Black has hit a man late in the bear-off. He has managed to take off eight of his own men before White re-enters, reaching the position above. Should Black double? If he does, should White drop or take?

How should you evaluate positions like this? You could try using the Thorpe count, which I described a few weeks ago (the article contained an error in that when calculating the leader's Thorpe count the final step is to add 10 per cent to his total if his count is greater than 30, not less as originally published). The Thorpe counts here are Black 30 and White 30 indicating double/take, but Thorpe does not cope well with men in the outfield.

It is clear that Black will take three or four rolls to bear off his remaining men. What about White? First he has to get his straggler into his home board. The average dice roll contains 8.17 pips so for practical purposes we can use eight. This means it will take White two rolls to reach his home board and then another two to bear off. On average, then, it looks as if it will take White four rolls to bear off his men. Given that four rolls versus four rolls is normally a take, does that mean that White can take a double in this position?

Sadly for White, the answer is no. When he rolls a big double on his first roll he will quite often win, but too frequently he will take three rolls to reach his home board, or reach it in two and then only take one man off with his next. Meanwhile Black has the opportunity to roll doubles, and while most doubles are good for Black, the small doubles are not very effective for white. Black will win this position 80 per cent of the time, meaning that it is clearly a double and a drop.