# Backgammon

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This was problem two in the Christmas Quiz. Black to play 42. Should he play: (a) 19/13 (b) 21/15 (c) 7/5*/1* (d) 7/5*, 13/9?

Firstly, let's check the position of the doubling cube. Black has already doubled and therefore cannot win the game by doubling White out. This normally means that Black should play more aggressively than if the cube were in the middle.

What of our four candidate plays? We can quickly eliminate play (d). If it is right to hit it will be right to hit two men, because there will be fewer return shots and because it will lead to winning more gammons. Of the two more passive plays 19/13 is safer but provides less control of the outer boards. However, getting hit by an 8 or 10 could be disastrous and roll-outs show 19/13 to be superior. So we are down to two plays, the attacking play (c), or the passive play (a). Which is right?

The answer is play (c) and it's not even close. Unless White rolls an immediate 1 or double-5 he is likely to end up with two men closed out which in turn will lead to quite a few gammon losses. If White does roll a 1 then Black is certainly in some danger but both players will have a man on the bar against a 4-point board and it will be Black's turn to roll, still making him a small favourite. On the 24 rolls where White doesn't roll a 1 or 55, Black will become a massive favourite.

Having given the cube away this is exactly the sort of move Black should be looking for to bring the game to a swift conclusion. Sadly when confronted with this problem over the board, I played the weak 19/13 and was gammoned for my pusillanimity.