Saturday, September 24, 2011

The Fastest Path vs The Best Path

I am doing two Chess Tempo endgame problems a day to help with two things. One is to get faster at exact endings, and the other is to achieve a deeper understanding of piece interaction in a simpler context.

The Chess Tempo endgame problems have two modes: theory and practice. In theory mode, you fail the problem if you do not follow the fastest path to mate defined by a tablebase. In practice you keep going as long as you pick a winning move, and the extra count against your score. I am using practice mode, because I do not think it is humanly possible to memorize tablebase fast paths, and I want to move quickly in the endgame. So I work on understanding processes and patterns, which I can apply to solve the problems.

Chess Tempo problem 66560 is a good example of this difference.
White to move and win
The key elements for how I decided to play, was that White's king is in the square of the a-pawn, and the White knight prevents the Black king from taking the h-pawn. So White can march his king over and take the a-pawn, and Black cannot protect it without leaving the square of the h-pawn. Then the White king marches back and with the knight forces the h-pawn to queen.

The fewest moves path is to recognize that White can force the h-pawn home without the need to take the a-pawn by the threat of this position:

To achieve this, the knight will need to blockade the a-pawn, and be able to get to f7 before black's new queen can enter the game. From a4 to f7 is four moves, a3 to f7 is three moves, so either would work for the mate. However, it is three knight moves to control a4 and two to control a3, and white needs one move of the king to secure the h-pawn. So the blockade takes place on a3. This is a good counting and visualization exercise.

I would play the clearer but longer(more moves) plan in a game.

Apologies: I could not get my normal PGN viewer to work, today. I could not figure out how to make the board larger on this one. Here is the PGN if you want to take it somewhere else.

[Event "Chess Tempo Endgame"]
[Site "?"]
[Date "2011.09.24"]
[Round "?"]
[White "Us"]
[Black "Problem-66560"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/p4k2/8/7P/3K2N1/8/8/8 w - - 0 1"]
[PlyCount "19"]

1. Ke5 {to secure the h-pawn, Ke4 and Ke3 both work} a5 2. Ne3 a4 3. Nc2 {The
knight catches the a-pawn} Kg7 4. Kf5 Kh6 5. Kg4 Kh7 6. Kg5 Kg7 7. Na3 Kh7 {
now the h-pawn advances and the end is nigh} 8. h6 Kh8 9. Kg6 Kg8 10. h7+ {and
Black must choose between being mated and letting the h-pawn queen.} 1-0

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