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Comments by Robert Shimmin

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Robert Shimmin wrote on 2005-02-22 UTC
A large branching factor doesn't always give the human the advantage. 
When grandmasters play the computer, they often want to trade queens
early, because the computer seems to be better at using the queen
tactically as the boards opens up, while the grandmaster is better in
closed positions where positional play is more important.

A game that is highly positional and has a large branching factor (like
go) does seem to give the computer fits.  But I suspect a game that is
very tactical and has a large branching factor gives the computer the
edge.  I suspect the progressive variants fall into the latter category.

Robert Shimmin wrote on 2005-02-21 UTC
In all honesty, I don't think humans will lose interest in chess just
because computers can beat us at it.  It's already the case for the vast
majority of chess-players, and yet they still play.  Or to make another
comparison, we didn't stop holding foot-races because we had built
machines that can go faster than us.

Symmetrical Chess Collection Essay. Hidden Missing description[All Comments] [Add Comment or Rating]

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Falcon Chess 100. Falcon Chess played on an expanded board of a 100 squares with special Pawn rules. (12x10, Cells: 100) [All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2005-01-21 UTC
Having looked at USP 5,690,334, and noting that it claims 'A method of
playing an expanded chess-like game ... comprising the steps of ...,' I
have to ask, what is it that the inventor thinks he has actually patented?
 It seems that, the 'method of playing ... a chess-like game' having been
patented, the activity which infringes the patent is the playing of a
chess-like game according to that method: i.e., that anyone who plays
Falcon Chess infringes the patent!

While it is true that many chess-variants are invented to be admired more
than played, rarely is this design goal backed up with legal force.

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Robert Shimmin wrote on 2003-09-24 UTC
Sometimes changing the board size can actually change to outcome.  In shogi
on a board of 10x10 or smaller, king and gold vs. king is usually a win. 
On boards of 11x11 or larger, it is almost never a win.  This phenomenon
usually rears its head where most of the mating power available is in
short-range pieces.

Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2003-07-21 UTC
Michael --

Here's the data on the augmented knights, obtained from Zillions vs.
Zillions using 5-ply fixed-depth searches.  The augmented knights are
placed in the rook positions and played against the orthodox army.

All the augmented knights give an advantage vs. rooks, probably in part
due to their ease of development and the rook's lack thereof.  The
following values are the various pieces' advantages over the rook, in

ND, NA = 27
NW = 38
NF = 82 (!)

The standard deviation for these measurements is about 10 cP.

Robert Shimmin wrote on 2003-07-21 UTC
On another note, can anyone think of any reason why NF ought to be noticeably stronger than the rook, or any of the other knight+(one atom) pieces? Zillions wins rather more often with it than the others, and I'm trying to puzzle out if this is a quirk of Zillions', or if it could be duplicated in theory or human playtesting.

Robert Shimmin wrote on 2003-07-21 UTC
<i>'Archangel is Gryphon plus Bishop'. If your numbers do not show it as supeirior to Q, mustn't that be an eror in the numbers?</i> <p> The crowded-board mobility calculation for the Gryphon predicts that is very similar in value to a Cardinal. Because the Gryphon can move like F anyway, adding Bishop to its move is really only adding the longer Bishop-moves, and the Archangel is only one half-knight stronger than the Gryphon, and a piece one half-knight stronger than a Cardinal-class piece is a Queen-class piece, or so the numbers say. <p> Still, my gut instinct would think, like you, that an archangel would be noticeably superior to the queen. This is something that can only be resolved through playtesting. If the numbers are right, well, this somewhat bolsters our faith in using the mobility calculation to say two pieces are roughly the same in value. If the numbers are wrong, it is very interesting, because both the queen and the archangel are well-balanced pieces, and the first step to improving a theory is trying to identify those cases where it fails. <p> After calculating the 'forking power' for a number of these pieces, these are my second thoughts... <ul> <li>What I call 'forking power' is really only the average number of two-square combinations attacked by a piece, and therefore treats pins and forks as the same phenomenon. Perhaps this is wrong. <li>If two pieces have similar mobilities, they will almost certainly have similar FP's. Therefore, the theory can't make any predictions that couldn't also be made by invoking a multi-move mobility component to value, or simlper yet, a power-law dependence of value on mobility. I originally thought up the archangel to think of a piece with similar mobility as the queen, but vastly greater forking power. But this 'vastly greater' wasn't nearly as great as I hoped. :( <li>Not all two-square combinations of attack are created equal. Maybe two squares in the same direction are more or less valuable than two squares in different directions. <li>In short, I originally invoked this definition of forking power because it was something that would be calculated without any undue difficulty or assumption, and would be much larger for strong pieces than weak pieces, so with the right scaling factor, could be made to give the queen the right value. It may be an improvement to the theory, but I can't think of any test for it that would distinguish it from a few alternate improvements. </ul>

