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42P-51S-52S-55A-F-C plus seven relatives, ROLLOUTS

Posted By: Nack Ballard
Date: Thursday, 29 May 2014, at 8:51 p.m.

In Response To: 42P-51S-52S-55A-F-C plus five relatives, CORRECTED DIAGRAMS (Nack Ballard)

Here is a nacubracs summary of the six rollout results:

........#1.... 31P-51S-52S-55A-F-C.. [D 791–102] "<=5
........#2.... 61P-51S-52S-55A-F-C.. [D 950–172] "<=5
........#3.... 42P-51S-52S-55A-F-C.. [D 1000–212] "<=164
........#4.... 31P-52S-52S-55A-F-C.. [D 808–115] "<=5
........#5.... 61P-52S-52S-55A-F-C.. [D 1093–265] "<=5
........#6.... 42P-52S-52S-55A-F-C..
[D 1008–217] "<=20

Nactation tutorialexplanation of nacbracsnacubracs (nacbracs for cube actions)

According to these XG2 rollouts (with 3-ply checker play, and XGR cube actions), the ranking of the six positions (strongest to weakest) for Blue is:

........5, 6, 3, 2, 4, 1

This is the same order chosen (or implied) by the three respondents Mike, Igor and Tim, except for position #2, which all respondents passed (as did I, upon a time, before seeing the rollout).

Blue's positions where he has split to the 22pt (a pip closer to participating in the blitz, or starting a better anchor in case the blitz fails) are all stronger than the positions he has merely split to the 23pt, though the difference in value is small (.017 or .007) when the opponent owns her 5pt or 4pt. The value of the 22pt checker being closer to home is mostly offset by the cost of having 5s (or 5s and 3s), most notably double 5s, blocked.

The difference between #2 (61P-51S-52S-55A-F-T = 0.950) and #5 (61P-52S-52S-55A-F-T = 1.093), which is .143 if both positions are taken (though only .050 with correct cube action), understandably confounded the respondents. As Igor pointed out, Blue's 22pt checker sees the daylight of the 16pt (more important when the 18pt is blocked). The only roll that is played differently with any immediate meaningful gain is double 6s, but the possibility of future 6s and 1s (played 22/21, thereby releasing 5s) offer ongoing improvement.

As a bonus, here are two fourth-roll positions that I think belong with the set of six fifth roll positions:

........51S-11E-55A-F-C.. [D 892–152] "<=5
........52S-11E-55A-F-C.. [D 905–163] "<=5

These positions are most closely related to #1 and #4, in that Opp's 5pt is made. (The difference is that her second 6pt spare is back on her midpoint.)

Below, I've rearranged the positions in diagrammed pairs, with Blue's 52S on the left and his 51S on the right (assuming you widen your window enough). For reference, the original numberings (plus #1x and #4x for the two new positions) appear in green typeface. In this way, all eight positions are ordered from Blue's strongest to his weakest, with the exception of the second one (61P-51S...).

Nack





White is Player 2

score: 0
pip: 157
Unlimited Game
Jacoby Beaver
pip: 140
score: 0

Blue is Player 1
XGID=bB-B--C-B---cD---cbe--A-A-:0:0:1:00:0:0:3:0:10

#5.... 61P-52S-52S-55A-F-C [D 1093–265] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 66.61% (G:38.77% B:0.49%) 66.86% (G:41.90% B:0.49%)
Opponent Winning Chances: 33.39% (G:7.46% B:0.38%) 33.14% (G:8.01% B:0.46%)
Cubeless Equities +0.647 +1.353
Cubeful Equities
No double:+0.828 (-0.172)±0.005 (+0.822..+0.833)
Double/Take:+1.093 (+0.093)±0.009 (+1.083..+1.102)
Double/Pass:+1.000
Best Cube action: Double / Pass
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 70757351
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 2 hours 14 minutes




White is Player 2

score: 0
pip: 157
Unlimited Game
Jacoby Beaver
pip: 141
score: 0

Blue is Player 1
XGID=bB-B--C-B---cD---cbe---AA-:0:0:1:00:0:0:3:0:10

#2.... 61P-51S-52S-55A-F-C [D 950–172] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 64.97% (G:38.18% B:0.45%) 65.09% (G:40.18% B:0.43%)
Opponent Winning Chances: 35.03% (G:8.16% B:0.43%) 34.91% (G:8.57% B:0.47%)
Cubeless Equities +0.600 +1.235
Cubeful Equities
No double:+0.779 (-0.172)±0.006 (+0.772..+0.785)
Double/Take:+0.950±0.009 (+0.941..+0.960)
Double/Pass:+1.000 (+0.050)
Best Cube action: Double / Take
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 43835611
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 2 hours 41 minutes





White is Player 2

score: 0
pip: 158
Unlimited Game
Jacoby Beaver
pip: 140
score: 0

Blue is Player 1
XGID=bB-B--C-B---dD---c-d-bA-A-:0:0:1:00:0:0:3:0:10

#6.... 42P-52S-52S-55A-F-C [D 1008–217] "<=20


Analyzed in Rollout No double Double/Take
Player Winning Chances: 65.16% (G:39.75% B:0.43%) 65.52% (G:42.39% B:0.47%)
Opponent Winning Chances: 34.84% (G:8.85% B:0.50%) 34.48% (G:9.37% B:0.58%)
Cubeless Equities +0.612 +1.279
Cubeful Equities
No double:+0.791 (-0.209)±0.003 (+0.788..+0.795)
Double/Take:+1.008 (+0.008)±0.005 (+1.003..+1.013)
Double/Pass:+1.000
Best Cube action: Double / Pass
Rollout details
20736 Games rolled with Variance Reduction.
Dice Seed: 70757351
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:99.9%
Duration: 7 hours 55 minutes




