Michael Depreli recently posted what I call a "pre-backgame" checker-play decision. I found the rollout results puzzling so I spent some time studying the position.
First of all I wanted to try to understand why hitting twice came out on top, followed by not hitting at all, followed by hitting once. Is it because Blue wants to get hit and hitting twice increases the chances of getting hit? Or does Blue prefer not to get hit but is willing to risk it if he can destroy White's chances of anchoring? It's not so easy to disentangle these two theories, but I'm leaning towards the latter. In the first variant below, I've changed the roll to 11, and the bot hates leaving two blots in Blue's home board.
          
 
          
 | | White is Player 2
score: 0
pip: 163 | | Unlimited Game | pip: 111
score: 0
Blue is Player 1 |
|
| XGID=-aaBcBCBBB----AA-bacb---b-:1:-1:1:11:0:0:0:0:10 |
| Blue to play 11 |
| 1. | XG Roller++ | 3/2*(2) 2/1*(2) | eq: +1.058 |
| Player:
Opponent: | 84.41% (G:43.98% B:0.82%)
15.59% (G:1.97% B:0.07%) | |
|
| 2. | XG Roller++ | 15/14 3/2*(2) 2/1* | eq: +0.880 (-0.178) |
| Player:
Opponent: | 81.64% (G:33.57% B:0.90%)
18.36% (G:2.98% B:0.07%) | |
|
| 3. | XG Roller++ | 15/14 6/5 3/2* 2/1* | eq: +0.879 (-0.180) |
| Player:
Opponent: | 81.52% (G:33.79% B:0.93%)
18.48% (G:3.11% B:0.07%) | |
|
| 4. | XG Roller++ | 15/13 3/2* 2/1* | eq: +0.868 (-0.191) |
| Player:
Opponent: | 81.33% (G:33.68% B:0.92%)
18.67% (G:3.62% B:0.13%) | |
|
| 5. | XG Roller++ | 14/12 3/2* 2/1* | eq: +0.862 (-0.196) |
| Player:
Opponent: | 81.20% (G:33.44% B:0.92%)
18.80% (G:3.53% B:0.13%) | |
|
eXtreme Gammon Version: 2.10
How important is it to prevent White from anchoring? Variant 2 below suggests that it's not as important as sending another checker back, if that option is on the table.
| | White is Player 2
score: 0
pip: 168 | | Unlimited Game | pip: 111
score: 0
Blue is Player 1 |
|
| XGID=-aaBcBCBBB---aAA-b-cb---b-:1:-1:1:21:0:0:0:0:10 |
| Blue to play 21 |
| 1. | XG Roller++ | 15/13* 3/2* | eq: +0.934 |
| Player:
Opponent: | 80.27% (G:41.06% B:2.19%)
19.73% (G:2.68% B:0.08%) | |
|
| 2. | XG Roller++ | 14/13* 3/1* | eq: +0.915 (-0.018) |
| Player:
Opponent: | 80.25% (G:40.09% B:1.60%)
19.75% (G:2.89% B:0.09%) | |
|
| 3. | XG Roller++ | 14/13* 13/11 | eq: +0.889 (-0.044) |
| Player:
Opponent: | 77.51% (G:42.92% B:2.40%)
22.49% (G:2.15% B:0.06%) | |
|
| 4. | XG Roller++ | 15/13* 13/12 | eq: +0.883 (-0.051) |
| Player:
Opponent: | 77.33% (G:42.77% B:2.36%)
22.67% (G:2.21% B:0.06%) | |
|
| 5. | XG Roller++ | 15/13* 6/5 | eq: +0.877 (-0.057) |
| Player:
Opponent: | 77.20% (G:42.65% B:2.32%)
22.80% (G:2.35% B:0.07%) | |
|
| 6. | XG Roller++ | 15/13* 14/13 | eq: +0.872 (-0.062) |
| Player:
Opponent: | 77.17% (G:42.18% B:2.25%)
22.83% (G:2.21% B:0.06%) | |
|
| 7. | XG Roller++ | 3/2* 3/1* | eq: +0.852 (-0.082) |
| Player:
Opponent: | 79.02% (G:38.07% B:1.37%)
20.98% (G:4.43% B:0.16%) | |
|
eXtreme Gammon Version: 2.10
The final variant below is the one I find most interesting. If we free White's fifth wheel by moving the spare from the anchor around the board, then hitting appears to be in whopper territory.