Robert Shimmin wrote on 2003-07-20 UTC
In response to Ralph's comment, I've done the forking power calculation
for a few more pieces.  The magic number is 0.67

Piece        Mobility     Forking     Total     % Fork
Nightrider     7.82        29.53       9.09      14.0
Rook           7.72        29.23       8.97      14.0

One thing I've noticed (and should have expected) is that the 'forking
power' value is very close to being proportional to mobility squared. 
These pieces illustrate about the most variation I can create in FP for
'normal' pieces of about the same mobility.  Archangel is gryphon +

Piece        Mobility     Forking     Total     % Fork
Archangel      13.10       98.07      17.32       24.4
Queen          13.44       91.32      17.37       22.6
FAND           13.56       95.38      17.66       23.2

Clearly, these differences are too small to test.  So while we know there
is some superlinear dependence of value on mobility, we can't yet say
whether that is most related to forking power, multi-move mobility, or

Tiled Squares Chess. Drop tiles to create the board as you play. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2003-07-19 UTC
I wonder whether a player could drop enough anti-tiles to force a draw when each side could not bring enough force to bear on the other.

Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2003-07-13 UTC
For anyone who was curious about my previous prediction that an amazon may
be a full rook more powerful than the queen, I ran the following
experiment.  Whether it means anything is up to you to decide.

I ran scripted Zillions to play against itself for 500 games where
black's queen was promoted to amazon, but black was missing its queenside
rook.  At strength 4, results were 249-62-189, or 85 ratings points in
white's favor.  At strength 5, results were 265-57-178, or about 110
ratings points.

For comparison, samples of 1000 games each found pawn-and-move to be a
135-point advantage at strength 4 and a 260-point advantage at strength 5,
while giving white two opening tempi instead of one is a 50 point
advantage at strength 4 and a 140-point advantage a strength 5.

Based on this, I would guess that the amazon falls short of being a full
rook stronger than the queen by perhaps half a pawn, but that still leaves
the amazon a pawn stronger than a queen and a knight.

Robert Shimmin wrote on 2003-07-12 UTC
I've had this thought (2nd-move mobility etc.) before, and I think the correct way to express it is this: <p> Averaged over the possible locations on the board, let M1 be the average number of squares that can be attacked in one move (crowded-board mobility), M2 the average number of squares that require two moves to attack, etc. Then the practical value might be some weighted sum of these quantities: <pre> PV = k1 M1 + k2 M2 + k3 M3 + ... </pre> Of course we don't know these weighting values. But it is reasonable to believe the value of being able to attack a square diminishes by the same factor for each tempo required to do so, and if so, there's really only one adjustable parameter: <pre> PV = M1 + k M2 + k^2 M3 + k^3 M4 + ... </pre> This is at first sight a very promising approach, since it lets us lump a number of 'weakening' factors such as colorblindness, short range, etc. into one root cause: not being able to get there from here. Also, it provides an alternative explanation for the anomalous extra strength of queen-caliber pieces. Moreover, it would for the first time give a basis for calculating the practical values of pieces that move and capture differently. <p> However, there's one problem I've run into when I've pursued thoughts along these lines. The probability of being able to rest on a square is different from the probability of being able to pass through a square, so we need a second 'magic number' to calcuate the various M-values. Also, because the number of squares strong pieces can safely stop on is smaller, it may be necessary to make this value smaller from strong pieces than for weak pieces to account for the levelling effect. (Although I've <i>almost</i> convinced myself the levelling effect may cancel itself out for M1, I'm far less certain that it does for M2, etc.) Anyway, I've rambled about this enough. I think it's a very promising path to go down, but there are at least two arbitrary constants we need to know to go down it.

