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Posted By: Paul Weaver
Date: Friday, 1 November 2013, at 3:08 p.m.

In Response To: Fourth-Roll Quiz: Blue to play 32 (Paul Weaver)

First I will present the second roll position 52S-32 and its rollout result. Hitting two (6/3*/1*) leaves fewer shots that hit-and-down (13/11 6/3*), but hit-and-down has these advantages: Blue retains a much better chance of developing a prime and he has a lot more covers if missed.

Understanding the concept involved in this second-roll position helps one solve the related fourth-roll problems.

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-a-a--E-C---dE---d-e----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Book113/11 6/3* eq: -0.130
 Player:Opponent: 47.35% (G:12.89% B:0.71%)52.65% (G:16.56% B:1.24%) Conf.: ± 0.005 (-0.135...-0.125) - [100.0%]
2.Book124/21 13/11eq: -0.143 (-0.013)
 Player:Opponent: 46.87% (G:12.26% B:0.62%)53.13% (G:15.46% B:0.91%) Conf.: ± 0.004 (-0.147...-0.139) - [0.0%]
3.Book26/3* 3/1* eq: -0.148 (-0.018)
 Player:Opponent: 46.52% (G:12.83% B:0.54%)53.48% (G:15.65% B:0.96%) Conf.: ± 0.003 (-0.151...-0.144) - [0.0%]
4.Book124/22 6/3* eq: -0.149 (-0.019)
 Player:Opponent: 46.73% (G:12.09% B:0.61%)53.27% (G:15.42% B:0.95%) Conf.: ± 0.004 (-0.153...-0.145) - [0.0%]
5.Book313/11 13/10eq: -0.173 (-0.043)
 Player:Opponent: 46.10% (G:13.12% B:0.53%)53.90% (G:16.30% B:1.10%) Conf.: ± 0.007 (-0.181...-0.166) - [0.0%]
6.Book413/8eq: -0.182 (-0.053)
 Player:Opponent: 45.77% (G:11.56% B:0.44%)54.23% (G:15.04% B:0.74%) Conf.: ± 0.003 (-0.185...-0.180) - [0.0%]
1 Generated by Ken Bame on 10/18/2009 using eXtreme Gammon 1.04
36288 Games rolled with Variance Reduction.
using 21 dice rotation
Dice Seed: 1
Moves and cube decisions: 3-ply

2 Generated by Ken Bame on 2/9/2010 using eXtreme Gammon 1.12
62208 Games rolled with Variance Reduction.
Dice Seed: Random
Moves and cube decisions: 3-ply

3 Generated by GameSite 2000, Ltd on 2/26/2011 using eXtreme Gammon 2.00
10368 Games rolled with Variance Reduction.
Dice Seed: 77390818
Moves: 2-ply, cube decisions: 3-ply Red

4 Generated by Neil Kazaross on 10/6/2010 using eXtreme Gammon 1.21
46656 Games rolled with Variance Reduction.
Dice Seed: 60532124
Moves and cube decisions: 4-ply

eXtreme Gammon Version: 2.10

31P-31P-52S-32

Hitting-and-down (13/11 6/3*) is best here for the same reasons this play is best in the second roll position 52S-32 posted above. Hitting two (6/3*/1*) leaves fewer shots that hit-and-down (13/11 6/3*), but hit-and-down has these advantages: Blue retains a much better chance of developing a prime and he has a lot more covers if missed.

 White is NevzatDogan score: 0 pip: 156 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is peever
XGID=-a-a-BD-B---dE---c-db---B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout113/11 6/3* eq: -0.166
 Player:Opponent: 46.64% (G:14.13% B:0.64%)53.36% (G:18.18% B:1.35%) Conf.: ± 0.006 (-0.172...-0.160) - [100.0%]Duration: 1 hour 18 minutes
2.Rollout16/3* 3/1* eq: -0.184 (-0.018)
 Player:Opponent: 45.56% (G:14.48% B:0.42%)54.44% (G:17.27% B:0.96%) Conf.: ± 0.006 (-0.190...-0.178) - [0.0%]Duration: 1 hour 16 minutes
3.Rollout124/22 6/3* eq: -0.188 (-0.022)
 Player:Opponent: 45.96% (G:13.25% B:0.59%)54.04% (G:17.78% B:1.02%) Conf.: ± 0.006 (-0.194...-0.181) - [0.0%]Duration: 1 hour 20 minutes
4.Rollout124/21 13/11eq: -0.208 (-0.042)
 Player:Opponent: 45.73% (G:11.87% B:0.50%)54.27% (G:17.16% B:0.83%) Conf.: ± 0.005 (-0.213...-0.203) - [0.0%]Duration: 1 hour 12 minutes
5.Rollout213/8eq: -0.218 (-0.052)
 Player:Opponent: 44.72% (G:12.09% B:0.50%)55.28% (G:16.75% B:0.85%) Conf.: ± 0.017 (-0.235...-0.201) - [0.0%]Duration: 6 minutes 35 seconds
6.Rollout324/22 13/10eq: -0.229 (-0.063)
 Player:Opponent: 44.85% (G:11.53% B:0.48%)55.15% (G:17.23% B:0.77%) Conf.: ± 0.017 (-0.246...-0.212) - [0.0%]Duration: 6 minutes 48 seconds
1 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 917 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

