Independent Pursuits: Chess

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TODAY, A very difficult position of limited practical value, but with enormous potential to baffle and amaze: The "Three Pawns Problem" or "Szen Position".

The Szen Position

Examined by Carrera as early as 1617, this endgame is so complex that I know of people who've made a substantial amount of money by betting on and proving their ability to win with either colour!

It was finally solved by the Hungarian Joszef Szen in 1836, and is almost impossible to comprehend in terms of variations, but becomes surprisingly tractable if viewed in terms of key positions.

White's ideal queenside formation

The white king and black pawns cancel each other out, since the pawns can't move without being captured, but equally if the king is to move, then the pawns will force their way through.

But White wins, with or without the move, owing to his ideal formation on the queenside:

With White to play:

1 b4 Kc7

or alternatively 1 ...Kb7 2 c5 Kb8 3 b5 Kb7 4 b6

2 a6 Kb6 3 b5 Ka7 4 c5

With Black to play:

a) 1 ...Kc5 2 b4+ Kc6 3 a6!

b) 1 ...Kb7 2 c5 Kb8 3 b3! Kb7 4 b4 Kb8 5 b5;

c) 1 ...Kc7 2 c5 Kb7 3 b4! Kb8 4 b5

In the Szen position itself, both sides strive to set up this ideal pawn formation on a5, b2, c4 or, for Black, h4, g7, f5.

If both succeed then it will be a draw, since they will both be forced to move their kings up and down. But White crosses his opponent's intention by first bringing his king in front of the enemy pawns, and Black must do likewise. The main line goes:

1 Ke2! h5 2 Kf3 f5 3 Kg3! Kd7.

3 ...g5 4 a4 Kd7 5 a5 would lead to the key position above.

4 a4 Kc6 5 c4 Kb6 6 b4 g5 7 a5+ Ka7 8 c5 h4+ 9 Kh2.

Now Black can stop the pawns - but he will have to commit his king before White's:

a) 9 ...Kb8 10 b5 f4 11 Kg2! This is mutual zugzwang - whoever moves loses, eg: 11 ...g4 12 Kg1 f3 13 Kf2 h3 14 Kg3 Kb7 15 b6, etc.

b) 9 ...Kb7 10 b5 f4 11 Kg1! wins.

c) Or he can race. 9 ...f4 10 c6 f3 11 b5 g4 12 c7 Kb7 13 b6 f2 14 Kg2 g3 15 a6+ and wins.