Pocket knight. Each player has a knight that he can drop during the game. (Recognized!)[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2003-01-14 UTC
I forget whose idea it was or where I saw it, but the idea was you could
pocket any piece (as a move) and place a pocket piece (as a move), and
there was no restriction about how many pieces you could have pocketed,
but immediately following your drop, your opponent got a double move.

My reaction at the time was that the rule changes were only of tactical
value because in most situations the doublemove response should be able to
easily answer the dropped piece (not to mention that the teleportation of
the dropped piece required two tempi to complete, and in the meantime, the
piece did had only second-order usefulness.  It defended nothing and
attacked nothing, but could only threaten to defend or attack things. 
Granted, it threatened to attack and defend EVERYTHING, but I still think
the doublemove response is overkill.)

Dibs![Subject Thread] [Add Response]
Robert Shimmin wrote on 2003-01-13 UTC
If the goal is to avoid confusion, then you should be aware that 
Chess Plus is the name of an existing commercial four-player variant.
The author sells it at

If you're not concerned about avoiding confusion, then why bother with
calling dibs or anysuch?  Just look at how many superchesses there are.

L. The list of official nominations for the variant-by-committee.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2003-01-11 UTC

The contest says the rules will be selected by poll, but I've been unable
to find instructions as to how the poll will be conducted.

Vote for one, vote for two, rank all in order of your preference, what?

Thanks for any clarification.

Yalta. A three player chess variant. (Cells: 96) [All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-12-14 UTC
I don't think the 2-vs-1 scenario is all that big of a problem in 3-player
games, since if one player begins to pull ahead, it only becomes natural
for the other two to ally against the leader.

One problem in 3-player strategy games I've seldom seen solved though is
the kingmaker problem.  Suppose one player is losing hopelessly, but is
either able to hurt one of the other players enough on the way out to give
the other one the game, or is able to determine the winner more directly
(by deciding whose mating trap to walk his king into...).  Then the winner
ends up being decided not by who played better, but by whom the _loser_
was feeling better disposed towards.

L. Fun contest: Help us create a new chess variant by committee.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-12-09 UTC
Offhand, I suggest that since we're voting in the rules one at a time, we might just agree to the convention that later rules supercede earlier ones. At least this makes the most sense to me. Any other thoughts?

Fidchell. A large Great Chess variant with blended historical elements, invented for an RPG. (12x12, Cells: 144) [All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-12-05 UTC
When I'd read it the first time, my interpretation was that a player could
deliberately place the king in check and force the opponent to capture it,
but that if the opponent checked the king, that check had to be lifted or
the game was lost.  (ie, that placing the king in check was legal as a
deliberate sacrifice, but that if the the opponenet started the check, it
had to be responded to normally.)  This made sense to me because it kept
the king sacrifice (with mandatory capture) open as a tactical option, but
a multi-move mating combination found by the opponent still worked.

But I can definitely see Glenn's interpretation, too.  Would it be rude to
ask the inventor for one final clarification on the issue?

Cambodian Chess ZIP file. Mysterious 9x9 "Cambodian" Chess game that seems unknown in Cambodia.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-12-02 UTC
I can't imagine this game was ever played much, or if played much, ever
played well.