3 916 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

42P-31P-52S-32

Hit-and-down is again correct.

 White is Player 2 score: 0 pip: 154 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=-a-a-BD-B---dE---c-d-b--B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout113/11 6/3* eq: -0.046
 Player:Opponent: 49.34% (G:15.39% B:0.70%)50.66% (G:17.08% B:1.30%) Conf.: ± 0.018 (-0.064...-0.028) - [99.9%]Duration: 6 minutes 38 seconds
2.Rollout16/3* 3/1* eq: -0.084 (-0.038)
 Player:Opponent: 47.64% (G:15.39% B:0.39%)52.36% (G:16.26% B:0.86%) Conf.: ± 0.016 (-0.099...-0.068) - [0.1%]Duration: 6 minutes 29 seconds
3.Rollout124/22 6/3* eq: -0.100 (-0.054)
 Player:Opponent: 48.20% (G:14.25% B:0.63%)51.80% (G:17.22% B:1.04%) Conf.: ± 0.018 (-0.118...-0.082) - [0.0%]Duration: 6 minutes 56 seconds
4.Rollout113/8eq: -0.136 (-0.090)
 Player:Opponent: 47.13% (G:12.89% B:0.46%)52.87% (G:15.96% B:0.79%) Conf.: ± 0.015 (-0.152...-0.121) - [0.0%]Duration: 5 minutes 56 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

61P-31P-52S-32

Hit-and-down is correct again.

 White is Player 2 score: 0 pip: 153 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=-a-a-BD-B---cE---cbe----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout113/11 6/3* eq: +0.030
 Player:Opponent: 50.67% (G:15.73% B:0.63%)49.33% (G:15.21% B:1.03%) Conf.: ± 0.016 (+0.014...+0.046) - [99.5%]Duration: 6 minutes 47 seconds
2.Rollout124/22 6/3* eq: 0.000 (-0.030)
 Player:Opponent: 50.23% (G:14.18% B:0.58%)49.77% (G:15.00% B:0.79%) Conf.: ± 0.016 (-0.016...+0.015) - [0.4%]Duration: 7 minutes 06 seconds
3.Rollout16/3* 3/1* eq: -0.010 (-0.040)
 Player:Opponent: 49.19% (G:15.82% B:0.45%)50.81% (G:14.89% B:0.89%) Conf.: ± 0.015 (-0.025...+0.005) - [0.0%]Duration: 6 minutes 52 seconds
4.Rollout124/21 13/11eq: -0.030 (-0.060)
 Player:Opponent: 49.51% (G:12.86% B:0.51%)50.49% (G:14.47% B:0.68%) Conf.: ± 0.015 (-0.045...-0.016) - [0.0%]Duration: 6 minutes 33 seconds
5.Rollout124/22 13/10eq: -0.084 (-0.114)
 Player:Opponent: 48.24% (G:12.92% B:0.51%)51.76% (G:15.45% B:0.72%) Conf.: ± 0.015 (-0.099...-0.069) - [0.0%]Duration: 6 minutes 23 seconds
6.Rollout124/22 24/21eq: -0.094 (-0.123)
 Player:Opponent: 48.19% (G:11.91% B:0.46%)51.81% (G:15.10% B:0.54%) Conf.: ± 0.014 (-0.107...-0.080) - [0.0%]Duration: 6 minutes 25 seconds
7.Rollout113/8eq: -0.096 (-0.126)
 Player:Opponent: 47.57% (G:13.28% B:0.50%)52.43% (G:14.57% B:0.80%) Conf.: ± 0.015 (-0.111...-0.081) - [0.0%]Duration: 6 minutes 13 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

31P-42P-52S-32

Hit-and-down now leaves more shots because White's 65 hits on Blue's 11pt. Hit-and-down is weaker here because Blue has less chance of forming a prime when he owns his 4pt instead of his 5pt. Blitzing therefore becomes a more reasonable choice.

