FOUR SCORE: Sin-free 63 (Pos. of the Week, 10/15/23)

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FOUR SCORE: Sin-free 63 (Pos. of the Week, 10/15/23)

Posted By: Nack Ballard
Date: Saturday, 21 October 2023, at 6:08 a.m.

In Response To: Position of the Week (10/15/23): Sin-free 63 (Nack Ballard)

White is Player 2

score: 0
pip: 107

Unlimited Game
Jacoby Beaver

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:0:3:0:10

21$-31H-64H-41H-32@-65R-65@-11-42R- 31H-
31H-44M-63-331-6-64H-3-55P-22E-55R-
22R-44Z-55P-61U-53O-64Z-63S-62C-63
(perfectly played money sequence)........................Nactation tutorial

You have the Blue checkers. How do you play 63, for...
.....(1) Money ?
.....(2) DMP ?
.....(3) Gammon Save ?
.....(4) Gammon Go ?
Below is a nacbrac summary of the rollouts, for "m" (money), "d" (double match point), "s" (gammon save) and "g" (gammon go). The two 4-ply rollout results are indented. The rest are 3-ply.
.........m[B P15 C27 X60 Z86 p99] "<=31*5
.............m[B P14] "^15*5
..........d[p B5.4 X37 C40 P42 Z55] "<31*5
..............d[p B4.7] "^36
..........s[C B51 Z73 X119 P157 p193] "<5
..........g[P p48 X53 B93 C115 Z136] "<5
Key:..B = Both (23/17 10/7), C = Cross (23/17 8/5), P = Point (8/2* 5/2), p = point (13/7 10/7), X = hit and split (23/17 5/2*), and Z = reverse split (23/17 13/10).
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). Clearing a higher bar, it is also a "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, .0075 and .0075 "tied" margin (compared to any play that is best at some other score).
The power rating for this R4 is [sqrt15 + sqrt 5.4*20/9 + sqrt51*10/7 + sqrt 48*10/7] = 29.14. To compare to the power ratings of some other R4's, click here (scroll to the bottom). Also not yet included in that consolidation (chronologically listed here) are R4's with rolls of 41, 43, 64, 44, 65, 21, 54, 52, 31, 65, 55 and several others hence.
Having posed and provided rollout results for this 63 position, I have finally posted (either here or on Facebook) at least one R4 for each of the twenty-one rolls; for some rolls multiple R4s. It's been a long haul.
Detailed rollout results appear below.
Money 3-ply

White is Player 2

score: 0
pip: 107

Unlimited Game
Jacoby Beaver

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:0:3:0:10
Blue to play 63

1. Rollout¹ 23/17 10/7 eq: +0.341
Player:
Opponent: 59.97% (G:10.90% B:0.43%)
40.03% (G:13.56% B:0.15%) Conf.: ą 0.003 (+0.339...+0.344) - [100.0%]
Duration: 7 hours 09 minutes
2. Rollout¹ 8/2* 5/2 eq: +0.326 (-0.015)
Player:
Opponent: 58.43% (G:17.82% B:0.63%)
41.57% (G:16.42% B:0.51%) Conf.: ą 0.003 (+0.324...+0.329) - [0.0%]
Duration: 6 hours 20 minutes
3. Rollout² 23/17 8/5 eq: +0.315 (-0.027)
Player:
Opponent: 58.27% (G:11.21% B:0.39%)
41.73% (G:9.62% B:0.16%) Conf.: ą 0.006 (+0.308...+0.321) - [0.0%]
Duration: 1 hour 57 minutes
4. Rollout² 23/17 5/2* eq: +0.282 (-0.060)
Player:
Opponent: 58.32% (G:14.07% B:0.52%)
41.68% (G:15.22% B:0.25%) Conf.: ą 0.007 (+0.275...+0.289) - [0.0%]
Duration: 1 hour 57 minutes
5. Rollout² 23/17 13/10 eq: +0.256 (-0.086)
Player:
Opponent: 57.69% (G:11.06% B:0.46%)
42.31% (G:12.45% B:0.18%) Conf.: ą 0.006 (+0.249...+0.262) - [0.0%]
Duration: 1 hour 51 minutes
6. Rollout² 13/7 10/7 eq: +0.242 (-0.099)
Player:
Opponent: 60.35% (G:12.03% B:0.61%)
39.65% (G:19.85% B:0.46%) Conf.: ą 0.007 (+0.235...+0.249) - [0.0%]
Duration: 1 hour 06 minutes

¹ 31104 Games rolled with Variance Reduction.
Dice Seed: 80422712
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 80422712
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Money 4-ply

