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The Chess Variant Pages



This page is written by the game's inventor, Ralph Betza.

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H. G. Muller wrote on 2013-03-07 UTC
To make absolutely sure I have a good calibration of the Pawn-odds score, which is the yard stick I measure all piece-value differences against, I did a 2N vs R+P match. (I had never done that before with the mating-potential-aware Pair-o-Max.) This ended in favor of the Knights with 64% score, which is an advantage of 0.93 times the Pawn-odds score (which is ~15%). The difference R-N has been implicitly measured in 2 steps, the N+N+P vs R4+R4 difference and the R4+P vs R difference. I quoted 20cP and 0cP for these earlier, but I should really have said these were 0.2 and 0 times Pawn-odds. From the latter it follows R4 = N + 0.6, and R = R4 + 1, so that R = N + 1.6. While now we have 2N = R + 1.93.

Some algebra then shows 2N = N + 1.6 + 1.93, or N = 3.53 times Pawn odds. With the Kaufman value N = 325 cP, this gives

Pawn odds = 92 cP (= 15% score advantage)

This agrees excellently with the conclusions drawn from 2W vs N, but are a bit more reliable. R = N + 1.6 = 3.52 + 1.6 = 5.12 x Pawn odds, or 472 cP. That is 28 cP below the classical value, but it is for a Rook trapped behind Pawns. Recalibrated, R4 becomes R - 92cP = 380 cP.

The measurements of R2, R3 and R4 have become a bit ambiguous, as these pieces should also suffer from the quarter-Pawn penalty behind Pawns. But in some of the starting positions they were combined with Pawn odds, and although they never started on the open file caused by the Pawn removal, one of them was nevertheless very close to it. So in those cases one of the two Rn might have suffered appreciably less penalty.

So I really should redo these measurements under better controlled conditions. I am a bit dissatisfied with how long they take, though. I am currently playing 40 moves/min games. Perhaps I should switch to 40 moves/10 sec games. I am not sure that Fairy-Max is strong enough to deliver sufficient game quality at those speeds, though. Perhaps I should make its search a bit less minimalstic, using real move sorting, so that it can use killer heuristic and all these other nice techniques to reduce branching factor...

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