The two positions below (side by side, if your window is wide) are identical to each other except for the cube position, and resemble the original position (diagrammed at the bottom of this post).
I asked three questions, the answers for which will appear below the diagrams:
...(1) Should Blue have made an initial double before rolling his 61?
...(2) How do you play 61 if the cube is in the middle? (First diagram.)
...(3) How do you play 61 if the opponent owns the cube? (Second diagram.)
| 1. | Rollout1 | 18/11 | eq: +0.977 |
| Player:
Opponent: | 76.27% (G:5.44% B:0.15%)
23.73% (G:2.37% B:0.05%) | Conf.: ± 0.006 (+0.972...+0.983) - [100.0%]
Duration: 13 minutes 04 seconds |
|
| 2. | Rollout1 | 11/5 6/5 | eq: +0.930 (-0.047) |
| Player:
Opponent: | 74.74% (G:14.88% B:0.71%)
25.26% (G:5.59% B:0.12%) | Conf.: ± 0.006 (+0.924...+0.936) - [0.0%]
Duration: 7 minutes 36 seconds |
|
| 3. | 1-ply | 11/4 | eq: +0.048 (-0.929) |
| Player:
Opponent: | 52.93% (G:9.78% B:0.42%)
47.07% (G:14.01% B:0.22%) | |
|
| 4. | 1-ply | 18/17 13/7 | eq: -0.138 (-1.116) |
| Player:
Opponent: | 49.46% (G:9.65% B:0.44%)
50.54% (G:22.14% B:1.00%) | |
|
| 5. | 1-ply | 18/17 11/5 | eq: -0.188 (-1.165) |
| Player:
Opponent: | 48.18% (G:9.95% B:0.45%)
51.82% (G:23.81% B:0.88%) | |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 98091720
Moves: 3-ply, cube decisions: XG Roller
|
| 1. | Rollout1 | 11/5 6/5 | eq: +0.519 |
| Player:
Opponent: | 75.05% (G:14.77% B:0.73%)
24.95% (G:5.51% B:0.13%) | Conf.: ± 0.004 (+0.515...+0.523) - [100.0%]
Duration: 12 minutes 55 seconds |
|
| 2. | Rollout1 | 18/11 | eq: +0.488 (-0.031) |
| Player:
Opponent: | 76.27% (G:5.47% B:0.15%)
23.73% (G:2.38% B:0.05%) | Conf.: ± 0.003 (+0.485...+0.491) - [0.0%]
Duration: 12 minutes 20 seconds |
|
| 3. | 1-ply | 11/4 | eq: -0.148 (-0.667) |
| Player:
Opponent: | 52.93% (G:9.78% B:0.42%)
47.07% (G:14.01% B:0.22%) | |
|
| 4. | 1-ply | 18/17 13/7 | eq: -0.319 (-0.839) |
| Player:
Opponent: | 49.46% (G:9.65% B:0.44%)
50.54% (G:22.14% B:1.00%) | |
|
| 5. | 1-ply | 18/17 11/5 | eq: -0.362 (-0.881) |
| Player:
Opponent: | 48.18% (G:9.95% B:0.45%)
51.82% (G:23.81% B:0.88%) | |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 98091720
Moves: 3-ply, cube decisions: XG Roller
|
...(1) Should Blue have made an initial double before rolling his 61?
No. According to a 1k rollout (not shown), doubling is an error of .078.
...(2) How do you play 61 if the cube is in the middle?
According to the rollout in the first position above, covering the 11pt is better (than making the 5pt) by .047. ...
[BTW, if Blue owns the cube, 11pt beats 5pt by .041, rollout not shown.]
...(3) How do you play 61 if the opponent owns the cube?
According to the rollout in the second position above, making the 5pt is better (than covering the 11pt) by .031.
Hence, cube position (center vs opp-ownership) affects the move margin by .078, a significant difference that also happens to swing determination of the best play.
Rollouts (of 5k) for the original position, with both cube locations, are provided below (side-by-side, if your window is wide). Here, the margin difference is .058, which is still substantial.
Could one provide some reason or reasons other than cube position that argue logically in favor of the 11pt over the 5pt? Certainly. That would be another piece(s) of the puzzle. But that is true in my position (above), too, even when the opponent owns the cube (where making the 5pt is the better play overall).
Nack
| 1. | Rollout1 | 18/11 | eq: +0.889 |
| Player:
Opponent: | 74.57% (G:5.53% B:0.17%)
25.43% (G:2.96% B:0.07%) | Conf.: ± 0.007 (+0.882...+0.896) - [100.0%]
Duration: 9 minutes 48 seconds |
|
| 2. | Rollout1 | 11/5 6/5 | eq: +0.691 (-0.198) |
| Player:
Opponent: | 68.37% (G:12.06% B:0.56%)
31.63% (G:7.80% B:0.20%) | Conf.: ± 0.007 (+0.684...+0.698) - [0.0%]
Duration: 7 minutes 38 seconds |
|
| 3. | 1-ply | 18/17 7/1 | eq: +0.113 (-0.776) |
| Player:
Opponent: | 54.74% (G:11.06% B:0.40%)
45.26% (G:13.84% B:0.48%) | |
|
| 4. | 1-ply | 11/10 7/1 | eq: +0.043 (-0.846) |
| Player:
Opponent: | 52.76% (G:12.02% B:0.43%)
47.24% (G:15.93% B:0.53%) | |
|
| 5. | 1-ply | 18/17 11/5 | eq: -0.005 (-0.894) |
| Player:
Opponent: | 51.80% (G:11.14% B:0.47%)
48.20% (G:17.09% B:0.65%) | |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
| 1. | Rollout1 | 18/11 | eq: +0.444 |
| Player:
Opponent: | 74.58% (G:5.53% B:0.17%)
25.42% (G:2.96% B:0.07%) | Conf.: ± 0.003 (+0.441...+0.448) - [100.0%]
Duration: 9 minutes 46 seconds |
|
| 2. | Rollout1 | 11/5 6/5 | eq: +0.305 (-0.140) |
| Player:
Opponent: | 68.30% (G:12.51% B:0.59%)
31.70% (G:7.98% B:0.20%) | Conf.: ± 0.004 (+0.300...+0.309) - [0.0%]
Duration: 9 minutes 49 seconds |
|
| 3. | 1-ply | 18/17 7/1 | eq: -0.093 (-0.537) |
| Player:
Opponent: | 54.74% (G:11.06% B:0.40%)
45.26% (G:13.84% B:0.48%) | |
|
| 4. | 1-ply | 11/10 7/1 | eq: -0.152 (-0.596) |
| Player:
Opponent: | 52.76% (G:12.02% B:0.43%)
47.24% (G:15.93% B:0.53%) | |
|
| 5. | 1-ply | 18/17 11/5 | eq: -0.195 (-0.639) |
| Player:
Opponent: | 51.80% (G:11.14% B:0.47%)
48.20% (G:17.09% B:0.65%) | |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
