Problem of the Week #35: Solution


Cash game. White owns the cube. Black on move.




Black to play 4-3.

Something a little different this time. Identify the worst of these three plays:

(a) 11/7 5/2

(b) 11/4

(c) 7/4 6/2.


This one is actually pretty easy (for a change) and all of our respondents got it right. The worst play is the only completely safe play for this turn, 11/7 5/2. Black doesn’t need to be safe right now. White is helpless, with a busted board and some loose blots. White doesn’t want to hit right now; he wants a couple of turns to consolidate his position and hopefully hit later and get off the gammon.

Black’s idea should be to put his checkers in a good position for the bearoff. For that, he wants to clear his 7-point and 8-point, and make sure he has plenty of spares on the 4, 5, and 6-points. Playing 11/7 5/2 does all the wrong things: it (1) puts a checker on the 2-point, where it doesn’t belong, and (2) doesn’t put anyone on the 4-point, where Black wants spares, and (3) makes a point that Black will immediately want to clear. Conceptually, that’s about as bad as you can do.

What about the other two plays? They’re actually very close in equity, if you’re playing a strong player. But if you’re playing a weak player, they’re not close at all: 11/4 is much better than 7/4 6/2. The reason is that after 11/4, leaving a blot on the bar-point, White shouldn’t hit unless he rolls 6-6 or 4-4. For any other roll containing a 6 or a 4, the hit is a big mistake, exposing White to lots of extra gammons for relatively few winning chances. Weak players won’t necessarily see this, so leaving the blot on the 7-point can induce a blunder. After 7/4 6/2, however, even weak players will mostly handle the next roll correctly, moving their outfield blot.


Solution:

Worst is 11/7 5/2

Best is 11/4