Backgammon

This was the first puzzle in our Christmas quiz: Black on roll, should he double? And should White accept?

This type of bear-off problem arises frequently and it is good to know how to cope with it. Hugh Sconyers, a top US player, has produced a set of CDs that give the exact answers to such problems where each side has fewer than nine men left. Unfortunately - or perhaps fortunately - you can't have a PC at your side when playing, so mere mortals have to resort to a little hard work to come up with the right answer.

Let's look at the take side first. To take a double White needs 25 per cent winning chances. Time for a little calculation: unless Black rolls 6-6, 5-5 or 4-4, White will have a chance to take off his two men with one roll - which he can do with 10 rolls (6-6, 5-5, 4-4, 3-3, 6-5, 5-6, 6-4, 4-6, 5-4, 4-5). He will have the chance to roll these numbers in 33/36 games and will win the game 9.2 times in 36 attempts (10 x 33/36). Winning nine games would give him the required 25 per cent so it is apparent that White has a take. He has additional chances because Black may not bear off his men in two rolls. In fact after rolls of 1-1, 2-1 and 3-1 for Black it is correct for White to redouble!

But all of this suggests that White has only a borderline take. So it should be clear that Black has a strong double. He will lose his market if he waits. Using the Hugh Sconyers CD mentioned above the equities for Black are 0.32 points if he waits, 0.46 points if he doubles. So the answer is double/take.

Of course, in real life things can be different. When I recently had this position I doubled and my opponent dropped. Thus I raised my equity from 0.46 points to 1 full point. This reinforces the view that most significant errors are made with the doubling cube. Solutions to problems 2 and 3, and names of the winners, will be given in subsequent weeks.