Problem of the Week #141: Solution


Money game, White owns the cube, Black on roll.




Black to play 5-2.



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.


Problem 141 shows a somewhat unusual middle game position. Black, with one checker in the air, has an outside prime with the 5-point slotted. White has a bizarre position with four checkers back on his 24-point. His front game is normal enough, with the start of a little block. Last turn, Black doubled from the bar and White bravely took. (A small mistake, actually. The position is a pass, although not by much.)

Black’s 5-2 from the bar gives him a few choices. Here’s a quick list of the main options:

(1) Bar/23 13/8. The safest play, this keeps the back checker from being attacked on the 20-point, while adding another cover number for the 5-point.

(2) Bar/20 5/3. Another safe option, this time duplicating twos. This also prevents White from simultaneously hitting and getting to the edge of Black’s prime. The downside of the play is that it becomes hard for Black to build on his early advantage. Covering the 3-point won’t make his game appreciably stronger.

(3) Bar/20 13/11. This play is a different way of bringing down another cover number to make a 5-prime.

(4) Bar/20 7/5. This play shifts points, covering the 5-point and leaving the bar-point slotted.

Those are all the reasonable plays; anything else we can eliminate quickly. The next step is pruning our tree a little bit more. Are there any of these play that don’t stand up to a closer inspection?

To make progress, let’s focus on our opponent for a second. What is his big weakness, and what are his awkward numbers?

White’s main problem, clearly, is that mass of checkers on his 24-point (our ace-point). White needs to get those checkers moving quickly, before his front game stalls and collapses. He can move them with aces through fours, but his fives and sixes are blocked. That insight lets us toss two of our candidates right away. Move (1), Bar/23 13/8, makes fives and sixes somewhat useful by letting him hit on our 23-point. Move (4), Bar/20 7/5, makes sixes not only active but highly useful, letting him step out to our bar-point while hitting at the same time. Let’s eliminate both those moves and focus on the last two, Bar/20 5/3 and Bar/20 13/11.

The choice between these two plays hinges on the cube position. We’ve given the cube away, so we want to finish White off as quickly as possible. Making a prime is the best way to do that, and the risk (a single shot) is not that great. Playing 5/3, after all, still gives White a shot, and on a point we don’t really care about making. So let’s leave our blot where it belongs and play Bar/20 13/11. Making the prime wraps up the game – if White misses, he’s in a hopeless position with nowhere near the timing to play a back game.

(Incidentally, if we had forgotten to double last turn so the cube was still in the middle, then 5/3 would be right. The idea in that case would be to minimize the chance of a big downswing so we could keep our advantage and turn the cube on the following turn.)


Solution: Bar/20 13/11.