Backgammon: On the double

ACCORDING to a recent survey, there are 750,000 people in Britain who play at least one game of backgammon a month, and 17 per cent of British households have a backgammon board, writes Chris Bray. If you were to ask these players whether they use the doubling cube, 99 per cent would say that either they didn't understand it, or they didn't bother to use the funny little cube with the strange numbers on it. Yet the doubling cube is at the very heart of the game.

Until the 1920s, backgammon was just another dice and checker game, albeit a complex and challenging one. There were, however, a number of problems with it. Firstly, some games dragged on interminably and secondly, for those wishing to gamble there was little chance to do so. A long session could result in a very small gain or loss, especially as all games were played to completion and could take up to half an hour. Then an unknown genius invented doubling.

The concept of doubling is straightforward. Player A says to Player B: 'I think I have an advantage, therefore I wish to double the stake'. Player B then has two options: he can decline the double, pay Player A the original stake (say pounds 1) and start a new game, or he can accept the double and play on with the stake now at pounds 2. Player B now 'owns' the doubling cube, and if the game subsequently turns around and he gains the advantage, he may now offer a redouble to Player A, increasing the stake to pounds 4. Player A would have the same two options of paying Player B pounds 2 or continuing the game with the stake at pounds 4.

The initial reaction of most players when they first come across doubling is to think that if their opponent has an advantage, then obviously they should decline the double and start a new game. However, the basic mathematics of doubling disprove this theory.

Consider this - in four games if you are doubled and decline the double in all four, then your score will be minus four. If you accept the double and lose three games but win one, your score will still be minus four (losing six points in the three games you lose, but winning two points in the one game you win). Therefore winning one game in four at doubled stakes is the same as losing all four at the original stake. In other words, you need 25 per cent winning chances in order to accept a double.

What the invention of the doubling cube did was to solve at a stroke both of the problems mentioned earlier. In games where one player had an overwhelming advantage, the game would end quickly with the offer of a double, and for those wishing to gamble, the sky was now the limit. In a professional game it is rare for the doubling cube to rise above 4. In my playing career I have seen a couple of cubes on 128 - not a situation for the faint-hearted or impecunious.

Lest anyone think that backgammon is the only game which can benefit from the introduction of the doubling cube, be assured that it can be used for many games. I have played both chess and Scrabble with the doubling cube and once watched a golf match being played for pounds 200 per hole with the doubling cube being used. The cheque that changed hands at the 18th hole would have bought the winner many new golf clubs.