Thursday, January 17, 2008

Endgame Caveat #2 5x5-1

I've been playing Starcraft again. If chess is my wife, Starcraft must be an old mistress I look up from time to time.

One of the units, the Terran Dropship (highlighted in green), has a pilot who responds to commands with, "In the pipe, five by five." This brought me back to chess and Endgame Caveats.

The 5x5-1 rule is for the ending Queen against rook Pawn when the defending King threatens to draw by queening the pawn or stalemating itself in front of the pawn. The attacker can win if he has his King in the 5x5 region around the queening square, minus the corner in the center of the board, 5x5-1, AND he must have the move. Again, this differs from the Rule of the Square where a pursuing King gets into the square, but his opponent who has the fleeing pawn has the move.
In this diagram, even with the move, White can only draw because his King is in the minus one square.

The reason the shape of the region isn't a square is that it's really composed of the regions of two winning methods, both allowing the pawn to queen, then checkmate following soon after. If the king is closer to the d3 or d2 squares, then this mate is what he is after.

But if the king is closer to the b3 square, then this position is what he is after, with Black to move and be essentially helpless to stop checkmate.

So if you start with this position,
the moves are 1.Kd3 a1Q 2.Qc2#.

But a friend had pointed out that White can win in this position.

The trick is that White blocks his own queen for a move, eliminating the stalemate threat for a move while the king runs inside the 5x5 square. 1.Kb6 Kb1 2.Ka5+ Ka1 3.Qh2 Kb1 4.Kb4 a1Q 5.Kb3 Qa4+ (spite!) 6.Kxa4 Kc1 7.Kb3 Kd1 8.Qf2 Kc1 9.Qc2#

In Basic Chess Endings, there is a diagram which looks like the 5x5-1 rule plus the six additional squares a7, b7, c7, a6, b6, and c6 from where the king can block the queen's laser beam for a move. I forget if it was Muller's Fundamental Chess Endings or Dvoretsky's Endgame Manual which shows the 5x5-1 region. Here I've color coded the squares, yellow for the method where White checkmates with Qc2, green for the method where White plays Kb3 while Black is helpless, and red where White can choose either plan.
The above position is my failed attempt to compose my own study involving the "block stalemate" idea. It's supposed to be solved by 1.Qb8 (1.Qb7 is already a cook of the study.) 1...Nb6 2.Nxb6 cxb6 3.Kxb6 Kb1 4.Ka5+ with play just like above. However, another cook is simply 1.Qc2 Nb6 2.Qc1 mate.

If the attacking King is in the vicinity of a7, c7, a6, or c6, the attacking queen can try to maneuver backward to b8 in order to give him passage to a5, but the defender should recognize this, and follow Qb8+ with Kc1 instead of Ka1, threatening to promote the pawn while the queen is far away.

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