Problem of the Week #108: Solution


Cash game, center cube. Black on roll.




Black to play 5-3.



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.


In Problem 108, Black and White and been engaged in a bit of a hitting contest, and so far Black has the worst of it. Right now he has four men back to White’s two, and he’ll be a little behind in the race after he plays his roll.

Black’s roll of 5-3 presents him with a choice of two plans: he can enter and keep hitting, hoping that White throws something useless in return, or he can enter and consolidate, with the plan of weathering the immediate storm and emerging to fight again a little later. No matter which plan he likes, he’ll have a choice of moves to choose among. If he wants to hit, he can play Bar/20 8/5*, or Bar/22 10/5*. If he decides consolidating is better, he can pick from Bar/20 23/20, Bar/20 10/7, or Bar/22 15/10.

That’s a lot of choices, so let’s simplify the problem by choosing the best from each group, then matching those two against each other.

Let’s start with the hits. The choices are Bar/22 10/5*, and Bar/20 8/5*. Both are loose plays: hitting with 10/5* leaves five blots, while hitting with 8/5* leaves six blots. After 10/5*, White will return hit with 32 (!) numbers. That’s right – every number which enters also hits somewhere. Is 8/5* safer? No – White again hits back with 32 numbers! Given that information, Bar/20 8/5* is clearly better, since at least you have the 20-point slotted for a good anchor.

Now let’s look at the consolidating plays. Black can play Bar/20 23/20, making the 20-point and leaving three blots; or Bar/20 10/7, making his bar-point while leaving three blots; or Bar/22 15/10, making the 10-point while leaving three blots. Of these, the clear winner is Bar/20 23/20, just because the 20-point is the best point available as well as being a second anchor. With all his blots, Black may need all the anchors he can get.

So we’ve narrowed our choices down to two: hitting with Bar/20 8/5*, or consolidating by making the 20-point. The easiest way to see which is better is to take a look at Black’s points. Right now, he owns his 3-point, 6-point, and 8-point, but he doesn’t own anything else until we get to his 24-point. That’s a pretty long stretch of board where Black doesn’t have a solid foothold. Strategically, Black badly needs a point somewhere, and the only good point he can grab right now is White’s 5-point.

If Black’s attack had a realistic chance of succeeding, that might trump the need for a point. But as we just saw, after 8/5* every White roll that enters hits at least one blot, while some rolls hit two blots and one roll even hits four blots! With 32 hitting rolls for White, Black’s attack isn’t going anywhere, so he needs to think about battening down the hatches and surviving. Making the 20-point is the survivalist’s play.

Although the strategic case for the 20-point is compelling by itself, a look at the potential cube action makes the case even stronger. After Bar/20 23/20, White has at best a marginal double and Black has a very easy take. After hitting with 8/5*, White’s 32 hits and Black’s multiple blots give White a crystal-clear double. Black still has a take, but not as easy a take as if he had two points in White’s board.


Solution: Bar/20 23/20