Shartranj!

[hgm]

I posted a summary of my Shatranj tablebase effort on the CCRL tablebase forum. Basically, the conclusion is that of the 4-men (2+2 of course, due to the baring rule all others are won) only KRKF and KRKE are generally won. KRKN is draw, and practically identical to its normal Chess counterpart. (Give or take a few stalemates.)

Of the 5-men 3+2 end-games KFFKF, KFFKE are won with both like and unlike Ferzes, provided the opponent piece is not on a color where we cannot get. KFEKF is a boundary case. KNFKF is won . (No surprise, as KFFKF is already won, and N is strnger than F.)

To subdue a Knight is more difficult: KNNKN is a win, but KNFKN is a draw. A Rook is nmore difficult still: KRRKR is won, KRNKR is draw. So in general, you need duble of what the opponent has as last piece.

A Rook alone can not subdue a Knight, but with the help of anything else it can: both KRFKN and KREKN are won. Not so much because the extra piece helps in the chase (an Elephant is hardly able to threaten a Knight), but because it means that sacrificing the Rook for the Knight now is a win.

The only 5-men 2+3 that are won are KRKFE, and presumably KRKEE (I did not try that one). KRKFF is already draw, (both like and unlike Ferzes), unless one of the Ferzes is cut off from the rest and can be hunted down by the King. (This is a fairly big risk for any Ferz in an end-game, if there isn't a friendly Rook that can protect if from a distance.)

[hgm]

I have completed all test matches between a complete opening, one lacking a Ferz, one lacking two Pawns (c+f) and one lacking the two Elephants, all in matches of ~100-180 games (eliminating the advantage of the lead move, by letting both sides start equally often).

The advantage of the full opening array against the various type of odds was:

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P   56%
PP  64%
EE  69%
F   67.5%

The difference is all well within the statistical error (for P when compared to half the score of the others). Against each other:

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EE-F  50.7%
EE-PP 51.5%
F-PP  50.5%

When taking at face value (ignoring the ~2.5% standard error in these results), the 1.5% excess score of EE over PP would translate to ~1/4 Pawn, making the E-P difference about 1/8 Pawn.

I now restarted BB-PP and BB-F matches at 40/2' (twice longer TC), where I set the piece values programmed into the engine according to the preliminary results given above:

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R=500
N=325
F=160 (was 150)
E=85  (was 70)
P=75  (was 50)

Perhaps I should rescale all those values to be more in accordance with the (fixed) promotion bonus of 96 in ShaMax. It might be detrimental to the Pawn value that with the current settings Shamax is too prone to sac a Pawn to speed up the promotion of another one, when it is not yet within its horizon that it could keep the Pawn and promote as well. Suppressing this effect might increase the Pawn value even without scaling. It is important that the promotion bonus (which strictly speaking should be the difference between the value of a Ferz and that of a 7th-rank passer) is less than the value of a Pawn, in order to avoid such sacrifices. So with R=700, N=450, F=225, E=120, P=105 it might make better use of its Pawns.