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H. G. Muller wrote on Wed, May 7 08:55 PM UTC:

The Interactive Diagram's heuristic for estimating piece values is not really able to handle pieces that must change type on moving. It should be possible to fix that, though. On of my engines plays Kyoto Shogi, where pieces flip type on every move, and some pieces even get stuck after a finite number of moves. (The (Shogi) Knight / Gold General alternator must move up at least 1 rank in 2 moves.) I assigned piece values there based on 'future mobility': For each square the value was the sum of the number of squares a piece could go to, plus some factor times the value the piece would get if it would actually go there. This worked pretty well.

For the I.D. using the location-dependence of the number of moves might be a bit too advanced. (This was really only important for pieces that are doomed to get stuck because of the irreversibility of their move. For pieces that can move everywhere the value is usually not very location dependent.) But it derives the value now from the average number of moves a piece would have on a 25% filled board. It could weight those moves by a factor value(resulting piece)/value(initial piece) for moves that change the type. If the piece does not alter type this factor is 1, and we get the normal value. But moves that demote the piece would not fully count.

One would have to iterate this procedure to consistency, though, as the weights would change the values, which again would change the weights. E.g. an Amazon spperas to be worth as mucj as Queen plus Knight, say 9 + 3 = 12 to make the marth easy. But if the Amazon demores to a Knight on using a Knight move, the Knight moves should be weigthed with a factor 3/12 = 1/4, and such an enhanced Queen would be worth 9 + 3/4 = 9.75. But that would alter the weight to 3/9.75 = 0.3076, giving 9 + 0.3076*3 = 9.92. In the next iteration the weight would become 3/9.92 = 0.3024 and the value 9 + 0.3024*3 = 9.907. So it convergest fast, and a Queen in this game seems to be worth nearly one pawn more than a normal Queen.

The  Rook value would increase more, because the demotion is not that bad, and the moves that demote therefore more useful. The tricky thing is that there is synergy here: the value of RN is higher than the sum of the values of R and N, more like 9 rather than 8. Let's assume the synergy suffers the same penalty for demotion as the extra move, so that adding the N moves is worth 4.When these are demoting moves this should be multipled by 3/8, which gives value 5 + 3/8*4 = 6.5. In the 2nd iteration we get 5 + 3/6.5*4 = 6.846, then 5 + 3/6.846*4 = 6.753. So a gain of about 1.8 Pawn for a Rook in this game.


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