The Problem Corner #3
This week's position is an old standby for experienced players. One of the three hundred or so endgame positions in every master's toolbox. White to move wins; Black to move and it's a draw. Have at it!

White to move and win; Black to move and draw.
The Solution:
White to play and win: Symmetrical pawn structures tend to be drawish, but this position is a well-known exception. 1. b6! cxb6 2. a6! bxa6 3. c6 and the pawn cannot be stopped. No better is 1. ... axb6 2. c6! bxc6 3. a6.
Black to play and draw: The idea here, as given in Basic Chess Endings (#117, revised edition), is that Black can prevent White's break: 1. ... b6 (not 1. ... a6? 2. c6! or 1. ... c6 2. a6! and White wins) 2. cxb6 cxb6 3. axb6 axb6 4. Kf3 Kf5 5. Ke3 Ke5 6. Kd3 Kd5 7. Kc3 Kc5 (diagram).

This is a key position. Obviously, the White pawn on b5 is toast, but the question remains whether or not Black can win with his lone pawn.
Let us review the main rule for K+P vs. K. To win, the Black king (in this case) must be in front of the pawn and have the opposition. So if 8. Kb3? Kxb5, Black has the opposition and wins, e.g. 9. Kc3 Ka4 10. Kb2 Kb4 11. Kc2 Ka3 12. Kc3 b5 13. Kc2 b4 14. Kb1 Kb3 15. Kc1 Ka2 16. Kc2 b3+ and the pawn queens.
But White can force a draw by 8. Kb2! Kxb5 9. Kb3 (now White has the opposition) 9. ... Kc5 10. Kc3 b5 11. Kb3 b4 12. Kb2 Kc4 13. Kc2 b3+ 14. Kb2 Kb4 15. Kb1! (the only move -- White must take the opposition when the Black king reaches the third rank) 15. ... Kc3 16. Kc1 b2+ 17. Kb1 Kb3 stalemate. Black cannot make any progress by (continuing from the above diagram) 8. Kb2! Kb4 9. Kc2 Kc4 10. Kb2 Kd4 11. Kb3 Kc5 12. Kc3.
So, the position is a draw after 1. ... b6. The problem with this analysis is that the original position is cooked. In fact, Black wins after 1. ... Kf5! Now 2. b6 cxb6! 3. axb6 (3. a6 bxa6 4. c6 Ke6 and the Black king is within the square) 3. ... axb6! 4. cxb6 Ke4 5. Kf2 Kd4 6. Ke2 Kc5 7. Kd3 Kxb6 8. Kc4 Ka5 9. Kb3 Kb5 and Black has the opposition and wins.
Another line is 1. ... Kf5! 2. Kf3 Ke5! 3. Ke3 Kd5! 4. c6 bxc6 5. bxc6 Kxc6 6. Kd4 Kb5 7. Kd5 c5 8. a6 c4 9. Kd4 Kb4 and the pawn cannot be stopped.
In conclusion: White to move wins by 1. b6! Black to move draws by the thematic 1. ... b6 but can win by 1. ... Kf5! And Basic Chess Endings, even the new revised edition, has errors in it. Now, how can the original diagram be fixed so that it is "White to move and win, Black to move and draw"?



Comments
White wins with:b6 axb6 c6 bxc6 a6 Kf5 a7 Ke5 a8Q
Black draws with:Kf5 c6 bxc6 Ke5 Kf2 Kd5 Ke3 Kxc6
Posted by: John Ellison | April 17, 2010 7:40 AM
White to move and win is:
1.b6
If axb6 then c6 bxc6 a6.
If cxb6 then a6 bxa6 c6.
Black to move and draw is:
b6, axb6 then axb6, cxb6 then cxb6, if kf3 kf5.
Posted by: Matthew | April 16, 2010 8:56 PM