Author: Ricardo Gibert
Date: 09:52:53 10/21/00
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On October 21, 2000 at 05:28:14, Uri Blass wrote: >I composed this position to see if chessmaster can see perpetual check. > >[D]4k3/6RQ/6PP/8/r7/8/r7/7K b - - 0 1 > >The target is to see 0.00 score > >I found that chessmaster does not see the draw even after some minutes but after >Ra1+ Kg2 it can see the draw very quickly in clearly smaller depth. > >The same after Ra1+ Kh2 > >I tried also Fritz5.32 and it does not see the draw at least after a short time. > >If I give Fritz5.32 the moves Ra1+ Kg2 it can see the draw but after Ra1+ Kh2 >it has problems to see the draw. > >Fritz5.32 expects Kg2 when it plays Ra1+ and wants to play Kg2 at depth 13 with >evaluation 0.00. > >How many squares can the white king visit before the repetition?(it is clear >that the white king cannot visit all the 21 squares (b1-b3... h1-h3)) > >Uri By repetition, do you mean 2-fold repetion or 3-fold? For 3-fold, 29 moves. The bottleneck for white is he must visit the second rank on even numbered moves, but on odd numbered moves he can visit either the first or the third ranks. For example, the following line "saturates the visits" to the second rank after 28 moves: 1...Ra1+ 2.Kh2 R1a2+ 3.Kh3 R2a3+ 4.Kh2 Ra2+ 5.Kh1 Ra1+ 6.Kg2 R1a2+ 7.Kg3 R2a3+ 8.Kg2 Ra2+ 9.Kg1 Ra1+ 10.Kf2 R1a2+ 11.Kf3 R2a3+ 12.Kf2 Ra2+ 13.Kf1 Ra1+ 14.Ke2 R1a2+ 15.Ke3 R2a3+ 16.Ke2 Ra2+ 17.Ke1 Ra1+ 18.Kd2 R1a2+ 19.Kd3 R2a3+ 20.Kd2 Ra2+ 21.Kd1 Ra1+ 22.Kc2 R1a2+ 23.Kc3 R2a3+ 24.Kc2 Ra2+ 25.Kc1 Ra1+ 26.Kb2 R1a2+ 27.Kb3 R2a3+ 28.Kb2 Ra2+ 29.Kb1 Remember, Black moved first so that's only 28 moves for the King so far. White has visited all the squares of the 2nd rank twice already, fully saturating his visits there. Now after 29...Ra1+, he is forced to visit for a third time with 30.Kb2 or 30.Kc2, but neither is a 3-fold repetition, since b2 and c2 have each been inhabited by the King with a Rook at a3 *and* at a1. Note the move pairs "21...Ra1+ 22.Kc2", "23...R2a3+ 24.Kc2", "25...Ra1+ 26.Kb2" and "27...R2a3+ 28.Kb2" and this should be more clear. The 3-fold repetition does not occur until Black checks with 30...Rb2+ for 59 ply or 29 moves for the King. To prove at least a draw for Black, only 31 ply or 15 moves by the King is required. For example: Again the 2nd rank is the bottleneck, so: 1...Ra1+ 2.Kh2 R1a2+ 3.Kh3 R2a3+ 4.Kg2 Ra2+ 5.Kg1 Ra1+ 6.Kf2 R1a2+ 7.Kf3 R2a3+ 8.Ke2 Ra2+ 9.Ke1 Ra1+ 10.Kd2 R1a2+ 11.Kd3 R2a3+ 12.Kc2 Ra2+ 13.Kc1 Ra1+ 14.Kb2 R1a2+ 15.Kb3 R2a3+ and white has visited all the squares on the 2nd rank and must now repeat his visit. Now 16.Kc2 is a 2-fold repetition of position, but 16.Kb2 is not since the the Black Rook is on a3 rather than a1. The 2-fold repetion occurs after Black checks with 16...Ra2+ for 31 ply. I hope I got all this right. It's easy to get confused.
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