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BGonline.org Forums
42! Edge of Prime, Point or Bit of Both?
Posted By: Daniel Murphy In Response To: 42! Edge of Prime, Point or Bit of Both? (Rich Munitz)
Date: Tuesday, 13 October 2009, at 3:46 a.m.
Rich writes: Noting that the cube is still in the center, the thought should not be about what is needed to win this game, but how do we get enough of an advantage to cube when things go well, and how do we make the best of it when things do not. [analysis snipped] So making the 4 point renders the cube nearly worthless.
How so, worthless? The cube is live, so whichever play leads to higher cubeful equity is the better cubeful play, right? Right. And that is not necessarily the play that leads to double/take most often.
Recap:
Blue plays White enters both checkers White enters one checker White dances 23/21 13/9 25% 50% 25% 8/4 6/4 11.11% 44.44% 44.44% If White enters two checkers, advantage to 23/21 13/9 in each such sequence, but 8/4 6/4 prevents this sequence from happening 13.88% of the time.
And if White enters one checker, advantage again to 23/21 13/9 -- let's suppose that in fact 23/21 13/9 leads to double/take and 8/4 6/4 leads to no double -- but again, these sequences are slightly less frequent after 8/4 6/4.
Finally, if White dances, huge advantage to 8/4 6/4. Both plays lead to double/pass, but 8/4 6/4 makes this happen 19.44% more often.
Add them all up and which play emerges as the cubeful favorite? My choice would be 8/4 6/4, figuring that a 4-point board is much stronger than a 3-point board, that White will then enter both checkers much less often, that 6/4 pointing from the 6 point stack is a better use of a two now than 23/21, that when things don't go well or go fairly well Blue will have time to split and move up up and out, and that things will go very well (that is, Blue will get a quick double/pass) much more often.
As an aside (since there's mention of "huge" market loss after 8/4 6/4), if Gnubg evaluations are good, the play that leads to huge overkill on the cube whenever White dances is not 8/4 6/4, but 23/21 13/9.
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