White to move. Is this a win or draw? How should white proceed?
Daily Chess Improvement: Must Know K & P Endgame!
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White to move. Is this a win or draw? How should white proceed?
White king needs to get to f5/f6. For example:
1 Ke3 Kf6 (Ke6 2. Ke4 etc) 2. Kd4 Ke6 3. Ke4 Kf6 4. Kd5 Kf7 5. Ke5 Kg7 (Kg6 6. Ke6) 6. Kf5 Kh6 7. Kf6 wins
Of course the key line is when Black tries to block this by Kd5-e5: after 1. Ke3 Kd5 2. Kd3 Ke5 it is a draw.
Then white has to push through 1. Ke3 Kd5 2. f4! gf 3. Kxf4 Ke6 4. Kg5 Kf7 5. Kh6 Kg8 6. Kg6 Kh8 7. Kf7
(or 6… Kf8 7. Kh7) and white pawn will march to promote. White wins.
White wins, anyway… 2-1 pawns, if done correctly, wins.
I think that there are over 20000 positions in which the side with only one pawn wins in a 2 vs. 1 pawn endgame so you should probably do some calculation and learn something about K and P endgames as well Luke.
There really is only one obvious move to be avoided here- Kg3 taking the diagonal opposition (of course there are other drawing moves like f4, Ke2, Kg2 etc). This is a very good problem because it helps one identify the exceptions to the opposition rules in a couple of clean instances here. So, lets discuss the drawing move of Kg3:
1. Kg3?
When you take the diagonal opposition, your plan is to take the direct opposition if the opposing king moves to the file/rank between the kings- otherwise the enemy king has to give ground both ways. However, when the oppositions occur across pawns, it is often the case that key squares are unavailable for either king either due to enemy attack or simple blockage by their own pawns. This is the case here. After 1.Kg3, black has two drawing options- Ke6 and Kf6:
1. …………..Kf6
The black king has given ground. For now, the f4 square is unavailable to white’s king. However, white now tries to free that square:
2. f4 gf4!
The only drawing move for black now. If he tries Kg6, white then plays 3.f5! to reach a winning ending- so 2. …gxf4 is forced:
3. Kf4
The obvious move taking the pawn and the opposition, but it doesn’t matter now. This arrangement of a king and pawn vs king is a draw in every possible place on the board when black is to move except for the cases where the white king and the pawn are on the sixth rank; and it is still a draw even then if the white pawn is on h6 or a6. Here is why, continuing from above:
3. ………….Kg6!
The only drawing move. White can’t take the direct opposition any longer- his own pawn is on the g4 square. White’s options are to push g5 or try Ke5/Ke4 to make progress:
4. Ke5 Kg5 (Kg7 also draws)
Black takes the simple opposition across the files and attacks the pawn forcing white to play…
5. Kf4 Kf6!
Black now takes the opposition, and this arrangement of the K+P vs K with white to move is a draw in every possible case. The draw is identical when white plays 4. Ke4, too. So, at move 4, this leaves the pawn push:
4. g5 Kf7 (every possible move is a draw here, I think, though black can still err later)
5. Kf5
Again, we get the arrangement as above where it doesn’t matter who is to move- it is drawn. All black really need do is to avoid this exact arrangement on his move on the next iteration up the board:
5. ………..Kg7
6. g6 Kg8!
The only move that draws now. White can’t move the pawn. If he plays Kf6, black will play Kf8 or Kh8 for a standard draw by either stalemate or loss of the pawn (will show it explicitly below). If he plays Kg5, black will play Kg6 taking the direct opposition across the enemy pawn- another position that is drawn no matter where it occurs in a K+P vs K ending with K+P to move. Continuing:
7. Kf6 Kf8 (taking the direct opposition)
8. g7 Kg8!
And white can either give up the pawn, or stalemate black by playing Kg6.