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41S-32-C and 41S-32Z at p-2, cube rollouts

Posted By: Nack Ballard
Date: Thursday, 27 March 2014, at 6:31 a.m.

In Response To: 41S-32 P2a RO (David Rockwell)

Sorry to rain on whomever's parade, but I'm getting somewhat different results for two of the three positions. (I didn't bother rolling out 41S-32D-C, which looks like an obvious double/pass to me. In other words, I agree with that one.)

According to the rollout results below (which you'll see side-by-side if you widen your window enough), at the p–2 score, 41S-32S-C and 41S-32Z-C are both proper doubles (though in the second case with only 52% confidence, it is basically still a tie at 31k), i.e., NOT too good to double.

The equities of the player playing S (Split, 24/21 13/11) or Z (reverse split, 24/22 13/10) when the cube remains centered are:

........David:...S = –1.0044 (20k), or Z = –1.0125 (5k)
........Nack:....S = –0.9930 (20k), or Z = –1.0000 (31k)

What is the explanation for the differences between David's results and mine? Some factors that occur to me to explain all or part are:

(1) I used XGR++. He used XGR+.
(2) I used direct cube rollout. (Has it been proven that rolling out checker play equities yield proper cube decisions with the same reliability?)
(3) Variance.

Any thoughts?

Nack

.....Nactation tutorial ........(For larger text, click on the double-arrow to the right of “Bookmarks”)





White is Player 2

score: 1
pip: 162
2 point match
pip: 162
score: 0

Blue is Player 1
XGID=-a--a-E-CA--dDa--c-e---AA-:0:0:1:00:0:1:0:2:10

41S-32S-C
p–2 [D 1126–133] "<=20


Analyzed in Rollout No double Double/Take
Player Winning Chances: 53.210% (G:16.482% B:1.232%) 53.163% (G:19.434% B:2.581%)
Opponent Winning Chances: 46.790% (G:12.511% B:1.023%) 46.837% (G:13.196% B:1.636%)
Cubeless Equities +0.3938 +1.1265
Cubeful Equities
No double:+0.9930 (-0.0070)±0.0021 (+0.9909..+0.9951)
Double/Take:+1.1265 (+0.1265)±0.0029 (+1.1236..+1.1294)
Double/Pass:+1.0000
Best Cube action: Double / Pass
Rollout details
20736 Games rolled with Variance Reduction.
Dice Seed: 79553643
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 13 hours 46 minutes
White is Player 2

score: 1
pip: 162
2 point match
pip: 162
score: 0

Blue is Player 1
XGID=-a-a--E-CA--dD-a-c-e---AA-:0:0:1:00:0:1:0:2:10

41S-32Z-C
p–2 [D 1129–129] "<=31


Analyzed in Rollout No double Double/Take
Player Winning Chances: 53.255% (G:16.378% B:0.981%) 53.231% (G:19.238% B:2.476%)
Opponent Winning Chances: 46.745% (G:12.714% B:0.948%) 46.769% (G:13.781% B:1.630%)
Cubeless Equities +0.3927 +1.1293
Cubeful Equities
No double:+1.0000 (0.0000)±0.0016 (+0.9984..+1.0015)
Double/Take:+1.1293 (+0.1293)±0.0023 (+1.1269..+1.1316)
Double/Pass:+1.0000
Best Cube action: Double / Pass
Rollout details
31104 Games rolled with Variance Reduction.
Dice Seed: 64026929
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:52.0%
Take Decision confidence:100.0%
Duration: 16 hours 40 minutes

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