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Too good advanced exercise -- SPOILER

Posted By: Nack Ballard
Date: Tuesday, 3 November 2015, at 4:16 p.m.

In Response To: Too good advanced exercise (Phil Simborg)





White is Player 2

score: 0
pip: 76
Unlimited Game
Jacoby Beaver
pip: 25
score: 0

Blue is Player 1
XGID=-a-----A----------Acbcbbb-:1:1:1:00:0:0:3:0:10

Blue 17pt + 7pt, White 6pt + 4pt
NOT Too Good to Redouble


Analyzed in Rollout No redouble Redouble/Take
  Player Winning Chances: 79.04% (G:23.53% B:2.43%) 79.21% (G:23.34% B:2.58%)
  Opponent Winning Chances: 20.96% (G:0.00% B:0.00%) 20.79% (G:0.00% B:0.00%)
  Cubeless Equities +0.840 +1.687
Cubeful Equities
No redouble:+0.939 (-0.061)กำ0.004 (+0.935..+0.943)
Redouble/Take:+1.509 (+0.509)กำ0.008 (+1.501..+1.517)
Redouble/Pass:+1.000
 
Best Cube action: Redouble / Pass
Rollout details
5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
 
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 3 minutes 18 seconds
Good morning. Nice puzzle.

I like scotty's answer: "On the bar" (one or both checkers). In case you would argue that's not "on the board," then I suspect the solution above is unique.

If you advance Blue's trailing checker a pip (big gain on double 5s), the cube decision is very close (see 3- and 4-ply rollouts below -- if you widen your window enough, they'll appear side by side).

I recommend adjusting White's spares two (or three) pips, as shown in the final two diagrams, so that the 18pt + 7pt solution is more clearly unique (it is more likely to hold up with future bot rollouts).

Nack





White is Player 2

score: 0
pip: 76
Unlimited Game
Jacoby Beaver
pip: 24
score: 0

Blue is Player 1
XGID=-a-----A---------A-cbcbbb-:1:1:1:00:0:0:3:0:10

Blue 17pt + 7pt, White 6pt + 4pt, 3-ply
BARELY Too Good to Redouble


Analyzed in Rollout No redouble Redouble/Take
  Player Winning Chances: 80.11% (G:28.04% B:2.96%) 80.17% (G:27.75% B:3.33%)
  Opponent Winning Chances: 19.89% (G:0.00% B:0.00%) 19.83% (G:0.00% B:0.00%)
  Cubeless Equities +0.912 +1.829
Cubeful Equities
No redouble:+1.007กำ0.002 (+1.004..+1.009)
Redouble/Take:+1.662 (+0.656)กำ0.005 (+1.658..+1.667)
Redouble/Pass:+1.000 (-0.007)
 
Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 1.0%
Rollout details
15552 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
 
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 12 minutes 23 seconds
White is Player 2

score: 0
pip: 76
Unlimited Game
Jacoby Beaver
pip: 24
score: 0

Blue is Player 1
XGID=-a-----A---------A-cbcbbb-:1:1:1:00:0:0:3:0:10

Blue 17pt + 7pt, White 6pt + 4pt, 4-ply
BARELY Too Good to Redouble


Analyzed in Rollout No redouble Redouble/Take
  Player Winning Chances: 80.13% (G:27.75% B:2.90%) 80.36% (G:27.07% B:3.24%)
  Opponent Winning Chances: 19.87% (G:0.00% B:0.00%) 19.64% (G:0.00% B:0.00%)
  Cubeless Equities +0.909 +1.821
Cubeful Equities
No redouble:+1.004กำ0.003 (+1.001..+1.007)
Redouble/Take:+1.655 (+0.651)กำ0.007 (+1.648..+1.662)
Redouble/Pass:+1.000 (-0.004)
 
Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 0.6%
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 54270926
Moves and cube decisions: 4-ply
 
Double Decision confidence:99.5%
Take Decision confidence:100.0%
Duration: 28 minutes 58 seconds
 
White is Player 2

score: 0
pip: 74
Unlimited Game
Jacoby Beaver
pip: 25
score: 0

Blue is Player 1
XGID=-a-----A----------Abcbcbb-:1:1:1:00:0:0:3:0:10

Blue 18pt + 7pt, White 5pt + 3pt
(Still) NOT Too Good to Redouble


Analyzed in Rollout No redouble Redouble/Take
  Player Winning Chances: 80.32% (G:23.75% B:1.91%) 80.75% (G:23.29% B:2.07%)
  Opponent Winning Chances: 19.68% (G:0.00% B:0.00%) 19.25% (G:0.00% B:0.00%)
  Cubeless Equities +0.863 +1.737
Cubeful Equities
No redouble:+0.960 (-0.040)กำ0.004 (+0.956..+0.964)
Redouble/Take:+1.579 (+0.579)กำ0.007 (+1.572..+1.586)
Redouble/Pass:+1.000
 
Best Cube action: Redouble / Pass
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 31027603
Moves: 3-ply, cube decisions: XG Roller
 
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 6 minutes 49 seconds
White is Player 2

score: 0
pip: 74
Unlimited Game
Jacoby Beaver
pip: 24
score: 0

Blue is Player 1
XGID=-a-----A---------A-bcbcbb-:1:1:1:00:0:0:3:0:10

Blue 17pt + 7pt, White 5pt + 3pt
(Clearly) Too Good to Redouble


Analyzed in Rollout No redouble Redouble/Take
  Player Winning Chances: 81.49% (G:27.96% B:2.82%) 81.58% (G:27.59% B:3.12%)
  Opponent Winning Chances: 18.51% (G:0.00% B:0.00%) 18.42% (G:0.00% B:0.00%)
  Cubeless Equities +0.938 +1.878
Cubeful Equities
No redouble:+1.028กำ0.004 (+1.025..+1.032)
Redouble/Take:+1.717 (+0.689)กำ0.009 (+1.709..+1.726)
Redouble/Pass:+1.000 (-0.028)
 
Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 4.0%
Rollout details
5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
 
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 3 minutes 07 seconds

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