Games: Backgammon

Several readers have asked for some guidance on doubling, so let's remind ourselves of the basic theory. If Player A doubles Player B then B can drop and pay one point, or accept the double and play on with the doubling cube on his side of the board. B needs 25 per cent winning chances to accept the double. Consider four games: If B drops the double in all four he will be minus four on the scoresheet; if he accepts, and wins one but loses three, then he will still be minus four on the scoresheet (losing six points but winning two). Thus winning one game in four is good enough for B to break even. The position above is the only one known where White has exactly 25 per cent winning chances - Black wins with 27 rolls of the dice but loses with 9, and thus White can either take or drop a double from Black.

So doubling is easy, right? You wait until you are 75 per cent to win the game, and then double. Your opponent can either take or drop, and you won't mind which. Sadly, real life isn't like that. You may be 55 per cent to win one roll, and by the next time you are on roll you might be 85 per cent to win. You will then double and your opponent will drop, but you will not have doubled at the optimal 75 per cent figure.

The other big factor is that if your opponent accepts the double, he now owns the cube and has the right to play the game to the end. He can also redouble you if his position becomes strong enough. This last factor is very significant.

Backgammon can be likened to a game of rugby. At the start both sides have a 50 per cent chance. If one side reaches the opponent's 25-yard line he will win with the doubling cube. However, if he doubles and the opponent accepts, then the doubling side must now reach the try line to win the game whilst the opponent need only reach the doubler's 25-yard line before he in turn can win with a redouble. This rates clearly the high value of cube ownership.