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Posted: Wed Nov 14, 2018 5:38 pm
A simple piece value calculation applied to FIDE chess and Musketeer chess variant pieces.
Piece Value Calculation ms doc format
Re: Piece value
Posted: Sun Nov 18, 2018 3:39 pm
Note that numerological approaches to piece-value prediction like this are infamous for their unreliability. The underlying 'theories' contain so many free parameters that it is always very easy to tune it such that you get it exactly right for the 4 orthodox pieces. But then it usually utterly fails for any unorthodox piece. Which goes of course unnoticed, because the values of these are not commonly known, so that the calculated values take on a life of their own, and spread as a dis-info wildfire over the web.
So my all-important caveat is: never believe anything you read about piece values unless they were derived from a huge body of empirical game results.
That being said, the method being presented here has some specific problems:
1) You only judge the pieces by their mobility in the center. This ignores that not all pieces suffer equally when being closer to an edge. This is the opposite problem from the calculations one usually sees, which tend to average the mobility over the entire board. This then ignores that in actual game play one would usually avoid to put pieces on squares where they have low mobility. The truth must ly somewhere in between, through some weighted average.
2) Apart from color binding the proposed method is purely additive; So the value of (say) a Chancellor will always be predicted as the sum of the value of Knight and Rook. While the empirical values are R=5, N=3.25 and C=9. The cooperative effect of 75 centi-Pawn is completely missed.
3) You mask this on the Queen by using color binding as a fudge factor to get the Bishop right after hugely overestimating its mobility contribution to get the Queen right. In practice color binding only hurts if you do not have the pair, and the magnitude of this is well known: a Bishop pair is worth 50cP more than two lone Bishops. So the penalty on a single Bishop is only 25cP compared to half the pair, about 6 times less than what you speculate here. A pair of non-color-bound enhanced Bishops, which have an extra backward non-capture move that allow them to switch color, is hardly worth more than a pair of normal Bishops, and the value increase is almost purely due to the extra move increasing its tactical abilities, as the value of a pair of Knights increases similarly when they get such an extra move (while there is no color binding to break in that case).
Good points of your theory are that the value of distant slider moves decreases in importance. (Although I am not sure that Knight jumps deserve to be similarly discounted, as unlike the slider moves, they cannot be blocked. But you solved that by making the d=1 and d=2 weights nearly the same, which probably leads to an overestimate of their contribution for sliders.) And that the number of directions in which you move is also important. For instance, the empirical value of a Nightrider is 5.25 (measured compared to Rook=5), while its mobility isn't all that high.