31 January 2014

Square of the Pawn

A correspondence game that finished yesterday offered a few positions that illustrate well the square of the pawn, an important elementary pawn ending concept. I have previously discussed this concept in "Simple to Complex" (June 2012).

Yesterday's finish ended a game full of gross errors. In the beginning I overestimated my attack and let my opponent gain a rook. My attack ran aground and I was hopelessly lost. My faint hope of some counterplay was underestimated by my opponent and suddenly I seemed to have compensation for the rook. After mostly finding a series of strong moves, I exchanged into a queen and pawn ending where I had more pawns.

I captured the wrong enemy pawn and gave up a few of my own. We reached the position in the first diagram.

White to move
After 63...Kg7
With four pawns to three, I would like the queens off the board. However, forcing the exchange would be an error here as my king is too far away to stop Black's h-pawn.

Chess By Post, the app on which this game was played, offers an analysis board that lets players work out whether the king could stop the pawn. Of course, counting is easy enough even without such assistance. But even counting is unnecessary.

Rather, I imagined the exchange of queens on b2, thrust the h-pawn forward, and in my mind drew a diagonal arrow forward from the pawn to the first rank. From that arrow, two more arrows complete a triangle.

White to move
Hypothetical Position
My king is not able to step into any square of the triangle. This triangle comprises half of the square of the pawn--the space that the defending king must be able to occupy in order to stop the pawn. The diagonal arrow, resulting triangle, and derived square (two triangles) allow a player to quickly perceive by geometric observation, rather than calculation, whether a pawn may be stopped.

I played 64.Qc2 and the game continued.


Black could have played 64...h5 with a likely continuation 65.Qe2 h4 66.Qg2 h3! 67.Qxh3 Qd3+ and Black forces a draw by repetition.

65.Qd3 Qc7??

White to move
After 65...Qc7??
Now I am able to force an exchange of queens with my king one square closer to the h-file.

66.Qc3+ Qxc3 67.Kxc3 Kf6

Black could try 67...h5, but my king will enter the square.

White to move
Hypothetical Position
White's king is able to step into the triangle. The pawn may still promote on h1, but the White king will stand on g2 when it does. At that point, White's queenside majority assures the win (see "Fox in the Chicken Coop" [July 2013]).

My opponent opted for a different course.

67...Kf6 68.Kd4 h5

My king is already in the square.

69.b5 h4

White to move
After 69...h4

My king was forced to step into the square.

70...g5 71.a4 Ke6 72.a5 Kd6


White to move
After 72...Kd6
White has several ways to win, but I like the manner than I chose.

73.e5! Kxe5

Black might have tried 73...Kc7, leading to 74.e6 Kd6 75.b6 axb6 76.axb6

Black to move
Hypothetical Position
In this hypothetical position, Black's king is in the square of both pawns until each advances another square. Capturing the e-pawn removes the defending king from the square of the b-pawn. This floating square is a win for White.

74.b6 axb6

White to move

75.a6! 1-0

75.axb6?? loses because the Black king stops all White's threats. He enters the square of White's passed pawn with 75...Kd6.

Black resigned.

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