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Chess with Different Armies. Betza's classic variant where white and black play with different sets of pieces. (Recognized!)[All Comments] [Add Comment or Rating]
H. G. Muller wrote on Wed, May 29, 2019 06:39 AM UTC:

Well, this is the whole point of making KingSlayer play CwDA: its playing algorithm can take the effects of color binding into account. But it still requires some thought on what exactly it should pay attention to. The only things I discovered about color binding so far were obtained with Fairy-Max, which doesn't take any color binding into account. It thus might under-estimate the effects. E.g. it approximates the effect of the Bishop pair bonus by making all Bishops worth more than Knights. This biases it against trading B for N in general. Which helps to preserve the B pair, (as it should), but makes it unnecessarily shy in lone B vs N situations (which should be a self-inflicted disadvantage of having a Bishop), and it doesn't prevent it from breaking up the pair by Bishop trading in a BB vs BN situation.

But it still finds an effect of about half a Pawn. I.e. B tests about equal to N, also in 'anti-pairs' (on the same shade), but a true B-pair tests as 0.5 Pawn stronger than B+N or 2N. I also did tests with more than 2 Bishops, and concluded that with 3 Bishops (divided 2:1 over the shades) you get 1 pair bonus, and with 4 Bishops (2:2) you get 2, compared to the simple addition of lone-Bishop values. While one could argue that the number of pairs is 2 and 4, respectively, in those cases.

There is a completely different interpretation of this data, not in terms of a pair bonus, but of a binding penalty. With Kaufman values B=N=325, and the pair bonus=50, so 2B(2:0)=650, 2B(1:1)=700, 3B(2:1)=1025 and 4B(2:2)=1400. These same numbers would be obtained by setting B=350, and giving a penalty of 25 when they are not equally distributed over the shades. The remarkable thing is that the penalty doesn't seem any higher for a shade imbalance of 2 than for an imbalance of 1. So it doesn't seem to matter how much power you have on your strong shade (with non-color-bound pieces you could aim them all at the same shade anyway), but it hurts when you lack power on a shade. This would mean the magnitude of the bonus is not really dependent on the value of the color-bound piece, as it is mainly expressing the disadvantage of absence of a piece. Indeed a preliminary test with Pair-o-Max (a Fairy-Max derivative that takes pair effects into account in a primitive way) suggested that the bonus for Bede was also just 50. (Pitting 2 BD on like or unlike shade versus 2 BmW + Pawn.)

The situation in the Clobberers army should be pretty much like the 4B(2:2) case; after trading one BD or FAD you incur the penalty, which you lose again after you then trade BD or FAD on the opposite shade (making that effectively worth 50 less than the first), but which you would keep after trading the second of the same shade (effectively giving that the 'average' value). This is how KingSlayer treats it now.

But pair bonuses / binding penalties are relevant in the middle-game; in the late end-game you could be in a much graver danger than the penalty suggests, vulnerable to tactics that would destroy your mating potential. Like sacrifycing a Rook for the piece on the 'minority shade' in a 2:1 situation. (Similar to what makes KBNN-KR a draw in FIDE, while KBBN-KR is a general win.) But this weakness would only be fullly exploited if the defending engine would know about it; otherwise it would just randomly trade the Rook for a member of the pair that threatens checkmate, with a 50% probability that it leaves a 1:1 distribution, and will be checkmated later anyway. (Like that it should know in KBNN-KR that it should leave NN, and not BN.) Failing to fully exploit an advantage might lead to underestimation of the value of that advantage.