Here is data for all 31P-xxx-21 positions rolled out of which I'm aware. Rollout representations not underlined can be accessed by clicking here and navigating to the bank of Gnubg ROs on this site. For the three rolled out by Miran on XG, click on the (nacbrac) links below.
31P-11e-21 [E U9 S39 H49] #15k 5kS 1k
31P-11N-21 [E V22 U35] 10k
31P-21S-21 [E U1 S17 N21] 15k
31P-22E-21 [E S19] 5k
31P-31P-21 [E S31 U32 V38 N55] 5k
31P-32Z-21 [H N68 S80 E80] 1k
31P-33B-21 [E S22 N50] 10k
31P-41S-21 [E S1 N8 U11] 10k
31P-42P-21 [S E18 N31] 5k
31P-44P-21 [N E31 S64] 1k
31P-51S-21 [N E16 U24 S30] 10k 5kUS
31P-52S-21 [H N27 S40 U45 E45] 5k
31P-53P-21 [S N3 U17 D21] 20k 14kU 7kD, and [S N4 U16] #10k
31P-54D-21 [N S16 E49] 10k 1kE
31P-55P-21 [N D11] 1k
31P-61P-21 [E U18 S23 N41] 5k
31P-62S-21 [H L5 X34] 15k 5kX
31P-63S-21 [H1 X24] 10k 5kX
31P-64R-21 [N S16] 10k
31P-65R-21 [S N5 E28] 20k 5kE, and [S N2.6 E26] 4k
31P-66B-21 [E U2 W21] 10k 4kW
Legend for second roll plays: 11e = 24/22 6/5(2), 11N = 7(2) 5(2), 21S = 24/23 13/11, 22E = 24/22(2), 6/4(2), 31P = 8/5 6/5, 32Z = 24/22 13/10, 33B = 24/21(2) 13/10(2), 41S = 24/23 13/9, 42P = 8/4 6/4, 44P = 13/5(2), 51S = 24/23 13/8, 52S = 24/22 13/8, 53P = 8/3 6/3, 54D = 13/9 13/8, 55P = 13/3(2), 61P = 13/7 8/7, 62S = 24/18 13/11, 63S = 24/18 13/10, 64R = 24/14, 65R = 24/13, 66B = 24/18(2) 13/7(2).
Legend for third roll plays (within nacbracs): E = Each (24/22 6/5), N = Near (13/11 6/5), D = Down (13/10), U = Up (24/21), V = Variant-up (24/23 24/22), S = Split (24/23 13/11), H = Hit (6/3*), X = hit-and-split (24/22 8/7*), L = Lift (8/7*/5), W = Wild or split-and-slot (24/23 6/4).
Error sizes are in thousandths. After the brackets are the number of trials (in thousands, rounded down). For example, for 31P-21S-21, "[E U1 S17 N21] 15k" means that E is best, U is -.001, S is -.007 and N is -.021, after 15000+ trials.
Currently, we have no third roll data for 31P-xxx-21 positions where xxx (the second roll play) is a weak move. The closest cousin to 31P-62D-21 appears to be 31P-54D-21 (where the opponent brought two checkers down). 31P-44P-21 and 31P-55P-21, where Opp brought two checkers off the midpoint, can be considered as well.
Below is a list of evaluations (Ev) where Snowie and Gnu are averaged, and to the right of each is the rollout (Ro).
31P-54D-21: Ev = [N S20 D21 E28 U34], Ro = [N S16 E49]
31P-44P-21: Ev = [N D18 E57 S78 U124], Ro = [N E31 S64]
31P-55P-21: Ev = [N D22 S109 U132], Ro = [N D11]
31P-62D-21: Ev = [N S16 D29 U31 E51], Ro = ???
The goal is to predict "???," the 31P-62D-11 rollout value. We can use the rollouts from the first two positions to make eval-bias inferences about the S and E plays relative to the best play N.
The S bias is -14 and -4 (thousandths); averaging, I'll call it -7. The E bias is -26 and +21; I'll call it +5. (In both cases, I've chosen to weight-average 31P-54D-21 more heavily than 31P-44P-21 by a 2:1 ratio, because two checkers to the outer board with 54D better represents 62D than two checkers all the way to the inner board with 44P.)
Unfortunately, D was never rolled out for 31P-54D-21 (for 31P-44P-11 neither, aargh), so we'll have to make our D inference solely from 31P-55P-21; that shows a D bias of -11.
Applying these -7, +5 and -11 biases (for S, E and D, respectively) to the 31P-62D-21 eval (listed above) predicts [N S9 D18 U31 E56] for a 31P-62D-21 rollout. As we have no data for U from which we could infer a bias, I left the eval of U -.031 unemboldened.
The biggest uncertainty in this analysis is the fact that the 54D, 44P and 55P positions have been rolled out only 1296 trials :( So, even if the bias-carryover method is a guaranteed success, variance is through the roof; that is, even if [N S9 D18 U31 E56] were the actual 1k rollout it would definitely have to be taken with a grain of salt. Simply the Snowie-Gnu average eval of [N S16 D29 U31 E51] should be given ample consideration as well, then.
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| 31P-62D-21 | |
OTOH, this position differs from orthodox positions where White has brought two down (some of which further discourage splitting by putting a fourth checker on the 8pt) because she has (unorthodoxically) slotted her bar point. This increases Blue's incentive to split because the double-shot pressure sometimes forces White to sacrifice equity in looking after her 7pt blot. For example, after 31P-62D-21N if White rolls 61 or 31 she will make her 5pt, whereas after 31P-62D-21S she will settle for her 7pt; by splitting, Blue compels White to make the weaker point. Or after 31P-62D-21N White will make her 3pt with 53 or slot the 5pt with 52, whereas after 31P-62D-21S she has to settle for a pathetic hit on the 2pt.
In short, in support of N: Opp has ten checkers in the zone and is ahead in the race. I support of S: pressure on Opp's 7pt blot. I believe (and the tangential evaluation-bias analysis herein also suggests that) support for N outweighs support for S, though not by much. [N and S are the thematically primary candidates; D is just a weaker version of N, and U and E are just weaker versions of S.]
Nack