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H. G. Muller wrote on 2012-09-21 UTC
Results of tonights run (2 x 280 games, for a statistical error of ~2.5%):

2 N - P vs 2 AD: 62.5%
2 AD vs N + P: 55%

Both results suggest that Alibaba + Pawn is worth just slightly more than a Knight. I expect little systematic error in this, because I compare Alibabas directly to Knights, which are very similar pieces. (Neither of them has mating potential, alone or in pairs.)

Note there is a general effect that drives the value of nearly equal pieces (or to a lesser extent piece combinations) on opposing sides towards each other: A more valuable piece loses value through the presence of weaker opponent pieces, because it cannot go on squares covered by such a weaker piee even if protected. By this effect, if the difference is only small, the loss of value by treating it as stronger (i.e. avoiding trades) could reverse the difference. In this case better use of the stronger piece is made by treating it as exactly equal. Then you cannot avoid it will be traded for the weaker piece, but constantly having to protect it from attacks by the weaker piece would lose you even more. This effect is largely responsible for the fact that it is so very hard to say whether a Knight is better or worse than a lon Bishop in orthodox Chess.

I think the Alibaba case is similar, although not as outspoken: its intrinsic value is just a bit better than N minus P. But avoiding AD + P vs N trades (by not daring to go on squares protected by P that are twice attacked) loses you more of the value than no yielding to such an attack whe the opponent tries to chase away the Alibaba. The value loss is not as bad as having to avoid 1-on-1 trades, but squares protected by Pawns and nothing else are very common, and just the sort of 'outposts' where you would like to put your Alibabas in the middle game to have any use of them at all. So when the opponents has Knights on an 8x8 board, the Alibaba should probably be treated as if it is exactly one Pawn below a Knight (or lone Bishop).

Color-binding of the AD is of course very bad, and manifests itself in the end-game as that the reduction for 'unlike Bishops' now should even be applied in end-games of Alibaba versus a color-alternator like Knight (in presence of Pawns). In KBPPKN the two Pawns are usually enough to secure the win, because to stop a Pawn from crossing a square where the Bishop has no clout, the Knight has to stand on the color where it can be attacked by the Bishop (or, when blocking the Pawn, has to move because if zugzwang). So you cannot set up a defense purely on the color the Bishop cannot reach. But you ofen can set up a defense on a color the Alibaba cannot reach, even with a Knight, as the Knight keeps jumping between two 'meta-colors' unreachable by the Alibaba.

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