Why fiddling works
The subtleties of an endgame position can be made visible with the aid of an endgame tablebase. I already experimented with this with my composition generator Gregoriev back in 2006.
Let me experiment with that again. I'm trying to draw the diagrams in SCID
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| White to move |
[FEN "5k2/8/8/8/1P6/8/8/3K4 w - - 0 1"]
The = area is a result of the rule of the square. If the black king is in the = area, then the white pawn is out of reach. The rule of the square is meant to avoid calculation and to replace it by visualization. What I'm looking for is to show areas, so that calculating is no longer a necessity, because you can see it.
The next step is to show the key squares.
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| White to move |
The key squares are the circles. When the white king is on the key squares, he can promote the pawn. No matter whether he has the opposition or not.
The reason for that, is that when the white king is on a key square, he has a reserve move. That reserve move is represented by the exclamation mark. The king can pass a move by moving the pawn.
I noticed that opposition and triangulation are just special cases of corresponding squares.
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| White to move |
In order for black to prevent white from making progress, he must step on the squares with the equal numbers as white. He can't do that in time. The next problem is shouldering. If white takes the wrong route, black can shoulder him away.
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| White to move |
White must take the grey route (wrong route in red).
I'm going to try whether it is possible to see the corresponding squares and the shouldering routes instead of calculating them.
The "rule" (heuristic) for getting to one of the key squares is to go to the one that is farther away from the lone king. The Réti “rule” is also applicable: take the diagonal route because it’s the same number of squares on the diagonal as on the vertical. It’s fairly simple to just count the squares along the path to the key square that is farther away from both kings rather than calculate (“I go here, you go there, etc.”). Arithmetic using small numbers is much error prone than calculation.
ReplyDeleteThe g and b pawns are an exception as to which side of the pawn the king must be on to win. Surprisingly, the king with the pawn must go to the edge of the board (instead of to the c or f file) in order to win. Not so surprising, the reason is simple: the lone king must be given an escape square when the pawn has been advanced to the 7th rank (without check). If the lone king is on the a or h file, then at the crucial step, it can take diagonal opposition and draw because of stalemate possibilities. If the lone king’s mobility becomes restricted (and being in the corner is certainly restrictive!), that is a warning sign to check for possible stalemate.
Just another of a seemingly infinite number of exceptions to the “rules.”
Correction:
ReplyDelete"Arithmetic using small numbers is much error prone than calculation."
should read:
"Arithmetic using small numbers is much LESS error prone than calculation.