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BGonline.org Forums
Is this obvious?
Posted By: Nack Ballard In Response To: Is this obvious? (Chuck Bower)
Date: Thursday, 31 December 2009, at 7:57 p.m.
The most significant factor is that Blue's 53, 41 and 32 (covering the 3pt) will play better after 3/2 than they will after 2/1.
Doesn't 5-3 play better (i.e. leave a better position) after 3/2 (to be played 10/2) than after 2/1 (to be played 6/3, 6/1)?
Good question. (Obviously, you meant for 3/2 to go with 6/3 6/1 and for 2/1 to go with 10/2.)
In originally thinking of the follow-up, I gave White 62 -- a "nothing roll" of average pips, then with Blue's 53 I envisioned the same two plays you did, and judged the former 53 (leaving 14 shots) to be a bigger ouch for Blue than the latter 53 (breaking his 6pt).
To make analysis easier (hopefully), I've asked Snowie 3-ply eval to be arbiter. After Blue plays his ace (3/2 or 2/1), White 62 (the case I arbitrarily assumed), Blue 53, Blue emerges with respective equities of +.014 and -.034, which is .048 in favor of 3/2: it is confirmed.
However, it seems I was naive. If White is instead given a roll of 64, the equities become -.057 and +.017, which is .074 in favor of 2/1. Slotting the 4pt reverses the ranking, because if White hits the sudden 14pt shot (without covering), Blue can hit back with a 4 from the roof.
A third category of play is when White makes a five-point board: rolls of 66, 44 and 22. The equities are -.025 vs -.210, -.35 vs -.180 and -.186 vs -.264. Halving the differences (because they're doublets) yields .092, .073 and .039, respectively, an average of .068 in favor of 3/2.
The fourth category has a single member: 65, which should be played 13/8 13/7. That gives Black the out of 15/12 15/10 and yields .021 vs -.024, which is .045 in favor of 3/2.
Which of 3/2 or 2/1 comes out better on a subsequent 53 is probably determined by how many rolls White should slot the 4pt. I'm thinking that (in view of Blue's 2pt blot) she should slot even if it means leaving her 14pt blot where it is, though it could depend on the roll. It wouldn't surprise me if that's enough to put 2/1 ahead for the 53 roll, though if so it seems unlikely it would be by much.
I realize that you were only addressing 53 in your (valid) question, but to put things into perspective for the overall problem, the other swing rolls I mentioned of 41 and 32, with the test case of 62 (in), yield .295 vs .146, and .295 vs .232. For the test case of 64 (slot), the 41 and 32 rolls yield .237 vs .191, and .237 vs .088.
Averaging the 62 and 64 test cases, 3/2 is favored over 2/1 by .097 for Blue's 41, and by .106 for Blue's 32. To counteract those rolls by enough to make 2/1 an equal play overall, Blue's 53 would have to do about .203 better having played 2/1 instead of 3/2, and we don't know if it's better at all. So, I think it's quite safe to say that 3/2 is the stronger play.
Happy New Year,
Nack
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