 White is Player 2 score: 0 pip: 156 Unlimited GameJacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=-a-aB-D-B---dE---c-db---B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout16/3* 3/1* eq: -0.238
 Player:Opponent: 44.09% (G:14.17% B:0.44%)55.91% (G:17.97% B:1.03%) Conf.: ± 0.019 (-0.257...-0.219) - [99.4%]Duration: 6 minutes 34 seconds
2.Rollout124/21 13/11eq: -0.269 (-0.032)
 Player:Opponent: 44.08% (G:12.71% B:0.65%)55.92% (G:19.37% B:1.04%) Conf.: ± 0.016 (-0.285...-0.254) - [0.5%]Duration: 6 minutes 04 seconds
3.Rollout113/11 6/3* eq: -0.280 (-0.043)
 Player:Opponent: 44.04% (G:12.84% B:0.67%)55.96% (G:19.53% B:1.52%) Conf.: ± 0.018 (-0.299...-0.262) - [0.1%]Duration: 6 minutes 54 seconds
4.Rollout124/22 6/3* eq: -0.286 (-0.048)
 Player:Opponent: 43.37% (G:12.13% B:0.50%)56.63% (G:17.61% B:0.96%) Conf.: ± 0.015 (-0.301...-0.271) - [0.0%]Duration: 6 minutes 43 seconds
5.Rollout124/22 24/21eq: -0.286 (-0.048)
 Player:Opponent: 43.86% (G:11.73% B:0.60%)56.14% (G:18.97% B:0.77%) Conf.: ± 0.016 (-0.302...-0.270) - [0.0%]Duration: 6 minutes 15 seconds
6.Rollout113/8eq: -0.292 (-0.054)
 Player:Opponent: 43.17% (G:11.82% B:0.45%)56.83% (G:17.46% B:0.84%) Conf.: ± 0.015 (-0.306...-0.277) - [0.0%]Duration: 6 minutes 03 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

42P-42P-52S-32

Hit-and-down again leaves a shot on Blue's 11pt.

 White is Player 2 score: 0 pip: 154 Unlimited GameJacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=-a-aB-D-B---dE---c-d-b--B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout16/3* 3/1* eq: -0.146
 Player:Opponent: 46.57% (G:15.14% B:0.44%)53.43% (G:17.54% B:1.10%) Conf.: ± 0.009 (-0.155...-0.137) - [99.6%]Duration: 23 minutes 51 seconds
2.Rollout113/11 6/3* eq: -0.162 (-0.016)
 Player:Opponent: 46.86% (G:14.07% B:0.69%)53.14% (G:18.55% B:1.49%) Conf.: ± 0.008 (-0.171...-0.154) - [0.4%]Duration: 25 minutes 28 seconds
3.Rollout224/22 6/3* eq: -0.191 (-0.045)
 Player:Opponent: 45.87% (G:13.15% B:0.58%)54.13% (G:17.66% B:1.03%) Conf.: ± 0.016 (-0.207...-0.175) - [0.0%]Duration: 6 minutes 37 seconds
4.Rollout213/8eq: -0.232 (-0.085)
 Player:Opponent: 44.98% (G:11.91% B:0.47%)55.02% (G:16.95% B:0.83%) Conf.: ± 0.015 (-0.246...-0.217) - [0.0%]Duration: 5 minutes 53 seconds
1 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

42P-61P-52S-32

White's board is weaker now than above in 42P-42P-52S-32 and 42P-31P-52S-32, reducing Blue's cost of getting hit. Hit-and-down is now slightly better than hitting twice.

 White is Player 2 score: 0 pip: 153 Unlimited GameJacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=-a-aB-D-B---cE---cbe----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout113/11 6/3* eq: -0.078
 Player:Opponent: 48.34% (G:14.77% B:0.68%)51.66% (G:16.33% B:1.12%) Conf.: ± 0.004 (-0.081...-0.074) - [99.4%]Duration: 2 hours 23 minutes
2.Rollout16/3* 3/1* eq: -0.084 (-0.007)
 Player:Opponent: 47.48% (G:15.44% B:0.44%)52.52% (G:15.33% B:0.87%) Conf.: ± 0.004 (-0.088...-0.081) - [0.6%]Duration: 2 hours 17 minutes
3.Rollout224/21 13/11eq: -0.093 (-0.016)
 Player:Opponent: 48.08% (G:13.17% B:0.54%)51.92% (G:15.55% B:0.84%) Conf.: ± 0.005 (-0.099...-0.088) - [0.0%]Duration: 48 minutes 43 seconds
4.Rollout224/22 6/3* eq: -0.103 (-0.026)
 Player:Opponent: 47.60% (G:13.41% B:0.57%)52.40% (G:15.60% B:0.76%) Conf.: ± 0.005 (-0.109...-0.098) - [0.0%]Duration: 53 minutes 53 seconds
5.Rollout324/22 24/21eq: -0.158 (-0.081)
 Player:Opponent: 46.60% (G:11.35% B:0.44%)53.40% (G:15.79% B:0.57%) Conf.: ± 0.014 (-0.172...-0.144) - [0.0%]Duration: 6 minutes 11 seconds
6.Rollout313/8eq: -0.163 (-0.086)
 Player:Opponent: 45.84% (G:12.63% B:0.49%)54.16% (G:15.12% B:0.76%) Conf.: ± 0.015 (-0.178...-0.149) - [0.0%]Duration: 6 minutes 18 seconds
7.Rollout324/21 6/4eq: -0.173 (-0.095)
 Player:Opponent: 45.90% (G:11.61% B:0.50%)54.10% (G:15.22% B:0.68%) Conf.: ± 0.015 (-0.187...-0.158) - [0.0%]Duration: 6 minutes 18 seconds
1 27684 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

3 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

61P-61P-52S-32

Blue has only a one-point board with a stack on his 7pt while stripped on his 7pt and 8pt. Blue has little blitzing potential and he should instead view this as a prime-vs-prime position. Blue should split before White's prime gets more threatening. 24/21 13/11 also brings down a builder at little risk.

 White is Player 2 score: 0 pip: 153 Unlimited GameJacoby Beaver pip: 160 score: 0 Blue is Player 1
XGID=-a-a--EBB---cD---cbe----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout124/21 13/11eq: -0.148
 Player:Opponent: 46.75% (G:12.17% B:0.51%)53.25% (G:15.97% B:0.76%) Conf.: ± 0.006 (-0.153...-0.142) - [100.0%]Duration: 52 minutes 45 seconds
2.Rollout124/22 24/21eq: -0.161 (-0.013)
 Player:Opponent: 46.69% (G:10.83% B:0.45%)53.31% (G:15.92% B:0.54%) Conf.: ± 0.005 (-0.166...-0.155) - [0.0%]Duration: 49 minutes 44 seconds
3.Rollout124/22 6/3* eq: -0.185 (-0.037)
 Player:Opponent: 45.87% (G:11.69% B:0.47%)54.13% (G:15.87% B:0.77%) Conf.: ± 0.006 (-0.191...-0.179) - [0.0%]Duration: 57 minutes 01 second
4.Rollout213/11 6/3* eq: -0.194 (-0.046)
 Player:Opponent: 45.65% (G:12.98% B:0.56%)54.35% (G:17.52% B:1.24%) Conf.: ± 0.016 (-0.210...-0.178) - [0.0%]Duration: 7 minutes 13 seconds
5.Rollout26/3* 3/1* eq: -0.210 (-0.062)
 Player:Opponent: 44.87% (G:13.08% B:0.37%)55.13% (G:16.23% B:0.83%) Conf.: ± 0.014 (-0.224...-0.196) - [0.0%]Duration: 6 minutes 51 seconds
6.Rollout224/22 13/10eq: -0.230 (-0.082)
 Player:Opponent: 44.95% (G:11.47% B:0.45%)55.05% (G:16.91% B:0.80%) Conf.: ± 0.013 (-0.243...-0.217) - [0.0%]Duration: 6 minutes 13 seconds
7.Rollout213/8eq: -0.250 (-0.102)
 Player:Opponent: 44.17% (G:11.68% B:0.47%)55.83% (G:15.69% B:0.83%) Conf.: ± 0.015 (-0.264...-0.235) - [0.0%]Duration: 6 minutes 13 seconds
8.3-ply13/11 13/10eq: -0.250 (-0.102)
 Player:Opponent: 43.88% (G:11.77% B:0.48%)56.12% (G:17.05% B:1.22%)
1 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

31P-61P-52S-32

Blue needs to split now, before White's offense gets even stronger. Two-up (24/21 24/22) gives Blue his best chance to make an advanced anchor.

 White is Player 2 score: 0 pip: 156 Unlimited GameJacoby Beaver pip: 160 score: 0 Blue is Player 1
XGID=-a-a--EBB---dD---c-db---B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout124/22 24/21eq: -0.315
 Player:Opponent: 43.29% (G:10.50% B:0.51%)56.71% (G:18.90% B:0.67%) Conf.: ± 0.011 (-0.325...-0.304) - [100.0%]Duration: 12 minutes 21 seconds
2.Rollout124/22 6/3* eq: -0.345 (-0.030)
 Player:Opponent: 42.26% (G:10.20% B:0.45%)57.74% (G:17.83% B:0.88%) Conf.: ± 0.012 (-0.357...-0.333) - [0.0%]Duration: 13 minutes 46 seconds
3.Rollout16/3* 3/1* eq: -0.350 (-0.035)
 Player:Opponent: 41.85% (G:12.13% B:0.37%)58.15% (G:18.41% B:0.99%) Conf.: ± 0.011 (-0.360...-0.339) - [0.0%]Duration: 13 minutes 05 seconds
4.Rollout113/8eq: -0.354 (-0.039)
 Player:Opponent: 41.73% (G:10.85% B:0.40%)58.27% (G:17.26% B:0.79%) Conf.: ± 0.011 (-0.365...-0.343) - [0.0%]Duration: 12 minutes 09 seconds
5.Rollout224/21 13/11eq: -0.368 (-0.054)
 Player:Opponent: 42.38% (G:10.73% B:0.50%)57.62% (G:19.09% B:1.05%) Conf.: ± 0.019 (-0.387...-0.350) - [0.0%]Duration: 6 minutes 11 seconds
6.Rollout224/22 13/10eq: -0.384 (-0.069)
 Player:Opponent: 41.32% (G:10.64% B:0.53%)58.68% (G:19.04% B:1.00%) Conf.: ± 0.016 (-0.399...-0.368) - [0.0%]Duration: 6 minutes 14 seconds
7.Rollout213/11 6/3* eq: -0.404 (-0.089)
 Player:Opponent: 41.41% (G:11.31% B:0.51%)58.59% (G:20.63% B:1.64%) Conf.: ± 0.018 (-0.422...-0.386) - [0.0%]Duration: 7 minutes 06 seconds
1 2592 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

42P-61P-52S-31

Once again, Blue needs to split, but his 3s are blocked, so he can only split with the deuce. After splitting 24/22, Blue must find a 3. 13/10 leaves too many shots and gives White her full roll to play. Hit-and-split (24/22 6/3*) duplicates White's 3s and takes away half (or more) of White's roll.

 White is Player 2 score: 0 pip: 154 Unlimited GameJacoby Beaver pip: 160 score: 0 Blue is Player 1
XGID=-a-a--EBB---dD---c-d-b--B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Rollout124/22 6/3* eq: -0.251
 Player:Opponent: 44.34% (G:11.37% B:0.49%)55.66% (G:17.38% B:0.91%) Conf.: ± 0.011 (-0.262...-0.240) - [99.5%]Duration: 13 minutes 31 seconds
2.Rollout16/3* 3/1* eq: -0.273 (-0.021)
 Player:Opponent: 43.85% (G:12.59% B:0.37%)56.15% (G:17.75% B:1.03%) Conf.: ± 0.012 (-0.284...-0.261) - [0.5%]Duration: 12 minutes 27 seconds
3.Rollout113/8eq: -0.284 (-0.032)
 Player:Opponent: 43.50% (G:11.51% B:0.48%)56.50% (G:17.48% B:0.91%) Conf.: ± 0.012 (-0.295...-0.272) - [0.0%]Duration: 11 minutes 48 seconds
4.Rollout113/11 6/3* eq: -0.285 (-0.034)
 Player:Opponent: 44.08% (G:11.95% B:0.53%)55.92% (G:19.30% B:1.53%) Conf.: ± 0.013 (-0.298...-0.272) - [0.0%]Duration: 13 minutes 33 seconds
5.Rollout224/22 13/10eq: -0.327 (-0.076)
 Player:Opponent: 42.79% (G:11.01% B:0.53%)57.21% (G:19.07% B:0.94%) Conf.: ± 0.015 (-0.341...-0.312) - [0.0%]Duration: 6 minutes 08 seconds
1 2592 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

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