Great problem! I liked David Presser's analysis the best. Here is some more bot info.
Close White's board and take a look at how far down 8/4* drops in the rankings.
         
 
         
 | | White is Player 1
score: 0
pip: 70 | Unlimited Game
Jacoby | pip: 92
score: 0
Blue is Player 2 |
|
| XGID=-BBAaBB-AB-B-A-----bbccbb-:0:0:1:31:0:0:1:0:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 9/8 9/6 | eq: -0.570 |
| Player:
Opponent: | 33.20% (G:0.68% B:0.01%)
66.80% (G:7.78% B:0.07%) | |
|
| 2. | XG Roller++ | 11/10 11/8 | eq: -0.590 (-0.020) |
| Player:
Opponent: | 39.09% (G:0.92% B:0.02%)
60.91% (G:19.33% B:0.14%) | |
|
| 3. | XG Roller++ | 11/8 3/2 | eq: -0.664 (-0.094) |
| Player:
Opponent: | 33.57% (G:0.61% B:0.01%)
66.43% (G:12.59% B:0.11%) | |
|
| 4. | XG Roller++ | 13/12 11/8 | eq: -0.683 (-0.113) |
| Player:
Opponent: | 34.27% (G:0.82% B:0.02%)
65.73% (G:12.88% B:0.11%) | |
|
| 5. | XG Roller++ | 8/5 3/2 | eq: -0.714 (-0.144) |
| Player:
Opponent: | 30.53% (G:0.47% B:0.01%)
69.47% (G:8.58% B:0.06%) | |
|
| 6. | XG Roller++ | 13/12 8/5 | eq: -0.759 (-0.189) |
| Player:
Opponent: | 29.79% (G:0.61% B:0.01%)
70.21% (G:9.11% B:0.08%) | |
|
| 7. | XG Roller++ | 13/10 11/10 | eq: -0.810 (-0.240) |
| Player:
Opponent: | 34.88% (G:0.89% B:0.02%)
65.12% (G:20.62% B:0.13%) | |
|
| 8. | XG Roller++ | 8/4* | eq: -0.937 (-0.367) |
| Player:
Opponent: | 36.77% (G:1.10% B:0.02%)
63.23% (G:33.13% B:0.38%) | |
|
eXtreme Gammon Version: 2.10
Give White a six-prime as well as a bit of timing, and the bot won't give the time of day to any play besides 9/8 9/6 (though 11/10 11/8 might still win by a nose at DMP).
| | White is Player 1
score: 0
pip: 82 | Unlimited Game
Jacoby | pip: 92
score: 0
Blue is Player 2 |
|
| XGID=-BBAaBB-AB-B-A----bbbccb--:0:0:1:31:0:0:1:0:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 9/8 9/6 | eq: -0.213 |
| Player:
Opponent: | 41.03% (G:0.96% B:0.02%)
58.97% (G:6.63% B:0.10%) | |
|
| 2. | XG Roller++ | 8/5 3/2 | eq: -0.358 (-0.145) |
| Player:
Opponent: | 37.44% (G:0.72% B:0.01%)
62.56% (G:8.17% B:0.16%) | |
|
| 3. | XG Roller++ | 11/8 3/2 | eq: -0.359 (-0.146) |
| Player:
Opponent: | 38.90% (G:0.80% B:0.01%)
61.10% (G:10.09% B:0.19%) | |
|
| 4. | XG Roller++ | 13/12 8/5 | eq: -0.384 (-0.171) |
| Player:
Opponent: | 37.58% (G:1.06% B:0.02%)
62.42% (G:7.44% B:0.08%) | |
|
| 5. | XG Roller++ | 13/12 11/8 | eq: -0.434 (-0.221) |
| Player:
Opponent: | 38.97% (G:1.22% B:0.02%)
61.03% (G:11.56% B:0.32%) | |
|
| 6. | XG Roller++ | 11/10 11/8 | eq: -0.443 (-0.231) |
| Player:
Opponent: | 41.63% (G:1.42% B:0.03%)
58.37% (G:18.67% B:0.27%) | |
|
| 7. | XG Roller++ | 13/10 11/10 | eq: -0.602 (-0.389) |
| Player:
Opponent: | 38.38% (G:1.11% B:0.02%)
61.62% (G:18.04% B:0.33%) | |
|
| 8. | XG Roller++ | 11/8 2/1 | eq: -0.707 (-0.494) |
| Player:
Opponent: | 32.62% (G:0.67% B:0.01%)
67.38% (G:12.47% B:0.36%) | |
|
| 9. | XG Roller++ | 8/4* | eq: -0.713 (-0.501) |
| Player:
Opponent: | 38.72% (G:2.08% B:0.04%)
61.28% (G:30.71% B:0.76%) | |
|
| 10. | XG Roller++ | 8/5 2/1 | eq: -0.765 (-0.553) |
| Player:
Opponent: | 29.43% (G:0.37% B:0.01%)
70.57% (G:7.35% B:0.10%) | |
|
eXtreme Gammon Version: 2.10
Now let's take a look at some smaller changes. Suppose we give White a spare on the 6pt so that 66 doesn't expose a blot.
