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EPC

Posted By: Daniel Murphy
Date: Monday, 8 August 2011, at 6:03 p.m.

In Response To: EPC (Timothy Chow)

Yes, after 2/off, 3/2 should have been obvious. If we need to bear off 10 checkers in 3 rolls, we are allowed to roll one non-doublet. If we leave the 2 point empty with 6/4, we have only 14/36 numbers that bear off exactly 2 checkers. 3/2 6/5 gives us 21/36 such numbers. 3/2 5/4 actually gives us 1 more such number, but it's slightly worse because either our non-doublet must include a 6, or one of our doublets must be 6-6. Perversely, 3/off 2/1 maximizes the numbers that bear off exactly two checkers -- 23/36.

And yes, of course EPC did not control in our position because we needed to aim to be off in three rolls. Similarly here:

White3


3X ' ' ' ' ' ' ' ' ' ' '

 '1O1O1O '1O ' ' ' ' ' '

Blue15

Position ID: BwAAoBIAAAAAAA Match ID: UYkIAAAAAAAA

the best play is 4/3 2/off (EPC 17.91) because Blue needs to bear off in 1 roll. This play increases Blue's winning chances by 2.3%.

But here:

White5


5X ' ' ' ' ' ' ' ' ' ' '

 '1O1O1O '1O ' ' ' ' ' '

Blue15

Position ID: HwAAgEoAAAAAAA Match ID: UYkIAAAAAAAA

the best play is 6/5 2/off (EPC 17.65). 4/3 2/off wins 3.3% less often.

There is a software program or two that can analyze bearoff positions and tell you how often bear-off occurs in 1, 2, 3, 4, 5 ... rolls. Unfortunately I don't have a copy of one on this computer.

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