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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 2013-03-06 UTC
Unfortunately I never made webpages for this. I did post occasionally results here.

I have now tried to measure a Wazir directly against a Pawn. This was kind of interesting. An obvious way of doing it would be to replace the f- or g-Pawn (the one in front of the Bishop in the shuffled setup) by a Wazir. My Chess intuition immediately revolted against this, however: such a position has none of the characteristics of traditional Pawn odds, which I used to compare other material imbalances against. The Wazir nicely fills the hole that otherwise would be such a liability.

When I was doing Wazirs vs Knight one Wazir was replacing the Q-side Knight, and the other put just in front of it, moving up the b- or c-Pawn one step. To better compare with that, I took a position that did put a Wazir in front of the Q-side Knight, as an extra piece, and deleted the f- or g-Pawn in compensation as Pawn odds.

In fact, the two positions are somewhat reminiscent to comparing the value of an extra Pawn to that of Pawn odds. If I 'replace' the f-Pawn by a Pawn, I of course get an exact wash, as I did not change anything. But if I do it by deleting the f-Pawn, and adding an extra Pawn on c3, I do faithfully create the Pawn-odds motif. Of course any Chess player would know this position is much worse than the usual initial position. Doubled Pawns are worth less than two normal Pawns.

I tried both W vs P positions, and indeed the measurements give significantly different values. A Q-side Wazir and K-side a Pawn hole only show a 50.9% score in favor of the Wazir, hardly significant (1-SD error = 1%), and only 6 cP when taken at face value. But when a K-side Pawn is replaced by a Wazir, the score increases to 55.3% percent in favor of the Wazir (33 cP). That is significantly more (4 SD)! So a Wazir behaves a bit like a Pawn. Put on an open file to replace a Pawn it is worth about 27 cP more than when trapped behind another Pawn. Much like a doubled Pawn. 

Unlike a Pawn a Wazir can move sideways, but it takes so many moves to get from the Q-side to the K-side that this will be too expensive in itself. Unlike with doubled Pawns, there now the situation Wazir behind Pawn or Pawn behind Wazir are no longer equivalent. I expect Wazir in front of Pawns to be better, but did not measure from such positions. This is related to the earlier remark that Rook-like pieces are difficult to develop when they start behind Pawns. Remarkable enough the 27cP difference I measure between open-file Wazir and behind-Pawn-wall Wazir is almost exactly the deficit I usually measure in the Rook value with my method (475cP in stead of 500cP).

Anyway,when I use W = 1.06 x Pawn odds, the 2W vs Knight with Pawn-odds result (40cP in favor of the Knight) would say 3.12 x Pawn odds + 40cP = 325cP (=N), from which follows that Pawn odds = 91cP. So this particular Pawn in the early opening seems worth somewhat less than the abstraction of the 'average Pawn' (which probably corresponds to a well-centered Pawn in the mid-game). That puts the Wazir (behind Pawns) at 1.06 x 91cP = 97cP (where N=325cP). A developed Wazir, (on open file) would be 1.33 x 91cP = 121cP. Compare that to an old result where I played 2 Ferzes against Knight in the same setup (replacing Q-side N by F, and putting the second right in front of it, moving up the Pawn). There the pair proved worth ~300cP, i.e. 150 each average. (Undoubtedly a lone Ferz will be worth slightly less, and the second slightly more, due to its color binding.) Of course the Ferz does not suffer from being behind a Pawn wall; it sneaks out between them.