The original thread was initiated by Paul Weaver (a.k.a. "Wally Peever") on June 14th, in which he features an interesting position with two different best plays at the four main scores, and a third different best play at –2–4.
Paul's position inspired my variant (copied below), which is an R4 (real four-score position) and corrects a slight flaw by denying Blue a Money double before the roll. White owns her 12pt and 11pt (instead of her midpoint plus 10pt and 6pt spares) and her 2pt (instead of her 3pt).
[I was unable to match a fifth different best play with a fifth score. The closest is J (Jump, 10/6 7/1*), which rolls within .006 at c6 (Crawford, opp needs 6).]
The power rating for this R4 is [sqrt 21 + sqrt 13*20/9 + sqrt 10*10/7 + sqrt 72*10/7] = 23.88. To compare to the power ratings of other R4's, click here and scroll to the bottom. Also not yet included in that consolidation are R4's with rolls of 41 and 43.
Detailed rollout results follow (all with 3-ply checker play, XGR cube).
Nack
Money
1. | Rollout1 | 9/5 7/1* | eq: +0.191 |
| Player: Opponent: | 49.65% (G:19.97% B:0.16%) 50.35% (G:7.85% B:0.29%) | Conf.: ± 0.003 (+0.188...+0.194) - [100.0%] Duration: 13 minutes 55 seconds |
|
2. | Rollout1 | 20/16 7/1* | eq: +0.169 (-0.021) |
| Player: Opponent: | 50.02% (G:23.78% B:0.48%) 49.98% (G:19.92% B:2.51%) | Conf.: ± 0.002 (+0.167...+0.171) - [0.0%] Duration: 6 minutes 04 seconds |
|
3. | Rollout2 | 7/1* 6/2 | eq: +0.097 (-0.094) |
| Player: Opponent: | 50.48% (G:18.58% B:0.19%) 49.52% (G:8.45% B:0.45%) | Conf.: ± 0.008 (+0.089...+0.105) - [0.0%] Duration: 22 minutes 16 seconds |
|
4. | Rollout2 | 10/6 7/1* | eq: +0.051 (-0.140) |
| Player: Opponent: | 49.73% (G:16.31% B:0.20%) 50.27% (G:7.29% B:0.36%) | Conf.: ± 0.006 (+0.045...+0.057) - [0.0%] Duration: 21 minutes 17 seconds |
|
5. | Rollout2 | 10/4 7/3 | eq: +0.010 (-0.181) |
| Player: Opponent: | 49.61% (G:12.29% B:0.14%) 50.39% (G:6.82% B:0.32%) | Conf.: ± 0.006 (+0.004...+0.016) - [0.0%] Duration: 21 minutes 04 seconds |
|
|
1 10368 Games rolled with Variance Reduction. Dice Seed: 85506921 Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction. Dice Seed: 85506921 Moves: 3-ply, cube decisions: XG Roller
|
DMP

              
 
              
 | | White is Player 2
score: 0 pip: 128 | 1 point match | pip: 108 score: 0
Blue is Player 1 | |
XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:0:0:0:1:10 |
Blue to play 64 |
1. | Rollout1 | 7/1* 6/2 | eq: +0.006 |
| Player: Opponent: | 50.32% (G:17.83% B:0.29%) 49.68% (G:7.90% B:0.54%) | Conf.: ± 0.002 (+0.004...+0.009) - [100.0%] Duration: 16 minutes 10 seconds |
|
2. | Rollout1 | 9/5 7/1* | eq: -0.006 (-0.013) |
| Player: Opponent: | 49.69% (G:18.73% B:0.32%) 50.31% (G:8.08% B:0.44%) | Conf.: ± 0.002 (-0.008...-0.004) - [0.0%] Duration: 17 minutes 35 seconds |
|
3. | Rollout1 | 10/4 7/3 | eq: -0.009 (-0.015) |
| Player: Opponent: | 49.57% (G:11.43% B:0.22%) 50.43% (G:5.44% B:0.30%) | Conf.: ± 0.002 (-0.011...-0.007) - [0.0%] Duration: 14 minutes 38 seconds |
|
4. | Rollout1 | 20/16 7/1* | eq: -0.009 (-0.016) |
| Player: Opponent: | 49.54% (G:23.19% B:0.75%) 50.46% (G:19.39% B:2.65%) | Conf.: ± 0.002 (-0.011...-0.007) - [0.0%] Duration: 17 minutes 37 seconds |
|
5. | Rollout1 | 10/6 7/1* | eq: -0.009 (-0.016) |
| Player: Opponent: | 49.53% (G:15.37% B:0.30%) 50.47% (G:6.76% B:0.37%) | Conf.: ± 0.002 (-0.012...-0.007) - [0.0%] Duration: 15 minutes 25 seconds |
|
|
1 5184 Games rolled with Variance Reduction. Dice Seed: 37357246 Moves: 3-ply, cube decisions: XG Roller
|
Gammon Save

