## Friday, January 01, 2010

### The twelve puzzles of Christmas

Walkewitz, 1976

White to play and win

Tom Chivers said...

Is it 1. Kc2 Ka1 2. h4 b5 3. h5 b4 4. g5 hxg5 5. h6 g4 6. h7 g3 7. h8=R, etc?

David said...

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.

David said...

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.

an ordinary chessplayer said...

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.

David said...

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.

Anonymous said...

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.

Anonymous said...

No, strike 7. Kd2. That's no more than a draw or even a loss!

Anonymous said...

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

an ordinary chessplayer said...

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.htm

Re 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.

ejh said...

Embarrassingly, I don't seem ever to have provided the source for this puzzle, and now I have no idea where I found it!

ejh said...

Ah, I have it. It's from Schach, 1976, and I found it in MÃ¼ller and Lamprecht, Secrets of Pawn Endings, Everyman, 2000, p. 262.

The solution is as identified by Fritz12 in James' posting.