost 10-0, at 40/2' they
lost 9.5-0.5, because the Queen side went for a very early perpetual,
because it was overly afraid for the 8 connected passers, and it takes
some time for it to realize how won his position is.

Yes, I know, 40 moves in 2 min is like blowing a fan over the board, And
indeed it lookes much like a hurricane. Except that the fan seems to know
very well in which direction to blow! Can you show me any game at al where
the Pawns win? Could you beat Joker without Queen if Joker played without
Pawn and 1 min for the entire game, if you had unlimited thinking time?

Reinhard Scharnagl wrote on Sun, Apr 20, 2008 05:17 PM UTC:
To H.G.M.: There is no need for a polemic like: '1) Joker80 knows how to play a game of 10x8 Chess, and does so better than Smirf (oh, sorry about the 'insult', how politically incorrect of me to say such a thing...)' SMIRF still is behind, but that does not necessarily imply anything for used value models. The majority of Jokers losses were reached by SMIRF type engines, but I hesitate to derive some value related conclusions from that.

SMIRF lost several games by making a weird move instead of continuing a mating process. This has nothing to do with value models, but is related to other internal problems. So I hope e.g. for SMIRF-o-glot to ask for SMIRF's move decision explicitely instead of simply taking the move posted last as the optimal one during its thinking process, because there might indeed be a change during the last microseconds especially in such situations. Anyway SMIRF still does not handle mating scenarios correctly, which leads to some thrown away victories.

There are a lot of other design problems within SMIRF, thus I could explain its losses yet without having to throw away my piece value model.

H.G.Muller wrote on Sun, Apr 20, 2008 11:45 AM UTC:
To Derek: You don't seem to have grasped anything of what I am saying, and
are just ranting based on your misconceptions. For one, the
Battle-of-the-Goths tournament was played at 1 hour per game per side
(55'+5'/move, the time on the clocks is displayed in the viewer). And
you call it speed Chess. Poof, there goes half your argument up in smoke.
Not that it was any good to begin with: it is well known and amply tested
that the quality of computer play only is a very weak function of time
control. Results at these long time controls, after 20 days of non-stop
play for 280 games, are practically the same as in earlier blitz and
bullet tourneys.

The fact that you ask how 'my theory was constructed' is shocking.
Didn't you notice I did not present any theory at all? I just reported my
OBSERVATION that quiet positions with C in stead of A do not have a larger
probability to win the game, and that in my opinion thus any concept of
'piece value' that does not ascribe nearly equal value to A and C is
worse than useless. The near equality between A and C shows up at any time
control I tried, with any engine I tried. I furthermore find that piece
combinations that perform equal at one time control, do so at other time
controls as well (except that at extremely short time control, the value
of the Knight is suppressed a little, as the engine starts to bungle many
Knight endings for lack of depth to see promotions in time).

So what have I think I proved by the battle-of-the-Goths long TC tourney
about the value of A and C? Nothing of course! Did I claim I id? No, that
was just a figment of your imagination! I mentioned the tourney simply as
a source of high-quality games that shows:
1) Joker80 knows how to play a game of 10x8 Chess, and does so better than
Smirf (oh, sorry about the 'insult', how politically incorrect of me to
say such a thing...)
2) Smirf loses many games against weaker opponents (that ended below it)
from positions that it evaluated as +2 or +3, and that these obvious
misevaluations stongly correlate with trading an Archbishop for other
material.

As to your derogative remarks against the results of bullet games: before
I can take that serious, I would like to see you can beat Joker80 when it
is playing at 40/1', even with a time-odds factor of 60. From the way you
are talking about this it is not at all clear to me if you could actually
beat a 'fan', given 1 hour of thinking time... And if you would start
with B+N against Joker80's A, I would be really surprised if Joker80
would not crush you even when given 10 seconds per game! It might be of
interet to know that prof. Hyatt develops Crafty (one of the best
open-source Chess engines) based on 40/1' games, as he has found that
this is as accurate as using longer TC for relative performance
measurement, and that Rybka (the best engine in the World) is tuned
through games of 40 moves per second.

The method you used (testing the effect of changing the piece values,
rather than the effect of changing the pieces) is highly inferior, and
needs about 100 times as many games to get the statistical noise down to
the same level as my method. (Because in most games, the mis-evaluated
pieces would still be traded against each other.) So how many long TC
games did you play? Two million?

