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42P-51S-52S-55A-F-C plus seven relatives, ROLLOUTS
Posted By: Nack Ballard In Response To: 42P-51S-52S-55A-F-C plus five relatives, CORRECTED DIAGRAMS (Nack Ballard)
Date: Thursday, 29 May 2014, at 8:51 p.m.
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] "<=20Nactation tutorial • explanation of nacbracs • nacubracs
(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] "<=5These 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: 157Unlimited Game
Jacoby Beaverpip: 140
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 2 hours 14 minutes
White is Player 2
score: 0
pip: 157Unlimited Game
Jacoby Beaverpip: 141
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 2 hours 41 minutes
White is Player 2
score: 0
pip: 158Unlimited Game
Jacoby Beaverpip: 140
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 99.9% Duration: 7 hours 55 minutes
White is Player 2
score: 0
pip: 158Unlimited Game
Jacoby Beaverpip: 141
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 50.0% Duration: 1 day 07 hours 37 minutes
White is Player 2
score: 0
pip: 167Unlimited Game
Jacoby Beaverpip: 140
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 2 hours 30 minutes
White is Player 2
score: 0
pip: 167Unlimited Game
Jacoby Beaverpip: 141
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 2 hours 45 minutes
White is Player 2
score: 0
pip: 160Unlimited Game
Jacoby Beaverpip: 140
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 2 hours 38 minutes
White is Player 2
score: 0
pip: 160Unlimited Game
Jacoby Beaverpip: 141
score: 0
Blue is Player 1XGID=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 RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 1 hour 48 minutes
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