This was problem 3 in the Christmas quiz. Black to play 3-3. Should he play: (a) 7/1(2)* (b) 14/5, 10/7 (c) 5/2(2)*, 4/1(2)* (d) 14/2*

This is a difficult one. Black's plan is to escape the back man while extending his own 5-point prime to a full 6-point prime. The first part of the plan is more important. Note that the doubling cube is with White - which means that Black cannot win the game by doubling White out. White is in it to the end, whatever happens. When you have already doubled it is normally correct to be slightly more aggressive than usual to compensate for the lack of the cube. This position is no exception. So we can eliminate play (b) which picks up both of Black's loose blots but does little else to make progress.

One of the hitting plays is indicated, but which one? Play (d) is the pure play, keeping the 5-point prime and trying to extend it to the full 6-point prime. It's fine when it works, but when White hits the blot on the 2-point things can go wrong quickly. White's 5-point board is enough to make this play too risky. Play (a) is immediately safe (other than White entering with a double-2). However, if White enters and anchors with a 2 then Black still has a lot of work to do to win the game. It's good, but not the best.

This brings us to the apparently anti-positional play (c). This gives up the prime but has the huge advantage of putting two men on the bar, giving Black the precious time he needs to escape his back man. The other advantage of this play which is not immediately obvious is that Black will win many more gammons than with the other plays. These two factors combine to make this the best play by quite a long way. This is confirmed both by manual roll-outs and the roll-out feature of Jellyfish, the world's best backgammon program.