If you are not prepared to face the facts, this discussion is pointless.
Play a few dozen games with Smirf, at any time control you feel
trustworthy, where one side lacks A and the other B+N, and see who is
crushed. When you have done that, and report the results and games, we are
in a position to discuss this further. Until then, the rest of the World
beware that your theory of piece values sucks in the extreme!

Reinhard Scharnagl wrote on Sun, Apr 20, 2008 07:57 AM UTC:
To Derek: we know how much work you have invested in your piece value theory, so I understand, that you are somehow enraged on H.G.M.'s interpretations of his attempts. But all individuals I know to be investigating in that matter are strong-minded people. Thus please do not misinterpret their persisting in their viewpoints as pure animosity. 

To all: I understand, that the clearness and consistence of a value defining model is not enough to convince doubters to the 'truth' of such models. That way generated values have to be verified in practise. The easy part of that is to compare such figures to those experienced from 8x8 chess through centuries. The difficult rest of verification is to apply claimed value scales e.g. in 10x8 and to check out if they are well-working.

But it is unsufficient, to simply optimize a bunch of values within a given variant, because that does not establish a neutral theory, which could be applied on other scenarios, to be falsified or verified therein. A valid theory's conclusions have to exceed their input by magnitudes.

Watching the results of H.G.M.'s very interesting 'Battle of the Goths' experiments, what does this induce for our value theory discussion? In my opinion, there hardly could be derived anything concerning this question. Of course, some games have to be reviewed intensively for to see, whether there would have been structural imbalances. But to me it seems impossible to separate those engines' positional abilities from their tactical power, which is obviously very depending from the maturity of their implementation.

My program SMIRF is - as repeatedly stated - my first self-written playing chessengine, also often repaired and modified, but still caught in its initial naive design with a lot of detected basic weaknesses. Its detail evaluation as an example is incredible slow. Mating phases of games lead to concurring incompatible evaluations in SMIRF, thus some games will be lost even though having a clear mating line in view. SMIRF has been programmed without using foreign sources. By all of that it is no ripe engine - and thus I plan to put my experiences into a follow-up engine Octopus, which nevertheless will need a lot of time.

Derek and I have experimented with having different models applied to equal engines, identical beside of those different value approaches. Though this seems to be the more relyable approach for to verify value models, it nevertheless has structural weaknesses too, as in the realization of such a program there will be a lot of parts, reflecting the ideas of its creator, making it not completely independent of the ideas of that programmer.

So what is the arriving conclusion from H.G.M.'s event? SMIRF has to be rewritten as Octopus to become more mature. And maybe H.G.M. might try to embed his value model within a verificatable abstract theory, if he would like to widen its acceptance.

Derek Nalls wrote on Sun, Apr 20, 2008 07:00 AM UTC:
I prefer to await Scharnagl's expert opinion on why SMIRF does not win every game under computer tournament conditions where time allowances per move are extremely small.  Of course, this precariously presumes that he wishes to comment after your wholesale insulting remarks toward SMIRF.  

This 'Battle Of The Goths Championship 2008' is a strange exercise with AI results that are virtually worthless theoretically due to the 'virtually instantaneous' execution of moves for each program involved.  I suspect that the entire purpose of this 'tournament' is contrived to seem to demonstrate the universal superiority of Joker80 where, in fact, the limited superiority at 'speed chess' only- a trivial achievement- is being demonstrated.
______________

'The ones who determine the facts through accurate measurement thus contribute in an absolutely essential way to our understanding, as without such facts the theoreticians cannot even start their work.'

Exactly!  That is how I constructed my theory.  How did you construct your theory?  Let's discuss 'accurate measurement' in a bit more detail since you claim to know so much about it.

Except for opening books, endgame tablebases and some 'very obvious, checkmate or no choice moves' that may arise within the midgame, it is generally true that there is a direct relation between the maximum search time a computer is allowed per move [Ply depth completion is actually the more important criterion but it is a function of time.] and the quality of the moves found or generated.

Since 

every move within a game is important and potentially, critically so
(although the importance of the first move of the game is greatest and the
importance of the last move of the game is least)

AND

every move during the game depends critically upon all previous moves by both players for its best chance of being a successful step toward the goal of victory,

it is critically important that every move generated via computer AI be of the highest quality possible for the results to have the highest chances of being theoretically instructive, relevant and valuable instead of mostly-purely random.