| | White is Player 2
score: 0
pip: 148 | | Unlimited Game | pip: 111
score: 0
Blue is Player 1 |
|
| XGID=-aaBbBCBBB----AA-badb---b-:1:-1:1:21:0:0:0:0:10 |
| Blue to play 21 |
| 1. | XG Roller++ | 15/13 14/13 | eq: +0.786 |
| Player:
Opponent: | 83.22% (G:19.01% B:0.55%)
16.78% (G:1.33% B:0.04%) | |
|
| 2. | XG Roller++ | 14/11 | eq: +0.784 (-0.002) |
| Player:
Opponent: | 82.67% (G:20.22% B:0.85%)
17.33% (G:1.76% B:0.05%) | |
|
| 3. | XG Roller++ | 15/12 | eq: +0.779 (-0.007) |
| Player:
Opponent: | 82.67% (G:19.64% B:0.81%)
17.33% (G:1.63% B:0.04%) | |
|
| 4. | XG Roller++ | 14/12 6/5 | eq: +0.778 (-0.008) |
| Player:
Opponent: | 82.42% (G:20.20% B:0.94%)
17.58% (G:1.88% B:0.06%) | |
|
| 5. | XG Roller++ | 15/13 6/5 | eq: +0.772 (-0.014) |
| Player:
Opponent: | 82.38% (G:19.72% B:0.75%)
17.62% (G:1.64% B:0.04%) | |
|
| 6. | XG Roller++ | 6/3 | eq: +0.727 (-0.060) |
| Player:
Opponent: | 80.23% (G:20.75% B:0.90%)
19.77% (G:2.33% B:0.07%) | |
|
| 7. | XG Roller++ | 9/8 9/7 | eq: +0.716 (-0.070) |
| Player:
Opponent: | 80.05% (G:20.54% B:0.97%)
19.95% (G:2.76% B:0.08%) | |
|
| 8. | XG Roller++ | 15/14 9/7 | eq: +0.687 (-0.099) |
| Player:
Opponent: | 78.84% (G:20.73% B:1.12%)
21.16% (G:3.23% B:0.07%) | |
|
| 9. | XG Roller++ | 15/14 3/1* | eq: +0.684 (-0.102) |
| Player:
Opponent: | 78.82% (G:21.84% B:0.80%)
21.18% (G:4.23% B:0.09%) | |
|
| 10. | XG Roller++ | 3/2* 3/1* | eq: +0.683 (-0.103) |
| Player:
Opponent: | 78.67% (G:23.19% B:0.70%)
21.33% (G:5.14% B:0.20%) | |
|
| 11. | XG Roller++ | 8/7 8/6 | eq: +0.660 (-0.126) |
| Player:
Opponent: | 78.72% (G:18.70% B:0.82%)
21.28% (G:3.13% B:0.08%) | |
|
| 12. | XG Roller++ | 14/13 3/1* | eq: +0.639 (-0.147) |
| Player:
Opponent: | 77.49% (G:22.03% B:0.85%)
22.51% (G:5.67% B:0.21%) | |
|
| 13. | XG Roller++ | 7/6 7/5 | eq: +0.633 (-0.153) |
| Player:
Opponent: | 77.64% (G:18.62% B:0.91%)
22.36% (G:3.37% B:0.12%) | |
|
| 14. | XG Roller++ | 6/5 3/1* | eq: +0.628 (-0.158) |
| Player:
Opponent: | 77.02% (G:22.18% B:0.85%)
22.98% (G:5.81% B:0.22%) | |
|
| 15. | XG Roller++ | 14/12 3/2* | eq: +0.621 (-0.165) |
| Player:
Opponent: | 76.80% (G:22.81% B:1.08%)
23.20% (G:6.86% B:0.29%) | |
|
| 16. | XG Roller++ | 15/13 3/2* | eq: +0.620 (-0.167) |
| Player:
Opponent: | 76.78% (G:22.62% B:1.04%)
23.22% (G:6.72% B:0.26%) | |
|
eXtreme Gammon Version: 2.10