The best play for money and DMP is one that Neil mentioned: the voluntary triple shot play 21/16 13/10, leaving roughly 30 shots (including six numbers that hit two blots) when a perfectly "safe" play is available.
This position intrigued me when I first saw it last July because I knew no way would I have gotten it right over the board. When I saw it again six months later, I realized that I probably would have still missed it over the board. I figured if I wrote it up, I would be forced to think about it more thoroughly, perhaps enough so that I will be able to get one of these right over the board in the future.
Here is the order of things appearing below: (1) Money rollout result (2) Brief commentary on money and dmp play (3) Diagram of the "after" position for money (4) DMP rollout result (5) GS rollout result and (6) GS rollout result.
          
 
        
 | | White is Player 2
score: 0
pip: 146 | Unlimited Game
Jacoby Beaver | pip: 163
score: 0
Blue is Player 1 |
|
| XGID=----BbC-C---bD-b-c-fBA----:0:0:1:35:0:0:3:0:10 |
| Blue to play 35 |
| 1. | Rollout1 | 21/16 13/10 | eq: -0.126 |
| Player:
Opponent: | 46.42% (G:8.03% B:0.33%)
53.58% (G:9.92% B:0.27%) | Conf.: ± 0.014 (-0.139...-0.112) - [99.9%]
Duration: 7 minutes 41 seconds |
|
| 2. | Rollout1 | 8/3 6/3 | eq: -0.154 (-0.028) |
| Player:
Opponent: | 45.97% (G:8.08% B:0.33%)
54.03% (G:9.44% B:0.23%) | Conf.: ± 0.012 (-0.166...-0.142) - [0.1%]
Duration: 7 minutes 13 seconds |
|
| 3. | Rollout1 | 21/13 | eq: -0.161 (-0.035) |
| Player:
Opponent: | 45.33% (G:6.28% B:0.23%)
54.67% (G:7.36% B:0.16%) | Conf.: ± 0.010 (-0.171...-0.150) - [0.0%]
Duration: 6 minutes 52 seconds |
|
| 4. | Rollout1 | 21/16 6/3 | eq: -0.174 (-0.049) |
| Player:
Opponent: | 45.21% (G:7.79% B:0.26%)
54.79% (G:9.03% B:0.32%) | Conf.: ± 0.013 (-0.187...-0.162) - [0.0%]
Duration: 7 minutes 07 seconds |
|
| 5. | Rollout2 | 21/18 13/8 | eq: -0.204 (-0.078) |
| Player:
Opponent: | 44.38% (G:7.04% B:0.17%)
55.62% (G:8.25% B:0.21%) | Conf.: ± 0.026 (-0.230...-0.177) - [0.0%]
Duration: 2 minutes 01 second |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
2 172 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
Neil zeroed in on the issue when he observed that after Blue plays 21/16 13/10, all three of White's points (20pt 13pt 10pt) from which she could hit are stripped. She would be forced to leave many return shots with some of these numbers if she chose to hit. In fact, according to the XG eval, White should refrain from hitting with 13 of the the 30 numbers that could hit. White should not hit with 21 31 61 42 64 53 22. White should hit with only 17 numbers. Even after White hits twice with 65 54 51, she will still be under pressure to clean up a lot of blots on her next roll.
Blue trails in the race and is the underdog in this mutual holding game after all possible plays with his 53. He has a stronger board and a better distribution while White has an inner board blot. Blue should exploit these three positional advantages to give himself a chance to make a new outfield blocking point.
After Blue plays 21/16 13/10 (see diagram below), good things or bad things can happen to him. The good things that can happen are: (1) he gets hit but then hits a return shot (2) he does not get hit and makes a new outfield point next turn. The bad things that can happen are: (1) Blue gets hit and does not hit a return shot and (2) Blue is missed but fails to cover and must leave shots.
The rollout result suggests that the good things outweigh the bad things after playing 21/16 13/10 compared to the other plays.
 
