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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: 82
7 point match
Crawford
pip: 117
score: 6

Blue is Player 1
XGID=-BBB--BaBABa-------bbdbcB-:0:0:1:22:6:0:1:7:10

Original position


1.Rollout19/7* 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 seconds
2.Rollout110/6 9/7* 7/5eq: -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: 3-ply, cube decisions: XG Roller





White is Player 2

score: 0
pip: 81
7 point match
Crawford
pip: 117
score: 6

Blue is Player 1
XGID=-BBB--BaBAB-a------bbdbcB-:0:0:1:22:6:0:1:7:10

Variant (White's 14pt blot is moved to her 13pt)


1.Rollout110/6 9/7* 7/5eq: -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 seconds
2.Rollout19/7* 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: 3-ply, cube decisions: XG Roller

The 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 five-prime. 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 after-positions 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 1-pip (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 mere-5k rollouts there is still variance of +/- .0038 (accounting for +/- .0019 for each play in each position).]

Nice problem.

Nack

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