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22 to play  VARIANT (1 pip different)  Rollouts and explanation
Posted By: Nack Ballard
Date: Thursday, 15 November 2018, at 12:34 a.m.
In Response To: Help: 22 to play  VARIANT (1 pip different) (David Levy)
White is Player 2
score: 0
pip: 827 point match
Crawfordpip: 117
score: 6
Blue is Player 1XGID=BBBBaBABabbdbcB:0:0:1:22:6:0:1:7:10 Original position
1. Rollout^{1} 9/7* 7/5 6/4(2) eq: 0.471
Player:
Opponent:28.81% (G:3.27% B:0.03%)
71.19% (G:27.47% B:1.44%)Conf.: ± 0.002 (0.473...0.469)  [100.0%]
Duration: 10 minutes 30 seconds2. Rollout^{1} 10/6 9/7* 7/5 eq: 0.483 (0.011)
Player:
Opponent:28.93% (G:3.30% B:0.04%)
71.07% (G:32.05% B:2.10%)Conf.: ± 0.002 (0.485...0.481)  [0.0%]
Duration: 11 minutes 17 seconds^{1} 5184 Games rolled with Variance Reduction.
Dice Seed: 34574574
Moves: 3ply, cube decisions: XG Roller
White is Player 2
score: 0
pip: 817 point match
Crawfordpip: 117
score: 6
Blue is Player 1XGID=BBBBaBABabbdbcB:0:0:1:22:6:0:1:7:10 Variant (White's 14pt blot is moved to her 13pt)
1. Rollout^{1} 10/6 9/7* 7/5 eq: 0.461
Player:
Opponent:29.78% (G:4.22% B:0.05%)
70.22% (G:30.67% B:1.87%)Conf.: ± 0.002 (0.463...0.459)  [100.0%]
Duration: 12 minutes 43 seconds2. Rollout^{1} 9/7* 7/5 6/4(2) eq: 0.469 (0.008)
Player:
Opponent:28.94% (G:3.62% B:0.04%)
71.06% (G:26.83% B:1.46%)Conf.: ± 0.002 (0.470...0.467)  [0.0%]
Duration: 11 minutes 36 seconds^{1} 5184 Games rolled with Variance Reduction.
Dice Seed: 58946702
Moves: 3ply, cube decisions: XG RollerThe original position is first (on the left if your window is sufficiently wide). The variant position is second (on the right). The only difference is White's 1 pip in the outfield. Why does that cause 9/7*/5 6/4(2) to go from +.011 to –.008? For the answer, read on.
When Blue plays 10/6 9/7*/5 and White rolls 44 (from the bar):
In the first (original) position, White can play 14/2 in the first position, maintaining her fiveprime. In the second (variant) position, White must play 13/5 6/2, breaking her 6pt.
We can check the approximate impact of the double 4s by plugging the afterpositions into XGR++. White's equity is .370 in the first case, compared to –.284 in the second case. The difference x 1/36 (chances of rolling double 4s) = .018. This accounts for almost all of (.011 + .008) = .019 difference that is rolled out.
White's 1pip (14/13) difference is almost immaterial when Blue plays 9/7*/5 6/4(2) because White's 44 will fan either way.
[The difference on double 6s (using the same methodology) is 20/36 of .001, and actually if you go out an extra decimal place with all numbers the sum including 66 lands almost exactly on the (.0112 + .0075) = .0187 rollout swing, but that's partly luck because with these mere5k rollouts there is still variance of +/ .0038 (accounting for +/ .0019 for each play in each position).]
Nice problem.
Nack

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