White is Player 2

score: 0
pip: 107

Unlimited Game
Jacoby Beaver

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:0:3:0:10
Blue to play 63

1. Rollout¹ 23/17 10/7 eq: +0.345
Player:
Opponent: 60.03% (G:11.39% B:0.46%)
39.97% (G:13.79% B:0.15%) Conf.: ą 0.003 (+0.342...+0.348) - [100.0%]
Duration: 1 day 11 hours 01 minute
2. Rollout¹ 8/2* 5/2 eq: +0.331 (-0.014)
Player:
Opponent: 58.50% (G:17.95% B:0.67%)
41.50% (G:16.45% B:0.47%) Conf.: ą 0.003 (+0.328...+0.334) - [0.0%]
Duration: 1 day 02 hours 43 minutes

¹ 15552 Games rolled with Variance Reduction.
Dice Seed: 39164968
Moves and cube decisions: 4-ply

eXtreme Gammon Version: 2.10

DMP 3-ply

White is Player 2

score: 0
pip: 107

1 point match

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:0:0:1:10
Blue to play 63

1. Rollout¹ 13/7 10/7 eq: +0.221
Player:
Opponent: 61.07% (G:10.86% B:0.79%)
38.93% (G:20.41% B:0.51%) Conf.: ą 0.001 (+0.220...+0.222) - [100.0%]
Duration: 5 hours 40 minutes
2. Rollout¹ 23/17 10/7 eq: +0.216 (-0.005)
Player:
Opponent: 60.80% (G:9.85% B:0.63%)
39.20% (G:14.57% B:0.17%) Conf.: ą 0.001 (+0.215...+0.217) - [0.0%]
Duration: 6 hours 38 minutes
3. Rollout² 23/17 5/2* eq: +0.185 (-0.037)
Player:
Opponent: 59.23% (G:11.65% B:0.73%)
40.77% (G:15.91% B:0.29%) Conf.: ą 0.002 (+0.182...+0.187) - [0.0%]
Duration: 40 minutes 02 seconds
4. Rollout² 23/17 8/5 eq: +0.182 (-0.040)
Player:
Opponent: 59.08% (G:9.19% B:0.47%)
40.92% (G:10.16% B:0.18%) Conf.: ą 0.002 (+0.179...+0.184) - [0.0%]
Duration: 35 minutes 53 seconds
5. Rollout² 8/2* 5/2 eq: +0.180 (-0.042)
Player:
Opponent: 58.98% (G:14.30% B:0.89%)
41.02% (G:16.81% B:0.55%) Conf.: ą 0.002 (+0.178...+0.182) - [0.0%]
Duration: 30 minutes 26 seconds
6. Rollout² 23/17 13/10 eq: +0.167 (-0.055)
Player:
Opponent: 58.34% (G:9.57% B:0.66%)
41.66% (G:13.32% B:0.16%) Conf.: ą 0.002 (+0.164...+0.169) - [0.0%]
Duration: 37 minutes 08 seconds

¹ 31104 Games rolled with Variance Reduction.
Dice Seed: 80422712
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 80422712
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

DMP 4-ply

White is Player 2

score: 0
pip: 107

1 point match

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:0:0:1:10
Blue to play 63

1. Rollout¹ 13/7 10/7 eq: +0.2211
Player:
Opponent: 61.05% (G:11.04% B:0.79%)
38.95% (G:20.93% B:0.60%) Conf.: ą0.0006 (+0.2204...+0.2217) - [100.0%]
Duration: 2 days 00 hour 56 minutes
2. Rollout¹ 23/17 10/7 eq: +0.2164 (-0.0047)
Player:
Opponent: 60.82% (G:9.78% B:0.62%)
39.18% (G:14.93% B:0.18%) Conf.: ą0.0007 (+0.2157...+0.2170) - [0.0%]
Duration: 2 days 13 hours 28 minutes

¹ 36288 Games rolled with Variance Reduction.
Dice Seed: 92403627
Moves and cube decisions: 4-ply

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Gammon Save (3-ply)