| | White is Player 2
score: 0
pip: 146 | Unlimited Game
Jacoby Beaver | pip: 155
score: 0
Blue is Player 1 |
|
| XGID=----BbC-C-A-bC-bAc-fB-----:0:0:-1:00:0:0:3:0:10 |
| White on roll, cube action? |
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 53.95% (G:9.71% B:0.29%) | 54.06% (G:9.15% B:0.26%) |
| Opponent Winning Chances: | 46.05% (G:7.84% B:0.28%) | 45.94% (G:7.61% B:0.25%) |
| Cubeless Equities | +0.098 | +0.193 |
| Cubeful Equities |
| No double: | +0.144 | |
| Double/Beaver: | -0.283 (-0.426) | |
| Double/Pass: | +1.000 (+0.856) |
| |
| Best Cube action: No double / Beaver |
| Percentage of wrong pass needed to make the double decision right: 24.9% |
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 146 | | 1 point match | pip: 163
score: 0
Blue is Player 1 |
|
| XGID=----BbC-C---bD-b-c-fBA----:0:0:1:35:0:0:0:1:10 |
| Blue to play 35 |
| 1. | Rollout1 | 21/16 13/10 | eq: -0.068 |
| Player:
Opponent: | 46.62% (G:8.12% B:0.55%)
53.38% (G:13.35% B:0.90%) | Conf.: ± 0.005 (-0.073...-0.062) - [99.8%]
Duration: 6 minutes 54 seconds |
|
| 2. | Rollout1 | 8/3 6/3 | eq: -0.078 (-0.011) |
| Player:
Opponent: | 46.09% (G:9.21% B:1.10%)
53.91% (G:13.09% B:0.61%) | Conf.: ± 0.005 (-0.083...-0.073) - [0.2%]
Duration: 6 minutes 09 seconds |
|
| 3. | Rollout1 | 21/13 | eq: -0.094 (-0.027) |
| Player:
Opponent: | 45.29% (G:7.05% B:0.43%)
54.71% (G:9.39% B:0.39%) | Conf.: ± 0.004 (-0.099...-0.090) - [0.0%]
Duration: 6 minutes 09 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
| | White is Player 2
score: 0
pip: 146 | 2 point match
Crawford | pip: 163
score: 1
Blue is Player 1 |
|
| XGID=----BbC-C---bD-b-c-fBA----:0:0:1:35:1:0:1:2:10 |
| Blue to play 35 |
| 1. | Rollout1 | 21/13 | eq: -0.221 |
| Player:
Opponent: | 44.44% (G:6.04% B:0.55%)
55.56% (G:5.47% B:0.26%) | Conf.: ± 0.002 (-0.223...-0.218) - [100.0%]
Duration: 22 minutes 49 seconds |
|
| 2. | Rollout1 | 8/3 6/3 | eq: -0.255 (-0.034) |
| Player:
Opponent: | 45.01% (G:8.53% B:0.90%)
54.99% (G:7.75% B:0.34%) | Conf.: ± 0.003 (-0.258...-0.252) - [0.0%]
Duration: 21 minutes 50 seconds |
|
| 3. | Rollout1 | 21/18 13/8 | eq: -0.258 (-0.037) |
| Player:
Opponent: | 43.61% (G:7.05% B:0.47%)
56.39% (G:6.50% B:0.30%) | Conf.: ± 0.003 (-0.261...-0.255) - [0.0%]
Duration: 22 minutes 35 seconds |
|
| 4. | Rollout2 | 21/16 13/10 | eq: -0.260 (-0.039) |
| Player:
Opponent: | 45.59% (G:10.25% B:1.14%)
54.41% (G:8.59% B:0.96%) | Conf.: ± 0.013 (-0.273...-0.247) - [0.0%]
Duration: 2 minutes 13 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
2 229 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
| | White is Player 2
score: 0
pip: 146 | 2 point match
Crawford | pip: 163
score: 1
Blue is Player 1 |
|
| XGID=----BbC-C---bD-b-c-fBA----:0:0:1:35:1:0:1:2:10 |
| Blue to play 35 |
| 1. | Rollout1 | 21/13 | eq: -0.221 |
| Player:
Opponent: | 44.44% (G:6.04% B:0.55%)
55.56% (G:5.47% B:0.26%) | Conf.: ± 0.002 (-0.223...-0.218) - [100.0%]
Duration: 22 minutes 49 seconds |
|
| 2. | Rollout1 | 8/3 6/3 | eq: -0.255 (-0.034) |
| Player:
Opponent: | 45.01% (G:8.53% B:0.90%)
54.99% (G:7.75% B:0.34%) | Conf.: ± 0.003 (-0.258...-0.252) - [0.0%]
Duration: 21 minutes 50 seconds |
|
| 3. | Rollout1 | 21/18 13/8 | eq: -0.258 (-0.037) |
| Player:
Opponent: | 43.61% (G:7.05% B:0.47%)
56.39% (G:6.50% B:0.30%) | Conf.: ± 0.003 (-0.261...-0.255) - [0.0%]
Duration: 22 minutes 35 seconds |
|
| 4. | Rollout2 | 21/16 13/10 | eq: -0.260 (-0.039) |
| Player:
Opponent: | 45.59% (G:10.25% B:1.14%)
54.41% (G:8.59% B:0.96%) | Conf.: ± 0.013 (-0.273...-0.247) - [0.0%]
Duration: 2 minutes 13 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
2 229 Games rolled with Variance Reduction.
Dice Seed: 101
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2