If the second player adopts a symmetrical defense, then the first player
is forced to sacrifice material, possibly a lot of material, in order to
break symmetry.  The only way to break symmetry is to capture one ship
(rook) with another down a file, or to check the enemy king.  But either
of these require opening a gap in the pawn structure, and the second
player can always come out ahead materially in the process of opening such
a gap.

Revisiting the Crooked Bishop. Revisiting the Crooked Bishop.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-11-26 UTC
And there's another detail that all of us forgot!  When the crooked bishop
is on the edge of the board, one of its paths in the (0,2) direction is
blocked, even though the (0,2) square might be on the board.

When I included this in my evaluation, I got the result that the crooked
bishop has about 1.2 times the mobility of a rook for a broad range of
reasonable values of the magic number.

Ideal Values and Practical Values (part 1). A discussion of the values of chess pieces.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-11-19 UTC
<i> Remember, the principle is that Pawn and move may be 2:1 odds if the stronger player is rated 1800 USCF and the weaker is 1600; but if the stronger player is 2600, he can only give P+move to a 2200 (numbers are made-up examples for rhetorical effect). </i> <p> If chess is a theoretical draw, then this principle won't always apply, or rather it applies in a weaker form to small advantages than to big ones. <p> Let's assume chess is a theoretical draw. Two equally matched and very strong chess players (stronger than any grandmaster, but not perfect -- they usually lose when they play against God, but draw often enough to make things interesting) play at odds. The odds are small enough that the game is still a theoretical draw, but large enough that any larger advantage would be a theoretical win. Half the time, the side giving odds will make that infinitessimal slip-up that allows the other side to win, but the other half of the time, the side given odds will make that infinitessimal slip-up that gives the other side enough breathing space to ensure a draw. So the value of these odds to these inhumanly strong players is 3:1 money, or 190 ratings points. <p> When God plays Himself at these same odds, the game is always a draw, since He plays perfectly and the game is a theoretical draw. When weaker chess players play at these odds, the side giving odds may occasionally win, and the odds are worth somewhat less than 190 points. <p> The mathematics that inspired this thought experiment yields the following results: <p> (1) If chess is a theoretical draw, then no odds small enough to keep the game a theoretical draw are worth more than 190 points at any level of play. <p> (2) All such small odds have some level of play at which they are worth a maximum. At weaker levels of play, the side given odds is too weak to fully exploit them, and at stronger levels of play, the side giving odds is strong enough to overcome its disadvantage. <p> (3) As the odds increase, this critical level of play above which stronger players actually notice the odds <i>less</i> also increases. <p> (4) For even the smallest odds, however, this critical level of play is stronger (not too much stronger, but stronger nonetheless) than any human being plays.

Robert Shimmin wrote on 2002-11-11 UTC
On a re-read of parts 2-4 of About the Values of Chesspieces, I finally
became convinced that with good statistics (thousands of compiled games),
two things should be possible. (1) A workable handicap system for chess
players of different rank that could tie the 19th-century handicaps of two
moves, pawn and move, knight odds, etc. in with the modern rating system. 
(2) A theory of piece values that has better predictive power than what we
have now.

So I wrote some scripts to play Zillions against itself and compile the
results whenever I'm not using my computer, and if, Zillions' quirks
notwithstanding, these numbers have any relation to games played by human
beings, some of my initial results are intriguing.  Among them are

(1) Ralph Betza's intuition in designing Chigorin Chess seems to be
correct: averaged over the course of the entire game, knights may be more
valuable than bishops.  Conventional wisdom holds the opposite because by
the time the game gets around to trading knights for bishops, things have
often opened up enough to close the gap between them.

