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OLM 20141229A The Prime Factors
Posted By: Chuck Bower
Date: Tuesday, 30 December 2014, at 3:24 a.m.
In Response To: OLM 20141229A The Prime Factors (Jason Lee)
Is this one of those cases where you're supposed to fill in an empty homeboard point at the expense of moving outside pips?
If you fill the 2point you get a checker off with all 5's and 6's except 51 and 61 (16) plus 22, 33, 44 for a total of 19.
If you leave an outside checker on the 9point instead you miss with all 1's and 2's except 22 so 17 numbers bear off.
If you fill the 1point it's similar to filling the 2point except you can't get off with 22 so there are 18 rolls that bear off next time but you're guaranteed to be off the following roll so this is better than 11/9.
A) (Approximately) you need to be off next turn if opps roll 44 or better either of their next 2 rolls. B) Also (approximately) you always need to be off in the next two turns.
A) matters 1(11/12)^2 = 23/144. And 1/36 is the immediate gain so 23/5184.
B) matters the other 121/144. The gain there is 1/18^2 (back to back 21's) so multiplying: 121/(36^3) = (121/9)/5184. That's about half as often. I'm pretty sure the inaccuracy of the approximations won't account for such a 'large' discrepancy between the two plays.
7/6, 4/2

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