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Sac Chess. Game with 60 pieces. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]

H. G. Muller wrote on Fri, Dec 18, 2015 12:00 PM UTC:

> I'm still wondering about the value of an Amazon asserted to be only Q + N, in your opinion (besides that of other people). Well, it was not so much an opinion as an observation. The disclaimer is that I did not play-test the Amazon nearly as extensive as I did for the Capablanca pieces. The only test I did was replace Q by Z and delete one of the Knights in compensation from the FIDE setup, and play some 1000 games. To my surprise the score was very close to 50%; I had expected there to be some synergy. A possible explanation could be that the manoeuvrability at some point saturates when the piece gets too powerful. Because the set of squares that the piece can reach in a single move is already so large that what it can reach in two moves is mostly encompassed in it. The two-step N tours (N+N) are weighted into the value of the Knight, and the two-step Q tours in that of the Queen. The Amazon would have in addition two-step Q+N and N+Q tours. But it is doubtful whether this really adds much to what two-step Q+Q tours already do. (To show that quantitatively one would obviously have to make assumptions on a representative filling fraction of the board, as a Queen, or even a Rook on an empty board would already cover the entire board with its two-step tours. So simple arm-chair math won't cut it. But the play testing of course would exactly measure that.) > ... still ought to be measured from scratch by testplaying using Sac Chess games, if anyone is willing. You are absolutely right about that. Board size does have an effect, and in particular I found that diagonal sliders like B gain in value compared to orthogonal ones on wider board. The R-B difference decreases in going from FIDE to 10x8 Capablanca to Cylinder Chess. This because it gets more and more common that both forward moves attack the enemy position, rather than bumping into the board edge. The values I quoted were for a 10x8 board, though, which should be very similar to your 10x10 board with Pawns starting on 3rd rank. An extra rank behind the pieces were you virtually never can or want to go doesn't have much effect. But why don't you do it yourself? You seem to have a computer, as you post here (and I cannot imagine you would type such long messages from a phone...). So you could just download WinBoard and Sjaak II, set it to play Sac Chess, specify a list with materially imbalanced start positions featuring Amazons versus Queens+Knights or Chancellors+Bishops, let it run overnight and see what they did. > Whether just hundreds of games is a statistically satisfactory playtest sample size, I am not sure With a draw rate of 32% typically for orthodox Chess in these tests the statistical error in 100 games equals 40%/sqrt(100) = 4%. So I do at minimum 400 games, for an error of 2%. If a Pawn is worth 16% score advantage, that corresponds to 1/8 of a Pawn, and the 95% confidence interval of the result, which is 2 standard deviations, to 1/4 of a Pawn. Usually I play 400 games with many different opposing piece combinations each, though. The original determination of the piece values in Capablanca Chess for the benefit of optimizing the Joker80 engine was done with 20,000 games (but that was for all pieces together, not just Archbishop). And indeed I average over the first-move advantage. As to the strength of the computers, I found the obvious ways to vary that to have almost no effect, over a range of about 600 Elo. I should add that the programs play at a level where they would crush most humans, although probably not at GM level at these fast time controls. The score advantage to which a certain material advantage corresponds can vary with the level of play. But trying to convert an advantage of 100cP into a win, be it a plain Pawn or Q vs R+B, appparently requires approximately the same level of skill. So that the score excess drops similarly when you decrease the skill very much and play gets less accurate, meaning that in terms of Pawn values the result would still be the same. So your concerns are valid, but they can be (and have been) checked. Note that if it would be really true that the relation between material imbalance and score would be dependent on quality of play, it would imply that the piece values are not 'constants of nature', but would be different for players of different skill. It makes no sense to value a Bishop pair more than a Knight pair when your skill with Bishops is so poor that you would always lose with them against two Knights, but would be able to draw with two Knights against two Knights. Yet no one suggested this would be true for the values of the orthodox pieces. > Larry Kaufmam is an International Master as far as chess goes... I thought he was a GM, although it seems that he deserved this title by winning the U.S. Championship for players over age 60, so I don't know how much that is worth. But that is not really relevant. What matters in this case is only that he knows how to count. He obtained the piece value by identifying material imbalances in a database of GM games (reamining in effect long enough to exclude transient tactics), and determining the win rate in which these resulted. The only thing that matters is the strength of the GMs that actually played those games, not that of the person observing them and counting their number of wins... > In any event, I have not heard of any reasonably strong human chess players changing their strategies in regard to trading bishops for knights in over the board play, Well, perhaps this is one of the reasons why computers are about 1000 Elo stronger than humans. Note that Larry Kaufman was responsible for the evaluation function in both Rybka and Komodo, which were the strongest engines in existence at the time he was involved in them. Dutch soccer players also are firm believers that penalty kicks should be shot low in the corner, to avoid the chance that they would lift the ball over the goal. Statistics, however, shows that the chances that the goalkeeper will make a save there are several times larger, so that the overall scoring rate is far lower. Yet they keep aiming for the low corners. Needless to say that the Dutch national soccer team is virtually always knocked out when it comes to penalty shoot-outs... Old habits die hard, and people, even professionals with 7-digit salaries, are not always rational.