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Variance of Variants

Posted By: Nack Ballard
Date: Saturday, 10 October 2015, at 9:34 p.m.

In Response To: Variant (Stick)





White is Player 2

score: 0
pip: 138
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-FbbC-E-----------abbbca--:2:1:1:11:0:0:3:0:10

Original position


1.Rollout16/4 1/Off(2)eq: +1.017
Player:
Opponent:
67.26% (G:44.72% B:2.34%)
32.74% (G:0.00% B:0.00%)
Conf.: กำ 0.003 (+1.014...+1.020) - [100.0%]
Duration: 1 hour 03 minutes
2.Rollout11/Off(4)eq: +0.998 (-0.019)
Player:
Opponent:
66.32% (G:42.78% B:4.45%)
33.68% (G:0.00% B:0.00%)
Conf.: กำ 0.001 (+0.997...+0.999) - [0.0%]
Duration: 12 minutes 58 seconds
 
1 5184 Games rolled with Variance Reduction.
Dice Seed: 7059602
Moves: 3-ply, cube decisions: XG Roller

What is a little ... interesting(?) between the two rollouts that unless I'm misreading something because it's 3am on a Friday night and I'm completely sober per usual your rollout (5k, same settings) has virtually the same amount of variance as my 1k rollout.

That's a sobering observation.

Above is my 5k rollout of the original position. (Stick's was 1k.)

Below are rollouts of three variants. Playing four checkers off doesn't quite become best in the "4pt shift" position. It crosses over to best in the "5pt shift" (that I previously posted), and it's best by even more in the "6pt shift."

I'm not sure what to make of the confidence intervals, but I can make a guess. If White hits in the original position, she has an appreciably better chance to contain, with relative safety. In the shifted positions, she will be in constant jeopardy (of losing quickly or getting gammoned) until she remakes her high point (4pt, 5pt or 6pt). Many of the risks entailed in doing that increase variance.





White is Player 2

score: 0
pip: 132
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-FbbC-E-----------abb-cab-:2:1:1:11:0:0:3:0:10

4pt shift


1.Rollout16/4 1/Off(2)eq: +1.084
Player:
Opponent:
73.18% (G:47.59% B:2.14%)
26.82% (G:0.00% B:0.00%)
Conf.: กำ 0.003 (+1.081...+1.086) - [72.6%]
Duration: 49 minutes 55 seconds
2.Rollout11/Off(4)eq: +1.082 (-0.001)
Player:
Opponent:
73.41% (G:47.49% B:4.37%)
26.59% (G:0.00% B:0.00%)
Conf.: กำ 0.004 (+1.078...+1.087) - [27.4%]
Duration: 1 hour 02 minutes
 
1 5184 Games rolled with Variance Reduction.
Dice Seed: 9265210
Moves: 3-ply, cube decisions: XG Roller





White is Player 2

score: 0
pip: 130
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-FbbC-E-----------ab-bcab-:2:1:1:11:0:0:3:0:10

5pt shift


1.Rollout11/Off(4)eq: +1.109
Player:
Opponent:
74.70% (G:47.79% B:4.28%)
25.30% (G:0.00% B:0.00%)
Conf.: กำ 0.004 (+1.105...+1.113) - [100.0%]
Duration: 56 minutes 37 seconds
2.Rollout16/4 1/Off(2)eq: +1.093 (-0.016)
Player:
Opponent:
74.16% (G:47.39% B:2.10%)
25.84% (G:0.00% B:0.00%)
Conf.: กำ 0.003 (+1.090...+1.096) - [0.0%]
Duration: 45 minutes 44 seconds
 
1 5184 Games rolled with Variance Reduction.
Dice Seed: 9265210
Moves: 3-ply, cube decisions: XG Roller





White is Player 2

score: 0
pip: 128
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-FbbC-E-----------a-bbcab-:2:1:1:11:0:0:3:0:10

6pt shift


1.Rollout11/Off(4)eq: +1.187
Player:
Opponent:
77.71% (G:49.90% B:4.11%)
22.29% (G:0.00% B:0.00%)
Conf.: กำ 0.004 (+1.183...+1.192) - [100.0%]
Duration: 1 hour 07 minutes
2.Rollout16/4 1/Off(2)eq: +1.144 (-0.044)
Player:
Opponent:
77.10% (G:48.68% B:2.03%)
22.90% (G:0.00% B:0.00%)
Conf.: กำ 0.003 (+1.140...+1.147) - [0.0%]
Duration: 1 hour 06 minutes
 
1 5184 Games rolled with Variance Reduction.
Dice Seed: 9265210
Moves: 3-ply, cube decisions: XG Roller

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