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Related Paradoxes

Posted By: Paul Weaver
Date: Wednesday, 5 November 2014, at 4:28 p.m.

In Response To: Who gets this right over the board (Phil Simborg)

On the left, Blue is over 60% and should not double. On the right, he is under 54% but Blue should double. Scroll down to see another contrasting pair.





White is Player 2

score: 4
pip: 6
9 point match
pip: 8
score: 7

Blue is Player 1
XGID=---A-A---------------a-a--:0:0:1:00:7:4:0:9:10
Blue on roll, cube action?

Analyzed in Rollout No double Double/Take
Player Winning Chances: 60.51% (G:0.00% B:0.00%) 60.51% (G:0.00% B:0.00%)
Opponent Winning Chances: 39.49% (G:0.00% B:0.00%) 39.49% (G:0.00% B:0.00%)
Cubeless Equities +0.210 +1.001
Cubeful Equities
No double:+0.2150.000 (+0.215..+0.215)
Double/Take:0.000 (-0.215)0.000 (0.000..0.000)
Double/Pass:+1.000 (+0.785)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 17.7%
Rollout details
165888 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 8.7 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2





White is Player 2

score: 4
pip: 6
9 point match
pip: 8
score: 7

Blue is Player 1
XGID=---A-A-------------a------:0:0:1:00:7:4:0:9:10
Blue on roll, cube action?

Analyzed in Rollout No double Double/Take
Player Winning Chances: 53.86% (G:0.00% B:0.00%) 53.86% (G:0.00% B:0.00%)
Opponent Winning Chances: 46.14% (G:0.00% B:0.00%) 46.14% (G:0.00% B:0.00%)
Cubeless Equities +0.077 +0.693
Cubeful Equities
No double:-0.018 (-0.018)0.000 (-0.018..-0.018)
Double/Take:0.0000.000 (0.000..0.000)
Double/Pass:+1.000 (+1.000)
Best Cube action: Double / Take
Rollout details
165888 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 12.9 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

On the left, Blue leads 2a5a, Blue should double and White should pass. On the right, Blue trails 5a2a, Blue should not double and White has an easy take.





White is Player 1

score: 4
pip: 3
9 point match
pip: 6
score: 7

Blue is Player 2
XGID=--A-A-----------------a---:0:0:1:00:7:4:0:9:10
Blue on roll, cube action?

Analyzed in Rollout No double Double/Take
Player Winning Chances: 63.89% (G:0.00% B:0.00%) 63.89% (G:0.00% B:0.00%)
Opponent Winning Chances: 36.11% (G:0.00% B:0.00%) 36.11% (G:0.00% B:0.00%)
Cubeless Equities +0.278 +1.157
Cubeful Equities
No double:+0.278 (-0.722)0.000 (+0.278..+0.278)
Double/Take:+1.157 (+0.157)0.000 (+1.157..+1.157)
Double/Pass:+1.000
Best Cube action: Double / Pass
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 0.5 second

eXtreme Gammon Version: 2.10, MET: Kazaross XG2





White is Player 1

score: 7
pip: 3
9 point match
pip: 6
score: 4

Blue is Player 2
XGID=--A-A-----------------a---:0:0:1:00:4:7:0:9:10
Blue on roll, cube action?

Analyzed in Rollout No double Double/Take
Player Winning Chances: 63.89% (G:0.00% B:0.00%) 63.89% (G:0.00% B:0.00%)
Opponent Winning Chances: 36.11% (G:0.00% B:0.00%) 36.11% (G:0.00% B:0.00%)
Cubeless Equities +0.278 +0.129
Cubeful Equities
No double:+0.2780.000 (+0.278..+0.278)
Double/Take:+0.129 (-0.149)0.000 (+0.129..+0.129)
Double/Pass:+1.000 (+0.722)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 14.6%
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 0.3 second

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

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