Games: Backgammon

Time to eat humble pie. The first problem in the Christmas Quiz should have been published with the diagram above. The correct solution to this problem is that Black should double and White should drop, as published last week. Unfortunately, in writing the quiz I accidentally moved the third man on Black's one-point to his three point. This small difference is enough to change the answer from a drop to a take. I am indebted to several of my colleagues from the Double Fives club for pointing out the error of my ways. As a result I am awarding an additional prize and this is on its way to Michael Crapper of London SW18.

The main difference that the error in the diagram makes is that in the position above Black no longer wastes a roll on sequences where he rolls a number containing a `2' on both of his first two rolls, except if one of those rolls is 21. This small change makes quite a difference in equity. In the position above White's equity if he takes is -2.17. With the third man on the three-point his equity rises to -1.44. Thus the position above is a narrow pass, the quiz problem as published a clear take.

The lesson for everyone here is that in bear-offs very small differences in the position can lead to very different cube actions and it is only by objective analysis that you can come close to the right answer. Over the board you will get some of them wrong but with practise and experience you will get better.

Hugh Sconyers, an American analyst, has produced a CD which gives exact bear-off equities for all bear-offs where both players have nine men or fewer and all men are within the home boards. This is an invaluable analysis tool and although $99 is not cheap it is worth the investment if you want to study endgame bear-offs seriously.

The CD is available from Carol Joy Cole, 3719, Greenbrook Lane, Flint, MI 48507-1400, USA.