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Old 11-28-2010, 04:03 PM   #1
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Join Date: May 2004
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Problem of the Week #85: Solution

Problem of the Week #85: Solution

Cash game, Black owns the cube.

Black to play 2-1.

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 85 shows us one of the most interesting middle game positions possible: both sides have a 5-prime, and neither side has an anchor. The play will be razor-sharp, and gammons will be floating in the air for both Black and White.

What are the goals in these positions? Here’s what the players are trying to do, arranged roughly in order of importance:

(1) Escape a checker from behind the prime. In general, if you roll a six, you’re going to run a checker to the outfield. This not only releases a checker, but buys you several additional rolls of timing before your own prime comes under pressure.

(2) Hit checkers in the outfield. This is the converse of (1): you send a checker back to jail, and eliminate your opponent’s timing in the process.

(3) Get to the edge of your opponent’s prime. You can’t escape without getting to the edge, so get there when you can.

(4) Knock your opponent off the edge of your prime. (4) is just the converse of (3): if he wants to get to the edge, you want to knock him away.

(5) Do what is hard for you first; make your opponent do what is hard for him. Something is “hard” if you need a single number on the dice to do it, like rolling a six to escape. On any turn, you only have a 30% chance of doing a “hard” thing, so when you have the chance, take it, even if it seems to leave a vulnerable position. If you pass on doing something hard, you’ll find it doesn’t get easier later.

With the 2-1, we can quickly see that we can’t do anything about goals (1), (2), or (3). Only goal (4) applies here; we do have the ability to knock White off the edge of the prime, so we take it. Our deuce will be 5/3*. Now White needs a three to get back to the edge, and he may not roll a three for awhile.

What about our ace? If we have blots on our 1-point and our 3-point, White has 20 rolls to hit. We might as well push on and hit the second blot, because we’re just as likely to be hit back as before. It’s a free hit, and it has an added bonus: we create a new possible game plan. If White dances, or rolls 6-3, 5-3, or 4-3, we now have the possibility of a blitz, followed by escaping our back checker later. It’s not a likely variation, but just the possibility adds a lot of strength to our position.

Solution: 5/3*/2*.
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