Sunday, January 13, 2008

Endgame Caveat #1 4x5-2

The subject of endgame rules has come up the last two weeks. Some rule or other was invoked as the shortcut to analyzing a position. The shortcuts are helpful in allowing one to get way deep in the plies of analysis, but the rules are a little hazardous to use. Sometimes, when misapplied, they create the exact wrong evaluation. Several rules came to mind that I wasn't too clear on, so I decided to launch another endgame series about basic endgame rules that have caveats. To the potential user of such rules, Caveat emptor!

One of the games in Class D finished with the following position.

The game continued 1...Qg4+ 2.Kf8 Qc8+ 3.Kg7 Qxh8+?? (3...Qa1+ 4.Kh6 Qcxh8+ 5.Kg5 Qag7 mate.) 4.Kxh8

Neither side realized that Black has just gift-wrapped a book draw for White. I don't have the rest of the game score, but apparently White didn't realize how to draw the bishop pawn versus queen ending and ended up getting his king trapped at f8 with mate following soon after that.

Trying to generalize about the drawn nature of the ending was difficult because we had a little knowledge, but not all of it.

Some key ideas include the following:
-If Black's Queen takes the f7 pawn while the White King is at h8, it's a stalemate draw.
-If Black's King can get to d7 to help the Black Queen cover the queening square, Black wins.
-If Black's King can get to g6 to help the Black Queen deliver mate at h7, Black wins.

The ideas are summarized as a region drawn in endgame books as a rectangle encompassing the 4x5 rectangle d8-h8-d5-h5 minus d5 and e5, or in shorthand, 4x5-2.

The problem with applying this 4x5-2 rule is that the attacking side, Black in this case, is supposed have his king in the region AND have the move. This is different from the Rule of the Square that we all learn early in our chess careers where the king defending against the queening of a pawn gets into the square region bounded by the pawn and its queening square. But once the king gets in, he's supposedly safe, but it's his opponent's turn. For the 4x5-2 rule, you need the king inside AND the move.

In analyzing this with another player, we discovered that White must not be lackadaisical in his defense. He must whenever possible, go to the a8 square. From the above diagram, the following line turned a draw into a loss.

4...Ke5 5.Kg8 Qg2+ 6.Kh8 Qh3+ 7.Kg8 Qe6
8.Kh8 Qc8+ 9.Kg7! (9.Kh7?? Qf8 -+) 9...Qd7

10.Kg8?? Kf6 11.f8Q+ Kg6 with White being helpless to prevent Qh7 mate. The Black Queen on d7 prevents the White Queen from having any safe checks. Since the ending position has the queen on d7 and the king on g6, Black needs to allow the promotion to a queen to deliver check to his own king. If he arrives at g6 one move before promotion, an underpromition to a knight will fork the King and Queen and draw.

10.Kh8! holds the draw since 10...f8Q+ 11.Kg6 Qg8+! 10.Kh6 Qe6+ (or 10...Qf8+ perpetual) 11.Qxe6 stalemate.

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