Paul seems to have beaten me to the punch here, but here is the rollout and three contrasting positions, one of which Paul seems to have stumbled on as well. Be sure to see my final position showing what other factors contribute to the 20 pip breakeven point that Paul and I found.
The crowd did better on this than I. I played the "natural" (to use Stick's word) 7/6 7/4.
        
 
         
 | | White is Player 2
score: 4
pip: 107 | | 7 point match | pip: 81
score: 2
Blue is Player 1 |
|
| XGID=-C-BBbBBB--Ba----a-cbbbb--:1:-1:1:31:2:4:0:7:10 |
| Blue to play 31 |
| 1. | Rollout1 | 4/1 3/2 | eq: +0.374 |
| Player:
Opponent: | 70.83% (G:0.76% B:0.01%)
29.17% (G:2.10% B:0.09%) | Conf.: ± 0.004 (+0.370...+0.378) - [100.0%]
Duration: 13 minutes 44 seconds |
|
| 2. | Rollout1 | 4/3 4/1 | eq: +0.342 (-0.032) |
| Player:
Opponent: | 69.28% (G:0.66% B:0.01%)
30.72% (G:2.17% B:0.07%) | Conf.: ± 0.004 (+0.338...+0.345) - [0.0%]
Duration: 12 minutes 33 seconds |
|
| 3. | Rollout1 | 7/6 7/4 | eq: +0.321 (-0.053) |
| Player:
Opponent: | 68.06% (G:1.32% B:0.02%)
31.94% (G:2.05% B:0.07%) | Conf.: ± 0.003 (+0.318...+0.324) - [0.0%]
Duration: 11 minutes 51 seconds |
|
| 4. | 1-ply | 11/10 11/8 | eq: +0.046 (-0.328) |
| Player:
Opponent: | 57.18% (G:2.17% B:0.01%)
42.82% (G:4.83% B:0.05%) | |
|
| 5. | 1-ply | 8/4 | eq: -0.037 (-0.411) |
| Player:
Opponent: | 53.76% (G:2.13% B:0.02%)
46.24% (G:6.54% B:0.07%) | |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.03, MET: Kazaross XG2
With a closer race, the two plays are equal:
| | White is Player 2
score: 4
pip: 101 | | 7 point match | pip: 81
score: 2
Blue is Player 1 |
|
| XGID=-C-BBbBBB--B-----aacbbbb--:1:-1:1:31:2:4:0:7:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 7/6 7/4 | eq: +0.302 |
| Player:
Opponent: | 67.74% (G:1.17% B:0.01%)
32.26% (G:1.78% B:0.03%) | |
|
| 2. | XG Roller++ | 4/1 3/2 | eq: +0.298 (-0.004) |
| Player:
Opponent: | 68.25% (G:0.71% B:0.00%)
31.75% (G:1.98% B:0.04%) | |
|
| 3. | XG Roller++ | 4/3 4/1 | eq: +0.267 (-0.036) |
| Player:
Opponent: | 66.78% (G:0.66% B:0.00%)
33.22% (G:1.94% B:0.04%) | |
|
| 4. | 1-ply | 11/10 11/8 | eq: -0.032 (-0.334) |
| Player:
Opponent: | 54.01% (G:1.99% B:0.01%)
45.99% (G:5.92% B:0.05%) | |
|
| 5. | 1-ply | 8/4 | eq: -0.077 (-0.379) |
| Player:
Opponent: | 52.23% (G:1.88% B:0.01%)
47.77% (G:7.21% B:0.06%) | |
|
eXtreme Gammon Version: 2.03, MET: Kazaross XG2
And another couple of pips puts the natural play ahead:
| | White is Player 2
score: 4
pip: 99 | | 7 point match | pip: 81
score: 2
Blue is Player 1 |
|
| XGID=-C-BBbBBB--B-----aabbcbb--:1:-1:1:31:2:4:0:7:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 7/6 7/4 | eq: +0.291 |
| Player:
Opponent: | 67.52% (G:1.21% B:0.01%)
32.48% (G:1.75% B:0.03%) | |
|
| 2. | XG Roller++ | 4/1 3/2 | eq: +0.274 (-0.017) |
| Player:
Opponent: | 67.25% (G:0.64% B:0.01%)
32.75% (G:1.95% B:0.04%) | |
|
| 3. | XG Roller++ | 4/3 4/1 | eq: +0.242 (-0.049) |
| Player:
Opponent: | 65.86% (G:0.66% B:0.01%)
34.14% (G:1.90% B:0.03%) | |
|
| 4. | 1-ply | 11/10 11/8 | eq: -0.053 (-0.343) |
| Player:
Opponent: | 53.06% (G:2.02% B:0.01%)
46.94% (G:5.78% B:0.04%) | |
|
| 5. | 1-ply | 8/4 | eq: -0.079 (-0.370) |
| Player:
Opponent: | 52.07% (G:1.94% B:0.01%)
47.93% (G:6.90% B:0.06%) | |
|
eXtreme Gammon Version: 2.03, MET: Kazaross XG2
A final comment. It's not just ANY 20 pips that break even. In the position below, I've moved blue's checkers back in the home board. Now giving up the seven point is awful--you can shuffle checkers in your home board without destroying it.
| | White is Player 2
score: 4
pip: 109 | | 7 point match | pip: 89
score: 2
Blue is Player 1 |
|
| XGID=---CDbBBB--Ba--a---cbbbb--:1:-1:1:31:2:4:0:7:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 4/1 3/2 | eq: +0.425 |
| Player:
Opponent: | 73.55% (G:1.23% B:0.01%)
26.45% (G:1.04% B:0.01%) | |
|
| 2. | XG Roller++ | 7/6 7/4 | eq: +0.266 (-0.158) |
| Player:
Opponent: | 66.29% (G:1.38% B:0.02%)
33.71% (G:2.32% B:0.04%) | |
|
| 3. | 4-ply | 4/3 4/1 | eq: +0.377 (-0.048) |
| Player:
Opponent: | 71.96% (G:1.08% B:0.01%)
28.04% (G:1.35% B:0.01%) | |
|
| 4. | 1-ply | 11/10 11/8 | eq: -0.046 (-0.471) |
| Player:
Opponent: | 53.27% (G:1.96% B:0.03%)
46.73% (G:5.03% B:0.06%) | |
|
| 5. | 1-ply | 8/7 4/1 | eq: -0.056 (-0.481) |
| Player:
Opponent: | 52.95% (G:2.10% B:0.03%)
47.05% (G:6.65% B:0.10%) | |
|
eXtreme Gammon Version: 2.03, MET: Kazaross XG2