(2) The 19th-century source was nearly dead-on in calling pawn-and-move at
2:1 money odds -- if we can assume Zillions' strength is on par with that
of the average 19th-century club player, then my statistics so far
indicate pawn-and-move is worth about 130 USCF ratings points.  Knight or
bishop odds seems to be around 400 points so far, and rook odds (with
nowhere near enough games to have good statistics) seems to be worth a
little over 500 points.  Of course, since advantages become bigger with
the increasing skill of the players, it very much matters _which_ 500
points those are...

Anyway, as I've alluded above, the chief barrier in proceeding with this
work, or even in determining whether the numbers have any value at all, is
getting enough games.  Figuring that I actually have to use my machine, I
can only crank out a few hundred games a day.  So if anyone has interest
in donating their computer's downtime to the cause, please email me at
[email protected] with the particulars of the machine (processor, memory,
and operating system) you'd like to run it on, and I'll send you my
scripts for automating Zillions.  The first step will be seeing how much
Zillions' strength varies from system to system, but after that, we may
actually be able to answer some of these questions.

Revisiting the Crooked Bishop. Revisiting the Crooked Bishop.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-10-19 UTC
I'm going to weigh in on Peter's side.  The probability of getting to (0,4)
should be 0.51793.

There are two ways to get there.  One requires (1,1) and (1,3) open.  The
other requires (-1,1) and (-1,3) open.  Both require (0,2) open.  

The probability of (1,1) and (1,3) open is 0.49.  (Same for the other
route.)  So the probability of this part of each route being closed is
0.51.  So the probability of both being closed is 0.51^2 = .2601, and the
probability of at least one of them being open is 1-.2601 = .7399.

Of course, in either case (0,2) must be open, so the final probability of
getting to (0,4) is .51793.

This generalizes to the probability of getting to (0,2n) being 
(1-(1-p^n)^2)*p^(n-1), where p is the magic number.  This is equivalent to
Peter's original formula, although a more compact writing of the formula
is (2-p^n)*p^(2n-1) or 2*p^(2n-1) - p^(3n-1).

If you need help convincing yourself your original statement

> Would 0.91 times 0.7 times 0.7 be correct? Yes, this is the answer
> to 'it can move there if either d2 or f2 is empty AND e3 is empty AND
> the corresponding square (d4 if d2, or f4 if f2) is empty'. 

is wrong, try thinking about it this way: suppose both d2 and f2 are
empty.  Then the crooked bishop may pass through either d4 or f4 on its
way to e5.  And the probability of being blocked on BOTH squares is 0.09,
not 0.3.  So the difference between your calculation and the answer Peter
and I get lies entirely in the cases where d2 and f2 are both empty.  In
these cases, it doesn't matter which square (d2 or f2) it passed through
to get to e3, so no binding decision about which path was taken has been
made yet.  In fact, no such decision has to be made until the first d-file
or f-file blockade is encountered.  Your method of calculation forces the
decision to be made at the very first step, even when both paths are

Make any sense?

Spinal Tap Chess. Variant on an 11x11 board with a once-a-game mass 'Battle Move' of Pawns and Crabs. (11x11, Cells: 121) [All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-10-13 UTC
Note: in the graphical diagram of the opening setup, the black viceroy and squire on files i and j have been reversed from the other two descriptions on the page. By symmetry arguments, I assume the textual descriptions are correct?

Crab. Jumps as knight but only `narrow forwards' or `wide backwards'.[All Comments] [Add Comment or Rating]
Robert Shimmin wrote on 2002-10-10 UTC
Interesting side note: the crab, although able to visit every square on the
board, must change 'color' in a much more complicated way than the
fully-powered knight.  You can divide the squares of the board into six
sets in such a way that the crab must cycle through these sets as it
moves.  Just as the knight must change color with each move, the crab's
moves must go from squares of type 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 1...

This makes using the crab a rather tactical experience, since once moved,
it takes a total of six moves to get back to the square it started on.  In
practical terms, this means that if it ever relinquishes an attack on a
particular square, it is unlikely to ever be able to return to it.

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