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|---|---|
| Blue to play 31 or 41 | |
The short answer is "yes," though it is an incomplete diagnosis to make one roll or one factor the entire reason.
In the rollout results, the margins of S (Split: 24/23 and down) versus N (Near: down and 6/5) are fairly close. As S creates a greater swing with E (Each: split and 6/5) than N does, I'll simplify by ignoring N.
For the 31 position, consider Opp's equities (using Snowie evals -- close enough for our purposes) for these fourth roll plays:
31P-65R-31S-54D = -0.284
31P-65R-31S-54R = +0.070 (illegal)
Speaking in thousandths, S gains 284 + 70 = 354 as a result of having 24/15* blocked; that's a ton. (That factor is neutral for 31E, because there is no 10pt blot that could be hit even if the 5pt were vacant.)
The roll 54 occurs 1/18 of the time, so the effect of 24/15* being blocked comes to 354/18 = 19.7. I'll integrate this number in a moment.
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| Blue to play 31 or 41 | |
31P-65R-31
GnuBG .. [S N2.8 E15.7] 4k
XG 3-ply [S N2 E11] 31k 20kE
31P-65R-41
GnuBG .. [S E2.2 N2.6] 5k
XG 3-ply [E N10 S18] 20k 5kS
Using something between a straight bot average and a weighted trial average (the k numbers represent the thousands of trials), and removing N from the clutter, I'll combine and simplify to
31P-65R-31 [S E12]
31P-65R-41 [E S10]
Remember the 19.7 thousandths we calculated for the effect of the 24/15 hit being blocked? Whaddya know: that's pretty close to the actual difference of 22 between the S/E margins above.
It is a bad habit, however, to automatically halt an analysis after finding one factor that explains away a difference. In this case, for example, a far-from-trivial counterfactor is that the 5pt also blocks 44 from hitting on the 9pt. [Disregard 22; Opp shouldn't hit with that doublet even if she can.]
Consider the equities for these fourth roll positions (where for 44, N = Near 13/9(2) 6/2*(2), and B = Both 24/16* 13/9(2)):
31P-65R-41S-44N = +0.219
31P-65R-41S-44B = +0.404 (illegal)
The N play gains 404 - 219 = 185 (again, isolating the factor that the 5pt blocks the hit). Dividing by 36 shows an effect of 5.1.
Subtracting 5.1 from 19.7 leaves 14.6. There is a gap between that and the full difference of 22 in the rollout margins, so 7 or 8 thousandths should be nettable out in lesser factors (including other aspects of 54 and 44), and/or some of it may be variance. (I'll end the analysis here -- this post is mainly intended to convey concepts of reconciliation.)
In conclusion, the 10pt builder gets (due to the 5pt blocking 54) a significantly larger dispensation than the 9pt builder gets (due to the 5pt blocking 44). This is one way of explaining (the lion's share of) the reason that for 31P-65R-31 S (or N) beats E, but for 31P-65R-41 E beats S (or N).
Hope that helps.
Nack
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|---|---|
| 31: S (or N) beats E, but 41: E beats S (or N) | |
S = Split: 24/23 and down
N = Near: Down and 6/5
E = Each: Split and 6/5