09 January 2014

On the Edge with a Tablebase

In the past I've used Alan Lasser’s Game of the Week (GOTW) as a source of inspiration for this blog -- see, for example, Tablebase Monster for a post on a nontrivial Queen and Pawn endgame. A recent GOTW featured an unusual endgame of Rook vs. Pawns.

Endgame theory originated in the Rosendale Chess Club this week in a post-mortem analysis of a skittles game position. After the game ended in a draw we wondered what would have happened if White had pursued a different approach to that ending and I showed how Black could have sacrificed a Rook to obtain a position that appeared to be an obvious endgame win: White has the King on e6 and Rook on c7 while the Black King is on g8 with Black Pawns on e4, d4, and c3.

The position is shown in the following diagram. What do you think the correct outcome of the game will be?

White to move

Here's how Alan Lasser explained it.

After 1.Ke5 d3 2.Rc3 d2, the d-Pawn must queen. Basic Chess Endings says that, with no enemy King in front of them, three connected passed Pawns on the fifth rank will win; and here one of the Pawns is even further advanced than that. If you've studied endgames, you know these advanced Pawns are unstoppable; that's why instinctively I gave up my Rook without hesitation to obtain the menacing Pawns. Not so says the computer, in this particular position those magnificent Pawns can be held to a draw. How can such a mind-blowing thing happen?

A tablebase confirms the analysis, which I won't repeat here. The White King and Rook work together to threaten checkmating the Black King on the side of the board. Black is kept busy dodging mate threats and doesn't have time to promote the Pawns.

I conducted a small tablebase experiment to determine whether the position was unique. I moved the Black King around the side of the board -- a1, a2, ..., a8, b8, ..., h8, ..., h2, h1 -- stopping each time to note what the tablebase said for the particular position. For example, with the Black King on e8 (instead of g8, as in the diagram), White mates immediately. With the Black King on f8, White wins in 21 moves with Ke6-f6.

Of the 19 legal positions with the Black King on the a-file, eighth rank, or h-file, White wins seven times and nine positions are draws. That leaves three positions where Black wins, even with White on move: King on a1, b8, and h1.

There are several basic themes at work in the 19 different positions. A next step would be to identify the themes and perhaps catalog them, but there are only so many topics that can be tackled in a single blog post.

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