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Backgammon is fundamentally a race. After all contact has been broken between the two armies, it is a race to bear off your men before your opponent can bear off his. How do you know when to double (or redouble), and how do you know whether to accept or decline an opponent's double?

The first step is to calculate the pip count for both sides. A player's pip count is the number of pips on the dice he must throw in order to bear all his checkers into his home board and then off the board. It is simply calculated by multiplying the number of men on each point by the point number and then adding up the results.

In the diagrammed position Black's pip count is: (2x13)+(1x11)+(1x10)+(1x7)+ (4x6)+(2x5)+(1x4)+(2x3)+(1x2) = 100. Similarly, White's pip count is 110 (remember, what is labelled in the diagram as the 22 point is actually White's 3 point, and so on for all the points). This may seem like a lot of mental arithmetic, but after you've played the game for a while it becomes second nature and one learns a few mental shortcuts (eg a closed home board with two men on each point is 42 pips).

So, back to the problem. Black has a lead of 10. Is that good enough to double - should White accept? The simplest rules are as follows: with a difference (trailer's pip count minus leader's pip count) of 8 per cent or more, the leader should double. With a difference of 9 per cent or more, the leader should redouble. With a difference of 12 per cent or less, the trailer has a take. There are more sophisticated formulae which take account of distributional factors, but the above will suffice for the majority of players. In the problem, Black has a lead of 10 pips (10 per cent) and should therefore double or redouble, and White is trailing by less than 12 per cent, so he should accept a double. Generally, this method should not be used when the pip counts are below 30. At that point more accurate methods are available.