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Please clarify if you read this and know the answer.
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<i>The new pieces, the Archbishop (moving as either a Bishop or Knight) and the Chancellor (moving as either a Rook or Knight) are placed next to the Queen side and King side Rooks</i>
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Are the new pieces the outermost pieces in the array, or do they go between rook and knight?
You can see the initial setup on the PBM preset page for Aberg's variation <a href='/play/pbm/play.php?submit=Preview&game=Aberg+variation+of+Capablanca+Chess&rules=http%3A%2F%2Fwww.chessvariants.com%2Flarge.dir%2Fcapablancavariation.html&group=Chess&set=alfaerie&board=10.01.&code=ranbqkbnmrpppppppppp40PPPPPPPPPPRANBQKBNMR&patterns=%3A+%21*&cols=10&colors=339933+CCCC11+22BB22&hexcolors=red+green+blue+orange+yellow+indigo+violet+cyan+magenta+black&player=White&first=White&files=&ranks=&bcolor=111199&tcolor=EEEE22&bsize=16&shape=square'>here</a> The new pieces go between the rooks and knights.
Hans Aberg has provided a very nice graphic showing the setup. --Ed.
This reproduces EXACTLY the starting position of Carrera's variation of some four hundred years ago.
I just compared this game with Carrera's Chess at http://www.chessvariants.com/historic.dir/carrera.html and found that this game does not exactly match the starting position of Carrera's Chess. It is in fact the mirror image of Carrera's Chess. The difference is that the two new pieces have reversed positions in this game.
All the same, this game has more affinity to Carrera's game than to Capablanca's, to the point that it might more correctly be called 'Aberg's variation of Carrera's Chess'.
Since I'm working on updating my Chess,_Large.zrf file today, I was paying more attention to the various games in it, and I started tripping up over Aberg's variation. In this ZRF, which I originally wrote in 1998, I implemented both Aberg's variation, or what I thought was his variation, and a Capablanca variation of my own. When I originally wrote the ZRF, this page did not exist, and I based my ZRF on the description which is now at http://www.chessvariants.org/misc.dir/chessmods.html I've just noticed that this old description has a contradiction in it. The text description places the Chancellor on the Queen's side and the Archbishop on the King's side, but the diagram reverses this. I based the ZRF on the diagram, and my own Capablanca variation just reversed the positions of Chancellor and Archbishop. Since this page agrees with the old text and not with the old diagram, I take it that my variation was actually Aberg's variation. Furthermore, Pritchard's description of Carrera's Chess contradicts the description on this website. Pritchard points out that Murray reversed the names of the Champion and Centaur, and our page on Carrera's Chess was based on John Gollon, who probably got his information from Murray. I trust Pritchard more than Gollon or Murray, and so I take his description of the game as more authoritative. Therefore, it appears that Carrera's Chess, Aberg's Capablanca variation, and my Capablanca variation all have the same setup. It looks like my least original variant ever is even less original than I thought it was. :)
All three variations keep the relative order between the old chess pieces, keeping the positions of the rooks at the sides, and the queen and the king at the center, with the white queen to the left. The board colors are such that the white queen ends up on a white square. All three variations agree that the weaker of the two new pieces, the Archbishop, moving as a Bishop or a Knight, should be at the Queen side, and that the stronger piece, the Chancellor, moving as a Rook or Knight, should be at the King side. This seems natural, as the Queen side is already stronger in Orthodox Chess, thus balancing up the King side somewhat. Bird put the new pieces next to the King, Capa between the Knights and Bishops, and I suggested that they should be put next to the Rooks. I think the preferred positioning may depend on playing style: The more 'rough' it is, the more one might want to have the new pieces to the center. I like the Fianchetto where the Bishops point towards the center four squares, and I want the light pieces early into the game, as is customary playing in Orthodox Chess, therefore, I want the new, heavier pieces out of the way in the earliest stages of the opening game. In addition, widening the board I think will cause that too much moves are spent on castling preparations. Therefore I suggested an Enhanced Castling rule. The other variations do not have that, but those variations can be played with or without it.
Going on the assumption that Hans Aberg gets notified whenever a new comment is added to this page, let me mention here that I have now released a Zillions Rules File that plays Aberg's Capablanca variation. Unlike the ZRF I originally released years ago, this one gets the setup correct, and it implements free castling. There is a link to it just above the comments section.