Otherwise, you have not adequately distilled each side to play as resourcefully as possible to definitively determine which side probably possesses the ultimate advantage or disadvantage via your gametests with different armies.  This is a vital prerequisite to enable you to derive relative piece values that are reliable at all.

This is true to the extreme for chess variants related the Chess such as 
Capablanca chess variants for which the game-winning objective is to capture a single royal piece (i.e., king) regardless of material sacrifice.  Consequently, the levels of depth and irony inherent to chess variants of this type of design are very high.

The effectiveness of traps is based upon the fact that, upon naive inspection, what looks like 'the best move available upon the board' can, in reality, be 'the worst move available upon the board'.  Obviously, it is critical to correctly distinguish between the two wherever they arise within a game.  It is not just humans that are susceptible to falling into traps.  Chess supercomputers have made similar mistakes. [See Kasparov vs. Deep Blue I.]  

For example, an 8-ply search completion may lead a computer to recommend 
a very bad move that it would never recommend if allowed a 10-ply search 
completion.  However, the deeper the search ply completion, the less likely for a 'dramatic irony' of this type to exist and remain dangerously undiscovered.

So ... what do you think you have accomplished by generating 20,000+ very badly played games (obviously) via ultra-fast, ultra-shallow depth moves?
This monumental exercise in 'mindless woodpushing' can only have a 
statistically random effect reflecting the tendencies of the individual chess programs involved to spit-out moves when forced to do so before being given adequate time to explore enough plies to play any better than the moron level.  This could have some minimal value if chess variants related to chess were games well-suited for morons to play competently.  However, they are well-suited only for genii to play competently ... albeit usually and only with extensive training, effort and experience.

In summary, you might as well blow the pieces across the gameboard with strong fans.  The results of this type of 'mindless woodpushing' would be only slightly less significant to your misguided effort to devise the 'most accurate relative piece values for CRC in existence' (by your claim) than this method you are presently using.
________________________________________________

'Why would I read a 58-page monologue from someone adhering to such flawed logic?  It can only be a waste of time.'

I wish to echo Scharnagl's remark that (paraphrased) 'my published model is still a work in progress'.  Nonetheless ... If you fail to read anything, then you fail to learn anything.  You should be able to learn something from my mis-steps as well as my correct steps.

The figures within everyone else's published models for the relative piece values of CRC pieces upon the 10 x 8 board implicitly agree with mine that the archbishop is significantly less valuable than the chancellor.  So, you are not just characterizing my published work as 'worthless nonsense'.  Logically, you must also be characterizing the published works of everyone else of note (namely, Aberg, Trice, Scharnagl) likewise for the single reason that we do not share your radical view that the archbishop and the chancellor have appr. equal value.

Furthermore, under your model, the archbishop is only a little less valuable than the queen which is another radical contention on your part that demands much defense.

H.G.Muller wrote on Sat, Apr 19, 2008 02:34 PM UTC:
I agree that statistics from tablebases is very hard to interpret: more
than half the wins are usually tactical positions where pieces are
hanging, so that the outcome has nothing to do with the piece makeup in
question at all.

But this is a consequence of the inclusion of tactical initial positions
in the data set. The approximately 20,000 games I played to extract the
piece values given below were all played from tactically dead positions
(CRC-like opening positions, with some selected pieces deleted), where it
would take several moves to attack an enemy piece in the first place. Note
that I never played pieces in isolation (which could lead to the KNK effect
you mention), but always in a nearly full opening setup (34 or more Chess
men on the board).

As to the dependence of piece values on the fill fraction on the board:
one would only experience this effect to its full extent if the filling
fraction remained constant during the game (as in Crazyhouse, where indeed
the piece values are totally different from normal Chess). In games without
piece drops, the board will unavoidably get empty. So you will have to plan
to the future. It is true that in the early middle-game a Bishop is much
more dangerous than a Rook, (which, without open files, is almost
completely useless), but the difference is not so large that you can gain
enough material to neutralize the end-game-value difference before the
board gets empty enough that the advantage reverses. So it is still the
end-game value that dominates the piece value early on. The instantaneous
value tells you only the direction of a small correction that has to be
applied, and is very volatile.

Reinhard Scharnagl wrote on Sat, Apr 19, 2008 12:45 PM UTC:
A short remark on piece values: first, my published model is not my last word, I still am working on that. 

