In last week’s game, with more time and more ability I might have had to assess this king and pawn ending (with White to play) before choosing my move.
So what’s happening here? Let’s start by considering this position.
If Black has to move his king it’s clear he will lose. If it’s his move he will, if White is careful, run out of pawn moves first and White will win. But if it’s White’s move he can only draw because he’ll run out of pawn moves first.
So White’s aim is to reach this position with Black to move.
White needs to get his king in so, from the first diagram, obviously starts with 1. Kf3 Ke8 2. Kf4. After 2… Kd7 3. Ke5 White has achieved his aim, reaching the second diagram with Black to move. Now Black has a choice of pawn moves. We’ll look at each in turn.
After 3… g5 White can choose three pawn moves: one wins, one draws and one loses. The winning pawn move is 4. g4 h6 5. f3 and Black has to give way. If he prefers he can draw by playing 4. f4, for instance 4… gxf4 5. gxf4 h5 6. f5 exf5 7. Kxf5. Or he can choose to lose instead with 4. f3 h5 5. f4 h4 6. gxh4 gxh4 7. Ke4 Kxd6 8. Kf3 Kd5 9. Kg4 Ke4 10. Kxh4 Kxf4. Another way to draw is 4. Kf6 Kxd6 5. Kxg5 e5 6. Kh6 Kd5 7. Kxh7 Ke4 8. Kg6 Kf3 9. Kf5 Kxf2 10. g4 Kf3 11. g5 e4 12. g6 e3 13. g7 e2 14. g8Q e1Q
Returning to the second diagram Black might also play 3… h6. This time White has two winning pawn moves. 4. f4, which drew against g5, now wins. After 4… h5 5. Kf6 is now winning for White, while after 4… g5, 5. fxg5 hxg5 6. g4 forces Black to give way. 4. f3, which lost against 3… g5, also wins, meeting 4… h5 with 5. f4 and 4… g5 with 5. g4. But 4. g4, the only way to win against 3… g5, this time is only a draw after 4… h5. Another way for White to win is 4. Kf6, which was only a draw against 3… g5.
Back to the second diagram for the last time, and now Black plays 3… h5. It’s clear that 4. f4 wins at once. On the other hand, 4. g4 now loses after 4… h4 with a passed pawn (but 4… hxg4 only draws) and 4. f3 also loses after 4… g5 followed by 5… h4. 4. Kf6 this time is a win for White.
So to summarise from this position:
After 3… g5, g4 wins, f4 and Kf6 both draw, f3 loses.
After 3… h6, f3, f4 and Kf6 all win, g4 draws.
After 3… h5, f4 and Kf6 both win, f3 and g4 both lose.
So White can win with optimal play.
Back at the first diagram, then, after 1. Kf3 Ke8 2. Kf4 Black might want to consider alternatives. His best try is 2… g5. Now 3. Ke5 is met by h5, when Black’s passed h-pawn will distract White and enable him to draw. So White needs to play 3. g4 to prevent this.
We now need to consider another position.
If it’s White to move in this position it’s a draw with best play but Black has to get his timing right.
1. Kf6 Kxd6 2. Kxg5 Kd5 (Paradoxically, perhaps, 2… Ke5 loses because White gains an extra tempo: 3. f3 Kd4 4. Kh6 Ke3 5. Kxh7 Kxf3 6. g5 e5 7. g6 e4 8. g7 e3 9. g8=Q e2 10. Qg1 and White wins) 2. Kh6 Ke5 3. Kxh7 Kf4 4. f3 e5 5. Kh6 Kxf3 6. g5 e4 7. g6 e3 8. g7 e2 9. g8=Q e1=Q with a draw.
If it’s Black to move, though, White wins easily after 1… h6 2. f3 with Zugzwang.
Now consider what happens if White starts with 1. f3 h6.
This time it’s White who has to be careful if he wants to draw. Kf6 is now winning for Black so the only move is Ke4, to be able to take the opposition when Black takes on d6, after which he can make no progress.
2. Ke4 (2. Kd4 Kxd6 3. Ke4 Kc5 4. Ke5 Kc4 5. Kxe6 Kd3 6. Kf5 Ke3 7. Kg6 Kxf3 and Black wins) (2. Kf6 Kxd6 3. Kg6 Ke5 4. Kxh6 Kf4 5. Kh5 e5 and Black wins) 2… Kxd6 3. Kd4 e5+ 4. Ke4 Ke6 and Black, despite his extra pawn, only has a draw.
So, returning to our first diagram, after 1. Kf3 Ke8 2. Ke4 g5 3. g4 White’s primary aim is to reach the third diagram with Black to move while Black has to prevent this. So Black avoids 3… Kd7, instead playing Kd8, preparing to meet 4. Ke5 with Kd7. We now know that this is only a draw so White cannot achieve his primary aim but he still has a winning plan. His king has to take a journey to the queen side. He can win by playing Kc5 in reply to Kd7 (just as he can by playing Ke5 in reply to Kd7) or by playing Kc6 at some point. Black cannot prevent both these ideas.
White must continue 4. Kd4 (the only move to win) Kc8 5. Kc4 (again the only move to win: 5. Kc5 Kd7 is a draw) 5… Kb8 (or 5… Kd7 6. Kc5 and wins because it’s Black’s move) 6. Kb5 Kb7 7. Kc5 Kc8 8. Kc6 Kd8 9. d7 and wins.
Finally, we can conclude that the pawn ending is winning for White with best play (and that, returning to last week’s game, I could have won by selecting 38. Bd5). Chess is just too hard!