03 January 2012

Tablebase Monster

Endgame Tuesday, anyone? Endgames Without a King was my seventh consecutive Tuesday post about endgames (excluding one off-topic post which was too important to be ignored), and this post continues the series.

The following diagram is the conclusion of an interesting endgame with Rook and a-/b-Pawns vs. Rook and g-/h-Pawns (R+ab:R+gh) that a friend sent me for analysis. White had a slight advantage in the Pawn race, where several plausible variations resulted in positions like the diagram.

If you had to guess the outcome, you would probably say 'Draw!' In fact, the position is a mate in 92 moves for White.

White to move and ?

Just as I did in Simple Positions, Pretty Geometries, I like to shift the pieces around in tablebase positions to see what effect small differences have on the evaluation. For example, if you remove the Black Pawn, the position becomes a mate in 55.

If, instead, you shift the Black King to g7, it's mate in 93. On h7, it's mate in 82. On e7, d7, or c7, it's a draw. The diagrammed position is apparently smack dab on the edge of theory: if the White Pawn is on a5, or the Black Pawn on h4, it's also a draw. I didn't follow the tablebase analysis on any of these permutations, but I did follow the original mate in 92.

White first spends 30 moves reaching a position where the White and Black Pawns each advance one square. This requires the White King to defend its Pawn. Then White lets his King get checked across the board to capture the Black Pawn; that takes 10 moves. In this first phase, White can offer Queen swaps, because the resulting Pawn endgame is a win.

After winning the Pawn, White takes 20 moves getting checked back to a8, where Black runs out of checks. Finally, White forces a position with the King on c8, the Queen on c6, and the Black King on h7, where any further checks by the Black Queen allow a cross check forcing a Queen swap. Then it's easy.

As my friend commented in his newsletter (see Alan Lasser’s Game of the Week for some of his earlier issues), 'Over the board, those mates in 92 are hard to find!'

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