Friday, February 8, 2013

A positional draw

It is theoretically possible for a lone bishop, in certain very rare situations, to draw against two rooks. The bishop must be pinning one of the rooks against the enemy king, the bishop must have at least one additional square available to it on the pinning diagonal, the defender's king must also be attacking the rook, and the attacker's other rook and king must be tied up defending the rook. The "free" rook must be placed in such a way that it cannot check the defending king or pin the defending bishop. See diagram below.

Problemists have long known of this type of drawing position. It is also mentioned in some practical books, for example Ludek Pachman's Attack and Defence in Modern Chess Tactics. In actual practice, it is an extremely rare bird. Mega Database 2013 has about 5.5 million games. The position after Black's 75th move is the only example of this positional draw.

I remember being amazed when I first encountered this idea almost 40 years ago, in a comment by Manfred Zitzman in Robertson Sillars' "Reader's Showcase" column in Chess Life & Review (the magazine known today as simply Chess Life). (As I recall, Zitzman and his opponent might have reached such a position in their game, but didn't actually do so. Zitzman proposed calling this type of situation "the Zitzman theme," until readers pointed out that problemists had conceived this idea long before.)

Despite White's huge material advantage, he cannot make progress. If he waits with Rb5/c5/d5/e5, Black does the same by shuffling his bishop from h7 to g6 and back again. White's only winning try is to give up his rook and try to win the resultant rook versus bishop ending (a book draw). Adams realized this and immediately gave up his rook, but it was still a draw.

Incidentally, this sort of positional draw is one of the few instances where we humans can feel superior to chess engines. If one shows this position to Houdini 3 (for example), it is utterly unimpressed. It gives White a +6.17 advantage - a trivial win! Asked how it proposes to win, it produces 76.Rc5 Bg6 77.Rd5 Bh7 78.Re5 Bg6 79.Rc5, and keeps going that way until it's on the brink of a three-time repetition. Then it finally gives up the rook and changes its evaluation to +0.32 (small advantage to White).

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