backgammon

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Let's remind ourselves of the basic theory of doubling. The concept 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 offer a redouble, increasing the stake to pounds 4. Player A would have the same options: paying B pounds 2 or continuing with the stake now at pounds 4.

The initial reaction of most players when they first come across the concept of 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 immediately. Consider this: In four games if you are doubled and decline the double in all four then your score will be minus four points. If you accept the double and lose three games but win one, your score will still be minus four points (losing six points in the three games you lose, but winning two points in the one you win.)

So winning one game in four at doubled stakes is the same as losing all four at the original stake. In other words you need a 25 per cent winning chance in order to accept a double. How to estimate whether you have a 25 per cent winning chance in any given backgammon position is a very complex problem and one which I shall address in subsequent articles. Other influencing factors such as gammons and the value of owning of the cube will also be addressed later.

For now, consider this problem: the position illustrated is a very simple end-game which occurs fairly frequently. Should Black double? Should White accept the double? The answers will be given in the next article on Tuesday week.

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