# Backgammon

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The Independent Culture
THIS WEEK I will introduce Robertie's addition method, which is a useful aid when evaluating close bear-offs. In the above position, should black double, should white take?

Before answering this question there are some figures that you will need to be able to memorise: in a pure three-roll bear-off (neither side can fail to take off at least two men with each roll) the defender's winning chances are 21.2 per cent; in a pure two-roll ending the defender's chances are 13.9 per cent; the chance of throwing a particular number on one roll (excluding the double) is 27.8 per cent; the chance of throwing a particular number two rolls in succession (excluding the double) is 7.7 per cent; the chance of throwing a number three times in a row is 2.1 per cent.

How do we use these numbers to evaluate our position? First we note that it is nearly a pure three-roll position, so black must have a strong double. The question is, can white take? Robertie's method is to add up the winning chances and see whether they come to more than 25 per cent. If it were a pure position, then white would win 21.2 per cent of the time. If black rolls a "2" on both of his first two rolls then he will miss and white will have a redouble that black must drop. This adds 7.7 per cent winning chances (in fact it is slightly less than this because of the possibility that either side may throw a double). If black rolls a "1" on all three of his next three rolls, white will win. This adds another 2.1 per cent to the total, which is therefore 21.2 + 7.7 + 2.1 = 31 per cent.

These possibilities are not mutually exclusive, and so we probably need to lower our figure a bit; but even so we can see that white has a comfortable take. This addition method is an excellent way to try to assess your winning chances, and will improve your accuracy in giving and taking bear-off doubles.