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Buypoint Chess. Buy your fighting force - each piece costs a number of points.[All Comments] [Add Comment or Rating]

H. G. Muller wrote on Tue, Feb 19, 2013 06:16 AM UTC:

Final result for the R2:

Replacing Knights by R2, and favoring the latter with Pawn odds (deleting the Pawn in front of the K-side Bishop, i.e. f2/f7 or g2/g7, as I shuffled the minors in the initial setup to force more variation in the games) still left a small advantage for the Knights:

2N vs 2 R2 + P: 51.75% (592+ 536- 472=)

Without the Pawn odds

2N vs 2 R2: 67% (865+ 319- 416=)

The statistical error in 1600 games is 40%/sqrt(1600) = 1% (1 SD). The difference between the two results gives the effect of a Pawn (~15%). So the advantage 2N vs 2 R2 + P translates to 11.7 cP +/- 6.7 cP.

With N = 325 and P = 100 this gives R2 = 269 +/- 3.3 cP.

I never did a direct measurement of Wazir. I did play 2 Ferz vs Knight once, and the result (a quarter Pawn) suggested F = 150 (or actually 2F = 300, as there will be a pair bonus involved). With the rule of thumb that forward moves contribute twice as much value as sideway or backward moves (determined by taking out the various moves of the FWADN piece), that would make the Wazir 2.5/3 times the Ferz, i.e. W = 125 as best guestimate for the Wazir. SO we have

W = R1 = 125
R2 = 269
R = 500

This result is a bit sensitive to the value used for the Pawn, however. There are many differennt Pawns (center, edge, backward, isolated, passers, protected passers, connected passers), and most strong Chess engines do use an opening value 80-90 for the Pawn. In the standard setup the f-Pawn is the most valuable, (deleting it has no compensation in terms of development, and leaves a bad unsafe spot for the King), though, and deleting the g-Pawn in the shuffled setups produces an isolated h-Pawn.

Too bad Fairy-Max does not have limited-range sliders in its repertoire. I can do the R2 only by virtue of defining the W moves and lame-D moves as separate 'directions'. It can handle at most two-step lameness, however, so I cannot use a similar trick for R3. Perhaps I should change the code to keep a range counter, set to a value extracted from the move-rights flags (I think I still have 3 unused bits in there), and let it count down with the slider steps, and abort when it reaches 0. (So that starting value 0 gives unlimited range.) Then I could also do CWDA's Rookies army, which features an R3.

[Edit] OK, I managed to do this. So R3 measurements are under way!
[Edit2] A pair of R3 seems to fall almost exactly between 2 Knights or two Knights + Pawn. That would make R3 ~ 375, about as much as your first Bishop of a pair.