              
 
              
 | | White is Player 2
score: 0 pip: 128 | 2 point match Crawford | pip: 108 score: 1
Blue is Player 1 | |
XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:1:0:1:2:10 |
Blue to play 64 |
1. | Rollout1 | 10/4 7/3 | eq: -0.144 |
| Player: Opponent: | 50.28% (G:13.49% B:0.33%) 49.72% (G:7.47% B:0.44%) | Conf.: ± 0.001 (-0.145...-0.143) - [100.0%] Duration: 1 hour 28 minutes |
|
2. | Rollout1 | 10/6 7/1* | eq: -0.154 (-0.010) |
| Player: Opponent: | 50.13% (G:16.23% B:0.32%) 49.87% (G:7.81% B:0.49%) | Conf.: ± 0.001 (-0.155...-0.152) - [0.0%] Duration: 1 hour 44 minutes |
|
3. | Rollout2 | 7/1* 6/2 | eq: -0.162 (-0.018) |
| Player: Opponent: | 50.87% (G:18.09% B:0.32%) 49.13% (G:8.97% B:0.57%) | Conf.: ± 0.003 (-0.165...-0.159) - [0.0%] Duration: 12 minutes 35 seconds |
|
4. | Rollout2 | 9/3 7/3 | eq: -0.169 (-0.025) |
| Player: Opponent: | 49.45% (G:13.65% B:0.48%) 50.55% (G:7.91% B:0.49%) | Conf.: ± 0.003 (-0.172...-0.166) - [0.0%] Duration: 10 minutes 27 seconds |
|
5. | Rollout2 | 10/4 9/5 | eq: -0.172 (-0.028) |
| Player: Opponent: | 48.54% (G:15.45% B:0.29%) 51.46% (G:7.12% B:0.37%) | Conf.: ± 0.003 (-0.174...-0.169) - [0.0%] Duration: 12 minutes 30 seconds |
|
6. | Rollout2 | 9/5 7/1* | eq: -0.177 (-0.033) |
| Player: Opponent: | 50.63% (G:20.66% B:0.49%) 49.37% (G:9.48% B:0.67%) | Conf.: ± 0.003 (-0.180...-0.174) - [0.0%] Duration: 12 minutes 43 seconds |
|
|
1 41472 Games rolled with Variance Reduction. Dice Seed: 85506921 Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction. Dice Seed: 85506921 Moves: 3-ply, cube decisions: XG Roller
|
Gammon Go

              
 
              
 | | White is Player 2
score: 1 pip: 128 | 2 point match Crawford | pip: 108 score: 0
Blue is Player 1 | |
XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:0:1:1:2:10 |
Blue to play 64 |
1. | Rollout1 | 20/16 7/1* | eq: +0.455 |
| Player: Opponent: | 50.01% (G:22.76% B:0.65%) 49.99% (G:18.18% B:2.30%) | Conf.: ± 0.004 (+0.451...+0.459) - [100.0%] Duration: 16 minutes 40 seconds |
|
2. | Rollout1 | 9/5 7/1* | eq: +0.384 (-0.072) |
| Player: Opponent: | 49.72% (G:19.47% B:0.31%) 50.28% (G:8.12% B:0.43%) | Conf.: ± 0.004 (+0.380...+0.387) - [0.0%] Duration: 16 minutes 15 seconds |
|
3. | Rollout1 | 7/1* 6/2 | eq: +0.368 (-0.087) |
| Player: Opponent: | 50.56% (G:17.84% B:0.22%) 49.44% (G:8.00% B:0.69%) | Conf.: ± 0.004 (+0.364...+0.372) - [0.0%] Duration: 15 minutes 23 seconds |
|
4. | Rollout1 | 10/6 7/1* | eq: +0.314 (-0.141) |
| Player: Opponent: | 49.99% (G:15.71% B:0.24%) 50.01% (G:6.82% B:0.51%) | Conf.: ± 0.004 (+0.310...+0.318) - [0.0%] Duration: 14 minutes 57 seconds |
|
|
1 5184 Games rolled with Variance Reduction. Dice Seed: 85506921 Moves: 3-ply, cube decisions: XG Roller
|