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| 31P-33C, with Blue to play 32 or 11 | |
Snowie and Gnu rollouts (5k) almost exactly agree on the error size of Opp's play: 31P-33C is an error for money of -.045 or -.044. And it's hard to imagine that C is any better at the actual score of -2-5 (needs 2, needs 5). 31P-33C is a bad play at any score.
Hence, like Stick, I have no rollouts for third roll plays following that move, and hadn't really planned to, with the exception of doublets (for which I intend to be unusually thorough). So far, I have rollouts for double 1s and double 2s (the latter of which won't offer us any insight into the main position).
For 31P-33C-11 (position diagrammed above, with 11 to play), 24/22(2) is best by far -- about .100 better than the next best play. Therefore, I didn't bother to do a full rollout. However, I do have a 1k trunc: the next three plays, 24/21 6/5, 24/23 24/21 and 24/22 8/7(2) are within a .004 span of each other; and compared to the best of those, 24/22 6/5 is -.014, 23(2) 8/7(2) is -.028, and 24/23 8/7(2) 6/5 is -.039.
As playing 6/5 has a positive value of more than just a couple/few thousandths, that 31P-33C-11 trunc result suggests to me that coming up with an ace (24/23), thereby threatening the 8pt builder with a second checker, has positive value. Even if this trunc is 100% reliable, that doesn't prove that coming up with a deuce (24/22) has positive value, because 23pt 22pt is a different configuration from 23pt 21pt -- it gives Opp different attacking/bailout numbers, but it does point evidence in that direction. In other words, with a roll of 32 in the position above, the indication is that Blue does better with 24/21 24/22 than with 24/21 by itself.
Another third roll position that sheds some light is 21$-33C-11, shown below, for which I have extensive Snowie, GnuBG and XG full rollouts.
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| 21$-33C-11 | |
But also note: 24/23 24/22 6/5 is -.014. Threatening the 8pt blot with a second checker, 24/23, doesn't work out well. Why is the 21pt checker helped by adding 24/23 (first position), whereas the 22pt checker is hurt by adding 24/23 (second position)?
It has to do with the extra hitting numbers inside. The 23pt/21pt defense is efficient: it is hit on 6s, 4s and 2s (with the 2s duped for the double-hit). The 23pt/22pt defense allows 6s, 5s, 4s and 3s to hit, and 31 hits a second checker. (If 5s covering the 8pt weren't duped, then 51 would also be used to hit twice and the difference would be more pronounced.)
The same sort of problem exists for the 22pt/21pt defense that you would get playing 24/21 24/22 in the feature position (repeated below): 5s, 4s, 3s and 2s hit, with 41 21 hitting twice. This is the danger to which Stick alludes. Nevertheless, it seems to me that in looking at the effects in both of the related positions (31P-33C-11 and 21$-33C-11) that in the 31P-31C-32 position 24/22 should be more of an asset than a liability in conjunction with 24/21, say by .01.
For me, then, it comes down to whether 13/11 represents a bigger gain to Blue's position than 24/22. Getting hit with a 7 is bad but not terrible because of return shots and White would have constructive plays with 61, 52 and 43 (i.e., 13/7 8/7, 13/8 6/4(2), and 8/4* 6/3*, respectively) anyway. I estimate the cost of the 7 shot to be .100 but it will occur only 1/6 of the time = .017. By contrast, I'd estimate the gain of unstacking the midpoint and bringing the 11pt builder into play in the non-7 variations (which are mostly stable, but even averaging in the unfortunate blitzes) to be .05 or .06; multiply that by 5/6 (chances of not being hit with an immediate 7) comes to say .047. Subtracting the 7-roll cost of .017 yields a difference of .030.
Subtracting the estimated gain of .01 from 24/22 from the estimated gain of .030 from 13/11 gives us a difference of .020.
Summary: With the benefit of rollout results of the two related positions and some deductions (granting that some of the data is imperfect), I estimate that for the 31P-33C-32 position below, along with 24/21, Blue's 13/11 deuce is better than his 24/22 deuce by .02 -- give or take .01. :)
Perhaps the more useful conclusions, though, are: (a) Even after splitting with the 3 that playing a deuce is better than not playing a deuce, and (b) that (illegally) playing two deuces with 24/22 13/11 would be even better than the best legal play of 24/21 13/11. Note the 5 duplication; 24/22 weakens White's 4s, and it hurts her 2s more than it helps her 3s. The plays of 24/22 6/3 and 24/22 13/10 both incorporate the more desirable split, but they relatively suffer way too much in the 3 department.
Nack
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| 31P-33C-32 | |