White is Player 2

score: 0
pip: 107

2 point match
Crawford

pip: 135
score: 1

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:1:0:1:2:10
Blue to play 63

1. Rollout¹ 23/17 8/5 eq: +0.012
Player:
Opponent: 57.16% (G:8.13% B:0.50%)
42.84% (G:6.57% B:0.20%) Conf.: ą 0.003 (+0.009...+0.015) - [100.0%]
Duration: 1 hour 21 minutes
2. Rollout¹ 23/17 10/7 eq: -0.039 (-0.051)
Player:
Opponent: 58.99% (G:9.07% B:0.58%)
41.01% (G:10.93% B:0.25%) Conf.: ą 0.003 (-0.042...-0.036) - [0.0%]
Duration: 1 hour 27 minutes
3. Rollout¹ 23/17 13/10 eq: -0.061 (-0.073)
Player:
Opponent: 57.05% (G:8.63% B:0.63%)
42.95% (G:10.11% B:0.27%) Conf.: ą 0.003 (-0.064...-0.058) - [0.0%]
Duration: 1 hour 22 minutes
4. Rollout¹ 23/17 5/2* eq: -0.107 (-0.119)
Player:
Opponent: 56.87% (G:9.66% B:0.70%)
43.13% (G:12.20% B:0.27%) Conf.: ą 0.003 (-0.110...-0.103) - [0.0%]
Duration: 1 hour 30 minutes
5. Rollout¹ 8/2* 5/2 eq: -0.145 (-0.157)
Player:
Opponent: 57.91% (G:12.82% B:0.76%)
42.09% (G:15.16% B:0.69%) Conf.: ą 0.003 (-0.148...-0.142) - [0.0%]
Duration: 1 hour 08 minutes
6. Rollout¹ 13/7 10/7 eq: -0.181 (-0.193)
Player:
Opponent: 60.86% (G:12.58% B:1.28%)
39.14% (G:19.91% B:1.10%) Conf.: ą 0.003 (-0.184...-0.177) - [0.0%]
Duration: 1 hour 17 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 20812167
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Gammon Go (3-ply)

White is Player 2

score: 1
pip: 107

2 point match
Crawford

pip: 135
score: 0

Blue is Player 1

XGID=--a-BCB-C-A-bBb--A--dbbAb-:0:0:1:63:0:1:1:2:10
Blue to play 63

1. Rollout¹ 8/2* 5/2 eq: +0.546
Player:
Opponent: 56.10% (G:21.22% B:1.34%)
43.90% (G:19.30% B:0.81%) Conf.: ą 0.003 (+0.543...+0.550) - [100.0%]
Duration: 1 hour 01 minute
2. Rollout¹ 13/7 10/7 eq: +0.498 (-0.048)
Player:
Opponent: 59.63% (G:15.29% B:1.28%)
40.37% (G:21.49% B:0.66%) Conf.: ą 0.004 (+0.495...+0.502) - [0.0%]
Duration: 1 hour 09 minutes
3. Rollout¹ 23/17 5/2* eq: +0.494 (-0.053)
Player:
Opponent: 57.37% (G:17.31% B:1.06%)
42.63% (G:18.34% B:0.37%) Conf.: ą 0.004 (+0.490...+0.497) - [0.0%]
Duration: 1 hour 24 minutes
4. Rollout¹ 23/17 10/7 eq: +0.453 (-0.093)
Player:
Opponent: 59.26% (G:13.41% B:0.92%)
40.74% (G:15.68% B:0.27%) Conf.: ą 0.003 (+0.450...+0.457) - [0.0%]
Duration: 1 hour 20 minutes
5. Rollout¹ 23/17 8/5 eq: +0.431 (-0.115)
Player:
Opponent: 57.59% (G:13.97% B:0.70%)
42.41% (G:12.85% B:0.26%) Conf.: ą 0.003 (+0.428...+0.435) - [0.0%]
Duration: 1 hour 10 minutes
6. Rollout¹ 23/17 13/10 eq: +0.411 (-0.136)
Player:
Opponent: 57.01% (G:13.53% B:0.80%)
42.99% (G:14.71% B:0.34%) Conf.: ą 0.003 (+0.408...+0.414) - [0.0%]
Duration: 1 hour 13 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 76168428
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Messages In This Thread

Position of the Week (10/15/23): Sin-free 63
Nack Ballard -- Sunday, 15 October 2023, at 11:49 a.m.
- Position of the Week (10/15/23): Sin-free 63
  pierrez -- Sunday, 15 October 2023, at 4:06 p.m.
- Position of the Week (10/15/23): Sin-free 63
  John O'Hagan -- Monday, 16 October 2023, at 2:45 a.m.
- FOUR SCORE: Sin-free 63 (Pos. of the Week, 10/15/23)
  Nack Ballard -- Saturday, 21 October 2023, at 6:08 a.m.
  - FOUR SCORE: Sin-free 63 (Pos. of the Week, 10/15/23)
    Sam Pottle -- Saturday, 21 October 2023, at 8:47 a.m.
  - Nactation tutorial (corrected link)
    Nack Ballard -- Tuesday, 24 October 2023, at 5:38 a.m.
    - Nactation tutorial (corrected link)
      Stick -- Tuesday, 24 October 2023, at 5:47 p.m.
      - Nactation tutorial (corrected link)
        Nack Ballard -- Tuesday, 24 October 2023, at 8:47 p.m.

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