24 November 2009

Tablebase 1 - Roycroft ½

The diagrammed position is no.400 in A.J.Roycroft's 'Test Tube Chess' (1972), subtitled 'A Comprehensive Introduction to the Chess Endgame Study'. As the caption indicates, it is a 1960 endgame study by Roycroft himself. The solution given in his book is 1.b5 Nf3 2.b6 Ne5 3.b7+ Kd7 4.b8=N+ Kc8 5.Ka8 Bg1 6.Nc6 Nc4 7.Ne7+ and 'Draws; 7.Na7+ or 7.Ne5 also [draws]'.

Roycroft, Problem, 1960

White to play and ?

With the underpromotion on move four, resulting in Bishop and Knight vs. Knight, the study is very pretty, isn't it? Unfortunately, there's a small glitch. According to the trusty tablebase, the position after 7.Ne7+ is a win for Black in 94 moves. The moves 7.Na7+ and 7.Ne5 also lose in 50 and 58 moves respectively.

In fact, if we go back to the diagram, with best play it is a win for Black in 71 moves. Best play is 5...Nd3 instead of 5...Bg1, which is less than optimal by seven moves. Even after 5...Bg1 6.Nc6, the move 6...Nd3 is better than 6...Nc4, which is less than optimal by 22 moves.

It appears that Roycroft underestimated the danger of having the White King confined to the corner. It is not enough that the White Knight breaks free into the open board. The tablebase shows that, while the White King is under threat of checkmate, its Knight is eventually dominated by Black's minor pieces and left without moves. After that, the Black King strolls over and captures the hapless Knight, when the resulting position is an elementary mate with Bishop and Knight vs. bare King.

How sensitive is the defense to different positions of the White Knight? I didn't look at everything, of course, but after 7.Na7+ in Roycroft's solution, the main line is 7...Kc7 8.Nb5+ Kc6 9.Nc3. Although the White Knight is apparently out of danger on c3, Black wins it in less than 20 moves. Picking up the Knight from c3 and placing it on any other empty square also leads to eventual loss.

Roycroft's book has other examples of positions that have been completely solved by tablebases. Most of them were evaluated correctly, but like his own study, there are a few exceptions. I'll look at more of those in future posts.

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