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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.	Rollout1	7/5 6/5	eq: +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.	Rollout1	13/11* 8/7	eq: +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.	Rollout2	6/4* 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.	Rollout3	22/20 8/7	eq: -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.	Rollout1	13/11* 8/7	eq: +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.	Rollout1	7/5 6/5	eq: +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.	Rollout2	6/4* 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.	Rollout3	22/20 8/7	eq: -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.	Rollout1	22/20 8/7	eq: -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.	Rollout1	7/5 6/5	eq: -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.	Rollout1	13/11* 8/7	eq: -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.	Rollout1	6/4* 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.	Rollout1	6/4* 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.	Rollout1	7/5 6/5	eq: +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.	Rollout2	13/11* 8/7	eq: +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.	Rollout2	22/20 8/7	eq: +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

• Twicky 21
  Nack Ballard -- Monday, 25 September 2017, at 2:48 p.m.
  • Twicky 21
    Christian Munk-Christensen -- Monday, 25 September 2017, at 5:23 p.m.
    • Twicky 21
      Nack Ballard -- Monday, 25 September 2017, at 6:27 p.m.
    • Twicky 21
      Igor -- Tuesday, 26 September 2017, at 2:11 a.m.
  • Twicky 21
    ah_clem -- Tuesday, 26 September 2017, at 4:20 p.m.
  • Four Score Position with Twicky 21
    Nack Ballard -- Friday, 29 September 2017, at 4:34 a.m.
    • Four Score Position with Twicky 21
      christian munk-christensen -- Friday, 29 September 2017, at 7:30 a.m.
      • Four Score Position with Twicky 21
        Stick -- Friday, 29 September 2017, at 7:47 a.m.
      • An explanation
        Nack Ballard -- Friday, 29 September 2017, at 5:25 p.m.
        • An explanation
          Christian Munk-Christensen -- Friday, 29 September 2017, at 6:03 p.m.
    • Four Score Position with Twicky 21
      ah_clem -- Friday, 29 September 2017, at 7:02 p.m.