As I have stated already an amount of time ago, piece values are depending from the percentage of emptyness of the board. It concerns the mobility value part of sliding pieces. This would lead to dynamic piece values of sliding pieces slowly growing through a game. SMIRF unfortunately is far away from that.

Then I modified my thoughts on the nature of a bishop pair value bonus, which in fact had not been implemented in SMIRF yet at all. Errornously I derived that value modification from the fact, that a Bishop can reach merely one half of a board. But this is only a legal but misleading view on that strange effect. Today I am relating this paradoxon to the hideability of pieces more valued than a Bishop. Thus there is a chance to positionally devalue an opposite single Bishop by moving ones big pieces preferred on squares coloured oppositely to the Bishop's one. But that view demands the value bonus not to be applied statically by summing up piece values and such a bonus, but by writing an appropriate positional detail evaluation (as I have done intuitively in SMIRF).

To try to find out piece values by having teams of different armies fighting each other seems to be very promising at a first sight. But as you see in those huge table bases: a lot of optimal play is done pure combinatorically and could end contrarily, if placing one piece only a step aside. Thus it is hard to understand why to densly relate outcomes of a games and piece values. In an extreme constellation having King+Knight against King (which is a draw anyway) such an approach would lead to the conclusion, that a Knight is valued to nothing.

H.G.Muller wrote on Sat, Apr 19, 2008 08:15 AM UTC:
'Also, you might try to figure out the strength of a piece that can move
as
a queen and a knight. Call this piece say 'General' or G. One might use
an 12x8 board. One setup might be (white pieces)
  R C N B A Q K G B N C R
It is derived by imposing the condition that all pawns are protected by a
quality piece in the start position.'

I prefer to call this piece 'Amazon': the name 'General' is already
taken by several Shogi pieces, where the various brands of Generals are
all more or less handicapped Kings. Furthermore, Ferz means 'General',
and indeed can be described as a handicapped King. Although in English one
uses the Persian name for this piece (like for the Rook), most other
languages don't, and overloading the name 'General' would cause
problems in translation.

That being said: I ran a preliminary test for determining the Amazon value
(on a slow laptop, as my main PC is tied up in running the 'Battle of the
Goths' Championship), by playing games where one side had an Amazon in
stead of Q+N. I did this on 10x8 from the Capablanca setup (removing the
Queen's Knight and replacing Queen by Amazon), because there the piece
values are accurately known. I did not want to use 12x8, because I have no
piece values there for the pieces against which I would compare the
Amazon.

After 116 games, the Amazon is leading by 51.3% (52+ 49- 15=). The
statistical error over 116 games is 4.3%, though, so this difference with
equality if far below significance. At these settings (40/2' on a 1.3GHz
Pentium-M) the Pawn-odds score is about 62%, so the observed difference
corresponds to 10cP +/- 35cP. It thus seems there is hardly any synergy
between Q and N moves, and the values simply add. In other words, Q is
already so powerful that it doesn't really need the Knight moves, and
they provide little 'extra' in terms of making it possible to use the
moves it already had more efficiently.

To make this a hard conclusion, though, I would have to play better
quality games (either 40/5', or 4/2' on my 2.4GHz Core 2 Duo), as the
current setting is at the brink of underestimating the Knight because of
lack of depth in the end-game to use it efficiently, play at least 400 of
them, try sevral other piece combinations (e.g. also against C+B and A+B)
and average over a few different opening setups. That would take a few
days when I have my C2D machine available again.

H.G.Muller wrote on Fri, Apr 18, 2008 09:15 PM UTC:
FYI: Smirf falls way behind Joker80 in any real-life tournament played so far. See, for instance, the Battle of the Goths Championship 2008, which is currently playing at http://80.100.28.169/gothic/battle.html . And the main reason it does so is because it loses many points against engines in the lower part of the ranking. If you would look at the games (they can be downloaded from the mentioned page) you see the same pattern over and over again: Smirf voluntarily engages in losing trades, thinking it is +4 or +5 ahead, and subsequently is slaughtered by the weaker opponent because its piece material simply cannot keep up with the opponents overwhelming force, even if wielded by a less competent player. So I would say using Smirf in connection with piece values is a particularly bad example.

