MISCELLANY: Backgammon

THIS SORT of problem occurs quite frequently. Black has hit a late shot, contained white's blot and borne off some men. White has now re-entered and is heading for home as quickly as possible. Should black redouble? Should white take?

To analyse these positions, see how many rolls each side will take to complete the bear-off. Black's position is easy: if he doesn't roll a double he will be off in four rolls.

And white? First he has to get the man on his mid-point home. The average backgammon roll is 8.16 pips. For practical purposes we can use 8 pips. So we can assume that on his first roll, white will move his blot to his own 5-point. Then he will have five men to bear off and, again assuming no doubles, we can estimate he will be off in three more rolls.

Thus we have a four-roll vs four-roll situation. We know that four vs four is double/ take. So that's the answer here too, right? Wrong; in a true four vs four we assume that neither side can miss. In this position, small numbers for white on his first roll are ruinous. Look at the difference between the two sides when 11 is the first roll.

The difference is enough to turn what looks like a take into a very clear drop. In fact white's winning chances in this position are just 14 per cent. When confronted by positions like this, analyse them thoroughly or you could deplete your bank balance!