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short bearoff/calculating COMMENTS

Posted By: Bob Koca
Date: Sunday, 18 August 2013, at 2:52 p.m.

In Response To: short bearoff/calculating (Bob Koca)

Casper and Joe make good points about time management. A similar situation sometimes comes up when looking to position outfield checkers when running off the gammon.

Dmitry has it correct but I would do one step a bit more easily.

The first thing to realize OTB is that you do not need the win% at all but rather just which is better. After realizing that 6/5 5/0 is obviously bad and that 6/0 4/3 is dominated by 6/0 2/1 because for rolls of 41, 51, 61 we have candidate plays of 6/0 2/1 and 6/0 3/2. Since almost every play transposes we should just look at the swing rolls of 22 and 31.

Setting up for 22 gains when you get 22 and opponent would have gotten doubles in next two shakes. This is 1/36 X 11/36 = 11/1296. I would just leave it like that instead of multiplying by 36/36 as Dmitry did. It is not even necessary to multiply 36 x 36. Similar to how percent works think 11 per2ply.

Setting up to make 31 better matters 8/36 of the time (you will have 26 good rolls instead of 34) if opponent does not get doubles (25/36) and you get 31 (2/36). To compare directly leave denominator as 36 x 36 and get that you swing 50 x 8/36 per2ply. Reducing 8/36 to 2/9 gives 100/9 per 2ply. 100/9 is greater than 11 so setting up to make 31 better with 6/0 2/1 is the best play. The difference is 1/9 per2ply which is less than 1 game in 10000.

Rick asked about money game play. If the opponent holds the cube he will never be using it so the analysis is exactly the same. If you hold the cube or it is centered then you just made an error since it was double/pass before your roll. Going forward correctly though the best checker play owning the cube is 6/0 3/2 setting up for double 2. If your opponent does not get doubles immediately you cash so you make the best play assuming he does get immediate doubles. 1/6 of the time you gain 1/36 more wins on the current cube level. The equity difference is thus 1/108 times the value of the cube (or 12 per2ply). Also note here that all 3 of the non-optimal plays have exactly the same equity.

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