As for your scientific method, you seem to forget that science is about explaining observed FACTS. So if your 'coherent, logical, consistent' theory predicts that A is of nearly equal value as B+N, while in practice the B+N have a losing disadvantage, I would say the World would was better off without it. A theory not explaining the facts can at most contribute to MISunderstanding of relative piece values... The ones who determine the facts through accurate measurement thus contribute in an absolutely essential way to our understanding, as without such facts the theoreticians cannot even start their work.

Your 'understanding' of piece values is such that you consider piece values that do have C-A different from R-B 'flawed'. I.e., to be flawless in your eyes, a theory would have to predict that two pieces which perform equally (C and A) have to be assigned values that differ by several Pawns, or pieces that differ by several Pawns in strength (R and B) to be assigned a value that is equal. Why would I read a 58-page monologue from someone adhering to such flawed logic? It can only be a waste of time. And the FACT that C offers no significant advantage over A in Capablanca Chess games won't go away by it...

Derek Nalls wrote on Fri, Apr 18, 2008 08:28 PM UTC:
'If Archbishop and Chancellor have equal value, it DOES NOT IMPLY ANYTHING
for the value difference of Rook vs Bishop. They are all different pieces,
and have nothing to do with each other.'

YES it does according to my model and every quality, holistic model built upon a proper foundation I have ever seen.  Contrary to your statement, I think it obvious to any logical person that the component pieces have at least SOMETHING to do with their composite pieces.

Some computer chess programmers are notorious for achieving useful relative
piece values that are within decent range of their optimums based purely upon AI playing strength without creating any coherent, fully-developed theory that is logically explained, justified and consistent.  Unfortunately, such people contribute little to the understanding of
relative piece values for themselves or other interested parties.

I have appr. two years of experience working with Reinhard Scharnagl's 
excellent SMIRF program, my fast dual-CPU server and choice Capablanca chess variants.

Reinhard Scharnagl would compiled two, otherwise-identical versions of his 
program using his and my favorite sets of relative piece values (at that time) which would played against one another using a great amount of time per move.  Eventually, we carefully completed many games this way.  We would both analyze the game results and discuss conclusions.  Sometimes we would agree.  Sometimes we would disagree.  Subsequent tests would settle disagreements ... sometimes.  In this manner, we both improved our models over time until we reached a point where any further minor improvements became prohibitively difficult to achieve within a survivable time frame.

'In real life the value of a piece is not the sum of the value of each of its individual moves ...'

YES it is although not exactly.  The moves of component pieces of a composite piece have far more effect upon determining its relative piece value than ALL other factors added together.

'... but also depends critically on properties like mating potential,
color-boundedness, forwardness, speed, manoeuvrability, concentration,
sensitivity to blocking.'

I have also read ALL of the pioneering works of Betza on the subject.
Essentially, my model mathematicized a subject (to the extent possible
present day) he had only speculatively verbalized.  Rest assured, my model 
makes quantitative adjustments for all non-trivial, effecacious factors to relative piece values that I know of with certainty.

You need to read and thoroughly understand my 58-page paper on the subject.

universal calculation of piece values
http://www.symmetryperfect.com/shots/calc.pdf

'Theoretical considerations like you refer to are just nonsense, with no
connection to real life.'

The connection of my model to 'real life' is very strong.  My theory was
adjusted and refined numerous times to comply with game results over
different piece sets and game boards.  Experience dictated the details
of the theory in accordance with the scientific method.

'What would you rather have (if you can choose to make a trade or
not), a piece that is more 'valuable' according to some contrived
reasoning, or a piece that gives you a larger probability to win the game?'

Both.

Under a proper model, they should not be mutually exclusive at all.
In fact, they should be in agreement ... until a point in the endgame
where checkmate becomes possible.  Be mindful that significant
differences in relative piece values between the opening game, 
mid-game and endgame (to the limited extent that they are applicable)
are accommodated under sophisticated models.
____________________________________________

See the published values of Ed Trice and Reinhard Scharnagl for
CRC pieces upon the 10 x 8 board.

http://www.gothicchess.com/piece_values.html

In addition to the published values of Hans Aberg and Derek Nalls, this verifies that it is beyond dispute that your published values for the archbishop and chancellor are radical.  Your radical contention that an archbishop and a chancellor have appr. equal relative piece values requires an especially sound theoretical framework to be convincing.  Instead, all I am receiving from you is piecemeal descriptions of endgame scenarios where material values are likely to disappear and become meaningless compared to positional values (i.e., checkmate achievable regardless of material sacrifices) and consequently, conclusions drawn are likely to be faulty.

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