Backgammon

Many times you will end up playing an ace-point game: you still hold your opponent's one point while he has all his men in his home board. While this is by no means good, you still have a fighting chance. If you keep your men in your opponent's home board to the bitter end you will get a shot 90 per cent of the time! Of course staying until your opponent only has a few men left risks being backgammoned if the dice throws go against you.

On average you will hit the shot your opponent leaves about 25 per cent of the time. Whether you will then win depends on the state of your home board. If you can close out the man you have hit then your winning chances will depend upon how many men your opponent has already borne off. If you have a crashed board, that is only a few points made and most of your checkers on the 1, 2 and 3 points, then the best you can hope for is to save the gammon. Look at today's position:

White had borne off five checkers when he was hit. Black then closed out the hit checker and has a closed home board with his three spare checkers optimally distributed on the 3,5 and 6 points. The key question is when should Black redouble?

For years opinion varied, but double world champion Bill Robertie has developed a very useful rule of thumb: Assuming you have a closed board and good distribution of spares, then you should redouble when you have borne off five fewer checkers than your opponent. The above position is thus Black's optimal redouble and should be used as a benchmark. White has a very thin take and in practice many players would drop this redouble.

Change the position slightly and you need to reconsider your strategy. If White had already borne off seven checkers then Black would wait until he had borne off two of his own and then redouble. Again if, in the given position, Black's three spare checkers were all on his one point, then it would prudent to wait a roll before redoubling.

The rule also works when you have hit and closed out two checkers, here you should redouble when you have borne off ten fewer checkers than your opponent.