White is Player 2

score: 0
pip: 158
Unlimited Game
Jacoby Beaver
pip: 141
score: 0

Blue is Player 1
XGID=bB-B--C-B---dD---c-d-b-AA-:0:0:1:00:0:0:3:0:10

#3.... 42P-51S-52S-55A-F-C [D 1000–212] "<=164


Analyzed in Rollout No double Double/Take
Player Winning Chances: 65.045% (G:39.768% B:0.440%) 65.555% (G:42.074% B:0.474%)
Opponent Winning Chances: 34.955% (G:9.066% B:0.521%) 34.445% (G:9.550% B:0.600%)
Cubeless Equities +0.6071 +1.2701
Cubeful Equities
No double:+0.7882 (-0.2118)±0.0011 (+0.7871..+0.7894)
Double/Take:+1.0000±0.0016 (+0.9984..+1.0016)
Double/Pass:+1.0000 (+0.0000)
Best Cube action: Double / Take
Rollout details
164600 Games rolled with Variance Reduction.
Dice Seed: 85570326
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:50.0%
Duration: 1 day 07 hours 37 minutes





White is Player 2

score: 0
pip: 167
Unlimited Game
Jacoby Beaver
pip: 140
score: 0

Blue is Player 1
XGID=bB-B--C-B---eD---c-cb-A-A-:0:0:1:00:0:0:3:0:10

#4x.... 52S-11E-55A-F-C [D 905–163] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 63.21% (G:41.46% B:0.38%) 63.48% (G:42.97% B:0.37%)
Opponent Winning Chances: 36.79% (G:9.18% B:0.49%) 36.52% (G:9.44% B:0.51%)
Cubeless Equities +0.586 +1.207
Cubeful Equities
No double:+0.742 (-0.163)±0.008 (+0.735..+0.750)
Double/Take:+0.905±0.010 (+0.895..+0.916)
Double/Pass:+1.000 (+0.095)
Best Cube action: Double / Take
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 85570326
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 2 hours 30 minutes




White is Player 2

score: 0
pip: 167
Unlimited Game
Jacoby Beaver
pip: 141
score: 0

Blue is Player 1
XGID=bB-B--C-B---eD---c-cb--AA-:0:0:1:00:0:0:3:0:10

#1x.... 51S-11E-55A-F-C [D 892–152] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 63.22% (G:40.43% B:0.38%) 63.57% (G:41.72% B:0.42%)
Opponent Winning Chances: 36.78% (G:9.09% B:0.51%) 36.43% (G:9.31% B:0.52%)
Cubeless Equities +0.577 +1.189
Cubeful Equities
No double:+0.739 (-0.152)±0.007 (+0.733..+0.746)
Double/Take:+0.892±0.010 (+0.882..+0.901)
Double/Pass:+1.000 (+0.108)
Best Cube action: Double / Take
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 43835611
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 2 hours 45 minutes





White is Player 2

score: 0
pip: 160
Unlimited Game
Jacoby Beaver
pip: 140
score: 0

Blue is Player 1
XGID=bB-B--C-B---dD---c-db-A-A-:0:0:1:00:0:0:3:0:10

#4.... 31P-52S-52S-55A-F-C [D 808–115] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 62.43% (G:39.86% B:0.42%) 62.52% (G:41.30% B:0.42%)
Opponent Winning Chances: 37.57% (G:10.19% B:0.63%) 37.48% (G:10.66% B:0.69%)
Cubeless Equities +0.543 +1.108
Cubeful Equities
No double:+0.693 (-0.115)±0.007 (+0.686..+0.700)
Double/Take:+0.808±0.010 (+0.798..+0.817)
Double/Pass:+1.000 (+0.192)
Best Cube action: Double / Take
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 34942079
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 2 hours 38 minutes




White is Player 2

score: 0
pip: 160
Unlimited Game
Jacoby Beaver
pip: 141
score: 0

Blue is Player 1
XGID=bB-B--C-B---dD---c-db--AA-:0:0:1:00:0:0:3:0:10

#1.... 31P-51S-52S-55A-F-C [D 791–102] "<=5


Analyzed in Rollout No double Double/Take
Player Winning Chances: 62.36% (G:38.82% B:0.40%) 62.63% (G:40.23% B:0.40%)
Opponent Winning Chances: 37.64% (G:10.42% B:0.63%) 37.37% (G:10.78% B:0.71%)
Cubeless Equities +0.529 +1.088
Cubeful Equities
No double:+0.689 (-0.102)±0.007 (+0.682..+0.696)
Double/Take:+0.791±0.010 (+0.781..+0.801)
Double/Pass:+1.000 (+0.209)
Best Cube action: Double / Take
Rollout details
5184 Games rolled with Variance Reduction.
Dice Seed: 85570326
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 1 hour 48 minutes

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