Problem of the Week #99: Solution


Cash game, Black owns the cube. Black on roll.

Three scenes from the same game.





(a) Cube action, both sides?




(b) Cube action, both sides?




(c) Cube action, both sides?


Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.


These are fairly simple problems but they illustrate a common theme which occurs in some degenerate prime versus prime games. Let’s look at position (a) first.

Here both White and Black got stuck in an ace-point game behind a prime. Although Black had more men back, White’s prime actually collapsed first as he couldn’t release his back men. Now White has lost his 6-point, and Black is thinking about doubling.

Currently Black trails by 57 pips in the race (166 to 109) and has a man on the bar. Those might sound like big drawbacks, but in fact they don’t matter much at all in these positions. The following three features are the crucial ones:

(1) White has four dead checkers, while all Black’s men are in play.

(2) The game will go on a long time.

(3) On his next roll, White has 16 numbers (5-3, 5-2, 4-3, 4-2, 3-2, 3-1, 2-1, 3-3, and 2-2) that kill one or more additional checkers.

It’s incredibly hard to play a game with eleven checkers against fifteen; the longer the game, the harder it gets. Here White has not only lost the use of four checkers so far, but he has more breaking numbers than escaping numbers, so his game is likely to get worse. Black has no break numbers on his first turn, and he has to be very unlucky to ever roll a breaking sequence at all. Add all these factors together, and White’s in terrible shape.

Position (a) is already an easy double and a big pass.

Position (b) is even worse for White. He’s escaped one checker, but Black has escaped two. Black now has no breaking sequences for the foreseeable future. It’s a double and an even bigger pass.

Position (c) shows White’s game continuing to deteriorate. Now it’s too good to double by a wide margin, and a monster pass if doubled.


Solutions: (a) Double – pass.
(b) Double – pass.
(c) Too good to double.

Thank god....

Bill is there any merit to my idea to double position 3 anyway? If not, then how much better does this position have to be to double?

I like your general idea of doubling positions that are technically too good because you can get some takes in practical play. Certainly if White seemed to be steaming, or were obviously a fish, I would whip in a shot. Against an average-strength player who seemed to be in control I'd most likely play on.

In my local club I asked the player that is ranked(and regarded) to be the best player about these positions. I know she is poor in these prime vs prime(sort of here) positions and she would take the first two and drop the last one. So for practical reasons, I would certainly double all of these vs the right opposition.