'ABCLargeCV': An important family of chesses, a crowded art(because 50-100 instances extant), Aberg's is a left-right reflection of the original 17th century Carrera's. 'H.E.Bird had made an earlier variation(50 yrs. before) of Capablanca Chess.' And Chinese alchemists made gunpowder 500 yrs. before it was invented in 14th century Europe. Seriously, extreme free castling, where Rook ends up not necessarily even adjacent to King, makes sense. Carrera's and Aberg's spread out the compounds maximally whilst keeping Rooks at familiar corners. Piece-value table shows Bishop ahead of Knight on 8x10 though still close.
I've been playing a few games of Embassy Chess on BrainKing and have found that castling is something that is to be kept open and not used. Once you castle your opponent is on you unless you've done it to where he can't do much. This free castling would be a whole different kind of deal though. Castling in Embassy Chess is like the other games where the King moves three squares and the Rook is put on the other side. The King is a usefull piece in the center of the board if he's safe. Getting the Rooks out is still a problem, but there's ways to do it if you purposely plan on not castling. Embassy Chess with free castling would almost be like playing Grand Chess on a 10 × 8 board.
Just thought that I would mention Chancellor Chess (Book), which reprints the first part of Ben Foster's 1889 book, including a 'GIF' of the original diagram illustrating the interesting RNBQKCNBR setup for both players. This places Bishops on both light and dark squares on the 9x9 board.
Note that the piece values given on this page are not empirical values at all, but theoretical values: they are derived from the way the piece moves, and comparison with known values for another game (8x8 Chess) for pieces that move likewise. Empirical values are values that are derived from win probabilities (as derived by statistical analysis of games) from positions with material imbalance. I have played and analyzed many thousands of such games, using my engine Joker80 (currently the best free WinBoard-compatible 10x8 engine) in self play, and I can vouch for the fact that the piece values given here are no good. The true values are: P=85, N=300, B=350 (pairBonus=40), R=475, A=875, C=900, Q=950. Note in particular that there is no significant difference in value between A and C, and that A+P on the average lightly beats Q. The P=85 is for a Pawn in the initial position; a healthy Pawn in the center, or a passer, are of course worth much more, a backward or edge Pawn much less.
CRC practical attack values http://www.symmetryperfect.com/shots/values-capa.pdf Although Aberg's method of estimating the relative piece values for CRC pieces upon the 10 x 8 board was just an expedient extrapolation from established relative pieces values for FRC pieces upon the 8 x 8 board, his values are actually more accurate than yours. One major flaw in your system is approximately equating the values of the archbishop and the chancellor. This is a radical contention which implies that the values of the rook and bishop are equal (since the archbishop equals a knight plus a bishop and the chancellor equals a knight plus a rook). This is inconsistent with your own system internally whereby the rook is (correctly) ascribed a higher value than the bishop.
Values given for P N B R Q K are just the empirical values used before the days of computer programs, with an adjustment of the traditional B = 3, mostly used as a point of departure, and how to figure out how material in the long run would balance out. They also depend on position and the skill of the player, for example, knights weaken in closed positions, and weaker player might over-value them. I just put them up as a starting point so your analysis is welcome. The surprising closeness of the A and C values you get perhaps depends on the fact that A, unlike B, can move on squares of both colors. Pawns (just as knight) ought to weaken on large boards. So another pawn rule might be that it is allowed to move two steps if it has not reached the two middle rows (i.e., a pawn that has moved one square can still make a two-square move). 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.
