Marc Bourzutschky did send this email with his explorations of the 8-men Tablebase, where he investigates positions with
each side having one opposing pawn.
An chess endgame tablebase is a database with all the (legal) positions with the outcome, calculated by a chesscomputer program.
At the end of this email, some endgamestudies are shown where new cooks have been found.
Also some new findings very long lines are included in this article.
An interesting contribution to endgame theory.
Look also at: Kirill Kryukov or NULP.
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In this note I briefly describe my first foray into 8-man tablebases with pawns, including a new record-depth position. To simplify matters, I focus on endings where each side has exactly one pawn, which is facing the opposite pawn on the same file. In this case, no promotion can occur without a preceding capture, so that only 7-man subgames need to be considered to fully solve the endgame. If the pawns are not opposite each other, there are 24 8-man subgames arising from promotions that would have to be resolved first.
While still relatively rare, such “opposing pawn” endgames do occur occasionally in practice, such as in the 16-th game of the 1990 Kasparov-Karpov world championship match:
8/5k2/R5p1/B7/3K2P1/3n4/2b5/8 b - - 0 63
The win is not straightforward, but White played fairly accurately to achieve it in under 40 moves. A common theme in these kind of endings between strong players seems to be that the stronger side does not find the win until repeated probing, often helped along by the defender eventually not playing the most challenging defense, probably due to fatigue.
Before turning to the new record position, a brief aside about different depth metrics. At first blush, distance-to-mate (DTM) seems like the most natural way to measure depth since after all the goal of chess is to checkmate the opponent’s king! One complication with DTM for measuring records is that in most positions it is possible to inflate the mate count by a preamble of captures or promotions. A case in point is the current 549 mate record position 1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - -, with material QP vs. RBN. White under-promotes to a knight after a mere 6 moves to reach an ending with material QN vs. RBN where the real complexity lies. The distance-to-conversion (DTC) metric resets the counter not only after a mate, but also whenever the material distribution changes through a capture or pawn promotion and thus avoids confusing the count with artificial preambles. For endgames with pawns, it is possible to also reset the counter after any pawn move, not just a promotion, because pawn moves are irreversible and so essentially start a new game. This is the distance-to-zeroing (DTZ) metric, which is also used for the counter when applying the 50-move rule. In general, we always have DTM >= DTC >= DTZ by definition. For positions without pawns, or only blocked pawns, evidently DTZ = DTC which is the case for the new record shown below. The more pieces are in a position, the more DTM will likely increase relatively to DTC or DTZ without conveying any new insights, so I will not pursue DTM further.
Without further ado, here is the new record position:
R7/8/8/8/7q/2K1B2p/7P/2Bk4 w - - 0 1
It takes at least 584 moves for White to achieve checkmate or transition to a won 7-man ending, as shown in the attached records.pgn. The previous record was 517 moves in the pawnless ending QN vs. RBN discovered by Yakov Konoval and me in 2006. To test the new record, Yakov modified his 7-man generator to handle the special case of 8-man endings with one pair of blocked pawns and obtained identical results to my 8-man generator.
The position is strikingly similar to the 7-man ending with pawns with the largest DTC of 389 moves:
7R/4q3/8/BK6/8/k6P/8/B7 w - - 0 1
In both positions, white has same-colored bishops and a rook pawn whose promotion square has the same color as the bishops, so that Black cannot save the game by moving the king to the promotion square and sacrificing the Queen for the Rook.
One side having same-colored bishops of course means nothing close to the record position will likely occur in practice. More interesting for practical play is the material distribution RBP vs. BNP with opposite-colored bishops, the same configuration as in the Kasparov-Karpov game above. The deepest such ending with blocked pawns is 449 moves, which I include in records.pgn along with a few other blocked pawn endings that require more than 200 moves. While the generator covers positions where the pawns are facing each other without being blocked, those depths are usually not that different.
I provide practical examples between two reasonably strong players with 369 moves:
Finally, I attach a few examples of refuted studies: