[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Four Score Position with Twicky 21

Posted By: Nack Ballard
Date: Friday, 29 September 2017, at 4:34 a.m.

In Response To: Twicky 21 (Nack Ballard)

Thanks to respondents CMC, Igor and ah_clem for their worthy comments. One of them inverted the money and DMP moves; otherwise all respondents correctly guessed the best play at all four scores.

Below is a nacbrac summary of the rollouts (one line for each score). For each score, there is a 3-ply rollout (diagrammed). For Money (m) and DMP (d), there is also a 4-ply rollout (not diagrammed).

.........m[P D11 K18 B63] "<=215*10 5.....m[P D15] "^20
..........d[D P7 K15 B50] <51*5.................. d[D P8] "^5
..........s[B P41 D49 K71] "<5
..........g[K P18 D47 B97] "<10*5

Key:..P (Point) = 7/5 6/5, D (Down) = 13/11* 8/7, B (Both) = 22/20 8/7, K (Kill) = 6/4*/3*.
Nactation tutorial ....nacbracs explanation

Each of the four main scores has a different best play. In fact, this is not only a T4 (technical four-score position). It is also an "R4" (real four-score position), meaning that for each of money, DMP, gammon save and gammon go, the best play clears its respective .010, .0045, .007 and .007 "tied" margin (compared to any play that is best at some other score).

The power rating for this R4 is [sqrt 11 + sqrt 7*20/9 + sqrt 41*10/7 + sqrt 18*10/7] = 19.98. To compare to the power ratings of other R4's, click here (scroll to the bottom). Also not yet included in that consolidation are R4's with rolls of 41, 43, 64 and 65.

Detailed rollout results follow.

Nack

Money





White is Player 2

score: 0
pip: 161
Unlimited Game
Jacoby Beaver
pip: 166
score: 0

Blue is Player 1
XGID=---aa-EAC--abCd-b--bA-AbA-:0:0:1:21:0:0:3:0:10

.64P-63S-21H-64H-32H-41K-22G-41R-55R-F-64P-3-31@-21@-
-43S-62R-43S-65S-64H-61Z-63R-31H-F-43x-43-21

..Perfectly played money sequence.............Nactation tutorial



1.Rollout17/5 6/5eq: +0.018
Player:
Opponent:
50.07% (G:14.98% B:0.62%)
49.93% (G:13.06% B:0.74%)
Conf.: ± 0.001 (+0.017...+0.019) - [100.0%]
Duration: 1 day 12 hours 28 minutes
2.Rollout113/11* 8/7eq: +0.007 (-0.011)
Player:
Opponent:
50.47% (G:13.26% B:0.57%)
49.53% (G:13.37% B:0.73%)
Conf.: ± 0.001 (+0.006...+0.009) - [0.0%]
Duration: 1 day 18 hours 21 minutes
3.Rollout26/4* 4/3* eq: -0.001 (-0.018)
Player:
Opponent:
49.70% (G:16.15% B:0.81%)
50.30% (G:15.03% B:0.99%)
Conf.: ± 0.007 (-0.007...+0.006) - [0.0%]
Duration: 2 hours 17 minutes
4.Rollout322/20 8/7eq: -0.046 (-0.064)
Player:
Opponent:
47.95% (G:12.88% B:0.44%)
52.05% (G:9.60% B:0.41%)
Conf.: ± 0.008 (-0.054...-0.038) - [0.0%]
Duration: 1 hour 07 minutes
1 215136 Games rolled with Variance Reduction.
Dice Seed: 94188521
Moves: 3-ply, cube decisions: XG Roller

2 10368 Games rolled with Variance Reduction.
Dice Seed: 94188521
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 94188521
Moves: 3-ply, cube decisions: XG Roller

DMP





White is Player 2

score: 0
pip: 161
1 point match
pip: 166
score: 0

Blue is Player 1
XGID=---aa-EAC--abCd-b--bA-AbA-:0:0:1:21:0:0:0:1:10
Blue to play 21

1.Rollout113/11* 8/7eq: +0.013
Player:
Opponent:
50.66% (G:15.97% B:1.72%)
49.34% (G:15.79% B:2.28%)
Conf.: ± 0.001 (+0.012...+0.014) - [100.0%]
Duration: 15 hours 08 minutes
2.Rollout17/5 6/5eq: +0.006 (-0.007)
Player:
Opponent:
50.32% (G:16.39% B:1.97%)
49.68% (G:15.03% B:2.11%)
Conf.: ± 0.001 (+0.006...+0.007) - [0.0%]
Duration: 12 hours 44 minutes
3.Rollout26/4* 4/3* eq: -0.001 (-0.015)
Player:
Opponent:
49.93% (G:17.93% B:2.52%)
50.07% (G:17.79% B:2.94%)
Conf.: ± 0.003 (-0.004...+0.001) - [0.0%]
Duration: 1 hour 24 minutes
4.Rollout322/20 8/7eq: -0.037 (-0.050)
Player:
Opponent:
48.17% (G:14.21% B:1.61%)
51.83% (G:12.71% B:1.23%)
Conf.: ± 0.003 (-0.040...-0.033) - [0.0%]
Duration: 47 minutes 24 seconds
1 51840 Games rolled with Variance Reduction.
Dice Seed: 25083440
Moves: 3-ply, cube decisions: XG Roller

2 7776 Games rolled with Variance Reduction.
Dice Seed: 25083440
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 25083440
Moves: 3-ply, cube decisions: XG Roller

Gammon Save





White is Player 2

score: 0
pip: 161
2 point match
Crawford
pip: 166
score: 1

Blue is Player 1
XGID=---aa-EAC--abCd-b--bA-AbA-:0:0:1:21:1:0:1:2:10
Blue to play 21

1.Rollout122/20 8/7eq: -0.223
Player:
Opponent:
46.70% (G:13.51% B:1.22%)
53.30% (G:7.86% B:0.58%)
Conf.: ± 0.004 (-0.227...-0.219) - [100.0%]
Duration: 40 minutes 06 seconds
2.Rollout17/5 6/5eq: -0.264 (-0.041)
Player:
Opponent:
49.26% (G:16.44% B:2.20%)
50.74% (G:12.46% B:1.68%)
Conf.: ± 0.004 (-0.268...-0.260) - [0.0%]
Duration: 38 minutes 52 seconds
3.Rollout113/11* 8/7eq: -0.273 (-0.049)
Player:
Opponent:
49.29% (G:16.28% B:1.91%)
50.71% (G:12.91% B:1.56%)
Conf.: ± 0.004 (-0.277...-0.268) - [0.0%]
Duration: 46 minutes 47 seconds
4.Rollout16/4* 4/3* eq: -0.294 (-0.071)
Player:
Opponent:
48.35% (G:17.00% B:2.27%)
51.65% (G:13.05% B:2.10%)
Conf.: ± 0.004 (-0.298...-0.290) - [0.0%]
Duration: 45 minutes 29 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 52466768
Moves: 3-ply, cube decisions: XG Roller

Gammon Go





White is Player 2

score: 1
pip: 161
2 point match
Crawford
pip: 166
score: 0

Blue is Player 1
XGID=---aa-EAC--abCd-b--bA-AbA-:0:0:1:21:0:1:1:2:10
Blue to play 21

1.Rollout16/4* 4/3* eq: +0.328
Player:
Opponent:
50.50% (G:15.89% B:1.77%)
49.50% (G:18.81% B:3.06%)
Conf.: ± 0.003 (+0.324...+0.331) - [100.0%]
Duration: 1 hour 50 minutes
2.Rollout17/5 6/5eq: +0.310 (-0.018)
Player:
Opponent:
50.90% (G:14.59% B:1.27%)
49.10% (G:15.74% B:2.41%)
Conf.: ± 0.003 (+0.307...+0.313) - [0.0%]
Duration: 1 hour 28 minutes
3.Rollout213/11* 8/7eq: +0.280 (-0.047)
Player:
Opponent:
51.79% (G:12.24% B:1.17%)
48.21% (G:15.62% B:2.23%)
Conf.: ± 0.004 (+0.276...+0.285) - [0.0%]
Duration: 1 hour 01 minute
4.Rollout222/20 8/7eq: +0.231 (-0.097)
Player:
Opponent:
48.92% (G:12.63% B:0.95%)
51.08% (G:13.70% B:1.42%)
Conf.: ± 0.004 (+0.226...+0.235) - [0.0%]
Duration: 53 minutes 14 seconds
1 10368 Games rolled with Variance Reduction.
Dice Seed: 51800270
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 51800270
Moves: 3-ply, cube decisions: XG Roller

Messages In This Thread

 

Post Response

Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:

 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.