I ran an experiment where White has F2/W2/W2F2 instead of Bishop/Rook/Queen and Black has FA/WD/FAWD in place of the same. Black wins 78.33% of the games (500 games total), but if I delete the f7 pawn it only wins ~54% of the games (still running), putting the Black advantage at ~6p for the combination (a bit more, because it also needs to overcome the tempo advantage; I should run the same thing with reverse colours and average that out). Extending to range 3 (F3/W3/W3F3 vs FAG/WDH/FAGWDH) is a bloodbath (which is perhaps not that surprising).hgm wrote: The Horse is an extra poor case, because one square can block two moves. In addition, it does not attack the squares where moves can be blocked.
I never did a systematic investigation of this, though. But my feeling is that a the difference between WA and WnA should be larger than between FA and FnA (= F2).
I was hoping that approximating sliders as compound Lame-Leapers would give some handle on slider value guestimates, but this result suggests that the difference between a Leaper and a Lame-Leaper is simply too large to be useful for this type of estimate.
I know that for Leapers you can make very reasonable estimates for (relative) piece values based on the number of forward/backward moves and the capture move (forward moves carry weight 2/3, other moves 1/3, similarly capture moves carry weight 2/3 and quiet moves 1/3), and this works incredibly well even for pinning down the value of a Pawn relative to a Ferz if promotion is unimportant, and I was hoping to generalise it. This doesn't seem to be the way to go though.
I may try fitting a general function of the form
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V = (B + ff F) + fc*(B' + ff' F')where B and F are the number of Backward and Forward moves (B' and F' are possible captures) and ff, fc and ff are to be determined (above, ff=fc=ff'=2).