To Derek: 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. In real life the value of a piece is not the sum of the value of each of its individual moves, but also depends critically on properties like mating potential, color-boundedness, forwardness, speed, manoeuvrability, concentration, sensitivity to blocking. See the considerations of Ralph Betza. In particular, as to the R-B vs C-A difference: A Rook has mating potential, a Bishop not. But: A Chancellor has mating potential, and so does an Archbishop. A Rook can stray on all colors, a Bishop can only access half the board. But: A Chancellor can stray on all colors, and so can an Archbishop. Theoretical considerations like you refer to are just nonsense, with no connection to real life. Elaborate nonsense, admittedly, but nonsense nevertheless. No amount of _talk_ will increase the value of a Chancellor versus an Archbishop. Only what happens on the board counts. And on the board A+P beats C (in the presence of other material, between equal players) by a sizable margin (like 60-40). Just like B+P is no match for a Rook, in the presence of enough other material. If you consider that 'flawed', because the fact that R is more valuable than B+P 'implies' that C is more valuable than A+P, to be 'consistent', then I wonder what your concept of piece value really means. What would you rather have (if you can choose to make a trade or not), a piece that is more 'valuable' accoording to some contrived reasoning, or a piece that gives you a larger probability to win the game? If it is the latter, you should use the piece values I give, and not the 'more correct' ones of Aberg. In real life A performs nearly as well as C in almost any combination of material, and B gets crushed by R in almost any combination of material except the sterile KRKB ending.
Theoretical considerations are not nonsense but must tempered by empirical experimentation. Below is my theoretical analysis of C vs A situation. First let's take the following values: R: 4.5 B: 3 N: 3 Now the bishop is a slider so should have greater value then knight, but it is color bound so it gets a penalty by decreasing its value by a third, which reduce it to that of the knight. When Bishop is combined with Knight, the piece is no longer color bound so the bishop component gets back to its full strength (4.5), which is rookish. As a result Archbishop and Chancellor become similar in value.
First I want to stress that the B-N value difference is dependent on board size: on 8x8 they are roughly equal, while on 10x8 the difference is half a Pawn. (In addition there is half a Pawn bonus for having a pair of oppositely colored Bishops. So in these Capablanca-type variants, giving N+P to break the opponent's B-pair is an equal trade.) This increased B-N difference is not due to the Knight being weaker, but to the Bishop being stronger! B+N+N vs Q, (in an otherwise full 10x8 opening setup) is about equal, and the three minors beat the Queen by about half the Pawn-odds score if the Bishop is part of a pair. B(paired)+P vs R in the opening turns out to be an equal trade. My guess is that the wider board makes the Bishop relatively more valuable: its forward moves now attack the opponent usually in two places, while on 8x8 one move usually ends on the side edge of the board. I noticed this in an even more extreme way in Cylinder Chess, where the board is effectively infinitely wide. A Cylinder Bishop (B*) amongst normal Chess pieces is aworth a full Pawn more than a normal Bishop. R*-R is only about a quarter Pawn. The lateral over-the-edge attacks are comparatively worthless. Q*-Q, otoh, is about 2 Pawns. Strangely enough, the explanation that the Knight move of Archbishop breaks color-boundedness does not seem to fully explain the large synergy between B and N moves. I tried a piece that moved as B+P (so one extra forward non-capture step), which broke color-boundedness, but it hardly gave any advantage over a normal B (about 1/6 Pawn) A Dragon horse (B+K), however, is slightly stronger than R+P. But of course adding the K moves (or Wazir moves, really) both as capttures and non-captures also endows it with mating potential. My current guess is that breaking of color-boundedness and mating potential help a little to bridge the narrowed gap between R and B on a 10x8 board, but that the major contribution comes from the enhanced close-range manouvrability and concentration of attack power: an Archbishop covers several 2x2 blocks. Such contiguous attacked areas seem to be very valuable, and is likely to be also an important factor determining the value of the Bishop pair (because Bishops on bordering diagonals also covering a lot of contiguous squares).
'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.
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...
'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.
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.
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.
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.
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.
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!
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.
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?
'... 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.
'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...
'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.
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!
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?
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-)
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
Maybe it could be interesting to read some ideas of mine at http://www.10x8.net/Compu/schachwert1_e.html .
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.)
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.)
HG Muller, you are certainly allowed, and encouraged, to post on piece values in the Piece Values thread. Joe
No, I cannot: unlike this thread, it refuses my posts unless I fill in the ID field, and I do not have an ID...
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.
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.
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.
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.
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.
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.
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: | 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.
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'.
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'.
'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.
|| 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.
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.
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.
'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).
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.
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.
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: | 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: | 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, 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.
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.
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: | 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.
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.
'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?
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.
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.
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.
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.
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.
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: | 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: | 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: | 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.
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.
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: | 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.
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