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Racing Cube Decisions at -3/-4 and -4/-3

Posted By: Paul Weaver
Date: Sunday, 27 June 2010, at 10:58 p.m.

In Response To: What Stick fails to mention in 3 away 4 ayay article at GV (rew)

Seven racing positions have been rolled out on XG and will be posted below.

(1) Race-102-114-Money: Equity is 0.973, trailer wins 22.04%.

(2) Race-96-108-Money: Equity is 1.014, trailer wins 21.39%.

Interpolating between these two equities, I conclude that when the equity is 1.000, the trailer wins 21.61%. In other words, in a race of this length, the trailer, with heavy recube vig, can take a 21.61% position.

(3) Race-102-113-3A-4A: Equity is 0.991, trailer wins 23.51%.

(4) Race-102-113-3A-4A-Crossover: Equity is 0.982, trailer wins 23.60%.

(5) Race-102-114-3A-4A: Equity is 1.087, trailer wins 22.05%.

(3) and (4) have the same pip count; the difference is one crossover. Interesting to see that in this case, the crossover makes a difference in equity of 0.009 and a difference in winning % of 0.09%.

Interpolating between (4) and (5), I conclude that when the equity is 1.000, the trailer wins 23.33%. In other words, the trailer, at this score (3A-4A), in a race of this length can take a 23.33% position.

(6) Race-102-114-4A-3A: Equity is 0.971, trailer wins 22.04%.

(7) Race-96-108-4A-3A: Equity is 1.014, trailer wins 21.38%.

Notice that the equities and % in (1) and (6) are almost identical. Also notice that (2) and (7) are almost identical.

Interpolating between (6) and (7), I conclude that when the equity is 1.000, the trailer wins 21.59%. In other words, the trailer, at 4A-3A can take a 21.59% position.

Conclusions:

(1) Money marginal take/pass for race of this length occurs when trailer wins 21.61%.

(2) Marginal take/pass at 3A-4A occurs when trailer wins 23.33%.

(3) Marginal take/pass at 4A-3A occurs when trailer wins 21.59%.

The money take point appears to be essentially identical to the 4A-3A take point.

Observation that may be of interest to perverted readers: The trailer wins a gammon between 0.01% and 0.02%, 1 or 2 games in 10,000.

I welcome feedback regarding my methodology from anyone, but I would especially like to hear from Nack, Neil, Stick and David.

Rollouts posted below:





is Player 2

score: 0
pip: 114
Money session
Jacoby Beaver
pip: 102
score: 0

is Player 1
XGID=----BCC-DB-Ab--abc-cbb----:0:0:1:00:0:0:3:0:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 77.96% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.04% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 77.99% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.01% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.559
Double:+1.120
Cubeful Equities
No Double:+0.868 (-0.106)
Double/Take:+0.973
Double/Drop:+1.000 (+0.027)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.002 (+0.865...+0.870)
Confidence Double: ± 0.004 (+0.969...+0.977)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 3 hours 43 minutes

eXtreme Gammon Version: 1.12
is Player 2

score: 0
pip: 108
Money session
Jacoby Beaver
pip: 96
score: 0

is Player 1
XGID=----BDD-CA-Ab--aab-dcb----:0:0:1:00:0:0:3:0:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 78.61% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 21.39% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 78.68% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 21.32% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.572
Double:+1.147
Cubeful Equities
No Double:+0.881 (-0.119)
Double/Take:+1.014 (+0.014)
Double/Drop:+1.000
Best Cube action: Double / Drop
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.002 (+0.879...+0.883)
Confidence Double: ± 0.004 (+1.010...+1.018)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 2 hours 25 minutes

eXtreme Gammon Version: 1.12
is Player 2

score: 0
pip: 113
4 point match
pip: 102
score: 1

is Player 1
XGID=----BCC-DB-Ab--abbacbb----:0:0:1:00:1:0:0:4:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 76.49% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 23.51% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 76.63% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 23.37% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.530
Double:+1.504
Cubeful Equities
No Double:+0.848 (-0.143)
Double/Take:+0.991
Double/Drop:+1.000 (+0.009)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.004 (+0.844...+0.852)
Confidence Double: ± 0.005 (+0.986...+0.996)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 3 hours 59 minutes

eXtreme Gammon Version: 1.12, MET: eXtremeGammon
is Player 2

score: 0
pip: 113
4 point match
pip: 102
score: 1

is Player 1
XGID=----BCC-DB-Aaa-abc-cbb----:0:0:1:00:1:0:0:4:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 76.40% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 23.60% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 76.52% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 23.48% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.528
Double:+1.499
Cubeful Equities
No Double:+0.849 (-0.133)
Double/Take:+0.982
Double/Drop:+1.000 (+0.018)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.004 (+0.845...+0.853)
Confidence Double: ± 0.005 (+0.976...+0.987)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 4 hours 41 minutes

eXtreme Gammon Version: 1.12, MET: eXtremeGammon
is Player 2

score: 0
pip: 114
4 point match
pip: 102
score: 1

is Player 1
XGID=----BCC-DB-Ab--abc-cbb----:0:0:1:00:1:0:0:4:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 77.95% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.05% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 78.00% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.00% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.559
Double:+1.569
Cubeful Equities
No Double:+0.887 (-0.113)
Double/Take:+1.087 (+0.087)
Double/Drop:+1.000
Best Cube action: Double / Drop
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.003 (+0.884...+0.890)
Confidence Double: ± 0.005 (+1.082...+1.092)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 3 hours 45 minutes

eXtreme Gammon Version: 1.12, MET: eXtremeGammon
is Player 2

score: 1
pip: 114
4 point match
pip: 102
score: 0

is Player 1
XGID=----BCC-DB-Ab--abc-cbb----:0:0:1:00:0:1:0:4:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 77.96% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.04% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 77.97% (G: 0.02% B: 0.00%)
Opponent Winning Chances: 22.03% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.559
Double:+1.090
Cubeful Equities
No Double:+0.863 (-0.108)
Double/Take:+0.971
Double/Drop:+1.000 (+0.029)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.003 (+0.860...+0.866)
Confidence Double: ± 0.003 (+0.968...+0.975)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 4 hours 36 minutes

eXtreme Gammon Version: 1.12, MET: eXtremeGammon
is Player 2

score: 1
pip: 108
4 point match
pip: 96
score: 0

is Player 1
XGID=----BDD-CA-Ab--aab-dcb----:0:0:1:00:0:1:0:4:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 78.62% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 21.38% (G: 0.00% B: 0.00%)
Double/Take
Player Winning Chances: 78.68% (G: 0.01% B: 0.00%)
Opponent Winning Chances: 21.32% (G: 0.00% B: 0.00%)
Cubeless Equities
No Double:+0.572
Double:+1.123
Cubeful Equities
No Double:+0.874 (-0.126)
Double/Take:+1.014 (+0.014)
Double/Drop:+1.000
Best Cube action: Double / Drop
Rollout details
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.003 (+0.871...+0.876)
Confidence Double: ± 0.003 (+1.011...+1.017)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 2 hours 15 minutes

eXtreme Gammon Version: 1.12, MET: eXtremeGammon

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