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Is it 1. Kc2 Ka1 2. h4 b5 3. h5 b4 4. g5 hxg5 5. h6 g4 6. h7 g3 7. h8=R, etc?
I had something similar, but a computer check - it's so hard to resist the temptation - suggests that 1. ... b6 is going to be a tough nut to crack.
Ah, of course the inability of some software to solve the problem after 1. Kc2 b6 is a very strong clue as to what the solution involves.
Tom: Why did you underpromote?David: I don't get the "clue". 1 Kc2 b6 2 h4 b5 3 g5 hxg5 4 hxg5 b4 5 g6 Ka1 6 g7 a2 7 Kd3 Kb2(b1) 8 g8=Q a1=Q 9 Qg7(g1)+ Ka2 10 Qxa1+ Kxa1 11 Kc4.Maybe you are thinking the computer can't find 3 h5!? b4 4 g5 hxg5 5 h6 g4 6 h7 g3 7 h8=B ... ? Makes no sense to me. A stalemate is a stalemate. Since the top four candidates for the computer are going to be (7)Q,R,B,N, it is going to look at all four.
an ordinary chessplayer: try 9. ... Kxb3! in your main line.Some software - including the world's strongest chess-playing program - doesn't bother to look at underpromotions (or at any rate, at underpromotion to a bishop). Presumably the calculation is that the number of games where it actually makes a difference is so close to zero that they'd prefer to be that little bit faster in all other cases.
AOC will improve his line by substituting 7. Kd2 for Kd3. I don't think we have yet got the full solution, despite both David and AOC's best efforts.
No, strike 7. Kd2. That's no more than a draw or even a loss!
David has a point. I've just put the position into Fritz 12 and Rybka 3. Fritz 12 finds the key move (7.h8=B) very quickly. However, Rybka 3 doesn't. Its top two moves are promoting to a queen and promoting to a rook, both of which result in stalemate. Interestingly, it does consider promoting to a knight, which it evaluates as about –30 for White. Under-promotion is a common theme in studies and problems. But Rybka 3 is programmed for over the board chess. Presumably it will consider under-promotion to a knight because this does happen from time in time, notably in rook and pawn endings. But have there been any games where a player has chosen to under-promote to a bishop? James
David: Thanks for pointing out ...Kxb3. I was thinking this was a crummy study, but now it's looking better.James: Bishop underpromotions have no doubt occurred, but *necessary* bishopings are a different matter. Here is Tim Krabbe's take: http://www.xs4all.nl/~timkr/chess2/minor.htmRe the "pruning" of bishop underpromotions: I have no trouble believing it makes for a higher rated engine. But it's not something I would have thought of.
Embarrassingly, I don't seem ever to have provided the source for this puzzle, and now I have no idea where I found it!
Ah, I have it. It's from Schach, 1976, and I found it in Müller and Lamprecht, Secrets of Pawn Endings, Everyman, 2000, p. 262.The solution is as identified by Fritz12 in James' posting.
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