| | White is Player 2
score: 0
pip: 77 | Unlimited Game
Jacoby | pip: 92
score: 0
Blue is Player 1 |
|
| XGID=-BBAaBB-AB-B-A-----cbcdb--:0:0:1:31:0:0:1:0:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 9/8 9/6 | eq: -0.350 |
| Player:
Opponent: | 37.68% (G:0.91% B:0.01%)
62.32% (G:7.00% B:0.13%) | |
|
| 2. | XG Roller++ | 11/10 11/8 | eq: -0.435 (-0.085) |
| Player:
Opponent: | 40.80% (G:1.20% B:0.02%)
59.20% (G:17.68% B:0.30%) | |
|
| 3. | XG Roller++ | 11/8 3/2 | eq: -0.452 (-0.101) |
| Player:
Opponent: | 36.81% (G:0.82% B:0.01%)
63.19% (G:11.33% B:0.20%) | |
|
| 4. | XG Roller++ | 13/12 11/8 | eq: -0.493 (-0.142) |
| Player:
Opponent: | 37.08% (G:1.10% B:0.02%)
62.92% (G:11.33% B:0.24%) | |
|
| 5. | XG Roller++ | 8/5 3/2 | eq: -0.521 (-0.170) |
| Player:
Opponent: | 34.17% (G:0.54% B:0.01%)
65.83% (G:7.71% B:0.15%) | |
|
| 6. | XG Roller++ | 8/4* | eq: -0.556 (-0.205) |
| Player:
Opponent: | 40.78% (G:1.45% B:0.03%)
59.22% (G:28.12% B:0.69%) | |
|
| 7. | XG Roller++ | 13/12 8/5 | eq: -0.569 (-0.219) |
| Player:
Opponent: | 33.53% (G:0.73% B:0.01%)
66.47% (G:7.03% B:0.09%) | |
|
| 8. | XG Roller++ | 13/10 11/10 | eq: -0.574 (-0.223) |
| Player:
Opponent: | 38.07% (G:1.00% B:0.02%)
61.93% (G:16.92% B:0.27%) | |
|
eXtreme Gammon Version: 2.10
What about just shifting one checker from White's 3pt to her 4pt? Someone might want to do a full rollout for this one:
| | White is Player 2
score: 0
pip: 75 | Unlimited Game
Jacoby | pip: 92
score: 0
Blue is Player 1 |
|
| XGID=-BBAaBB-AB-B-A-----bbddb--:0:0:1:31:0:0:1:0:10 |
| Blue to play 31 |
| 1. | XG Roller++ | 9/8 9/6 | eq: -0.338 |
| Player:
Opponent: | 37.43% (G:0.97% B:0.02%)
62.57% (G:6.13% B:0.10%) | |
|
| 2. | XG Roller++ | 11/10 11/8 | eq: -0.338 (0.000) |
| Player:
Opponent: | 42.32% (G:1.19% B:0.02%)
57.68% (G:15.93% B:0.27%) | |
|
| 3. | XG Roller++ | 8/4* | eq: -0.373 (-0.034) |
| Player:
Opponent: | 43.17% (G:2.40% B:0.07%)
56.83% (G:25.82% B:0.61%) | |
|
eXtreme Gammon Version: 2.10