I have to say that I don't feel that I understand these positions yet, but here's my best current guess. I would think that in both cases, the chances of getting a second checker sent back must be higher if we pay now (though I'm not positive about this). Getting a second checker sent back is good if we can anchor and bad if we get both checkers closed out. In the second position, White currently has less ammunition up front so Blue has a better chance of anchoring. I guess it must be too optimistic for Blue, in the second position, to hope to never have to leave a direct shot, so it's better to leave it now rather than later.
I'll try to remember to test these theories later by shuffling the checkers around, and to post anything interesting that I find.
It seems hard to get direct information on how often Blue gets a second checker sent back after each play. GNU's "View Statistics" will tell us how often Blue gets hit, but this won't distinguish between hits on White's 1pt and hits that send a second checker back.
Problem 1
| | White is Player 2
score: 0 pip: 96 | Unlimited Game | pip: 75 score: 0
Blue is Player 1 | |
XGID=-aEC-DB-----a-----bbcbbbA-:1:1:1:61:0:0:0:0:10 |
Blue to play 61 |
1. | Rollout1 | 3/2 | eq: -1.011 |
| Player: Opponent: | 5.48% (G:0.18% B:0.00%) 94.52% (G:13.50% B:0.51%) | Conf.: ± 0.003 (-1.014...-1.007) - [100.0%] Duration: 2 minutes 26 seconds |
|
2. | Rollout1 | 2/1* | eq: -1.063 (-0.052) |
| Player: Opponent: | 4.50% (G:0.20% B:0.01%) 95.50% (G:16.58% B:0.50%) | Conf.: ± 0.003 (-1.066...-1.060) - [0.0%] Duration: 2 minutes 41 seconds |
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|
1 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
Problem 2
| | White is Player 1
score: 0 pip: 120 | Unlimited Game | pip: 69 score: 0
Blue is Player 2 | |
XGID=aaFCBBA-a---------bbbbbbA-:1:1:1:31:0:0:0:0:10 |
Blue to play 31 |
1. | Rollout1 | 6/3 2/1* | eq: -1.063 |
| Player: Opponent: | 4.38% (G:0.17% B:0.00%) 95.62% (G:15.86% B:0.69%) | Conf.: ± 0.003 (-1.066...-1.060) - [100.0%] Duration: 3 minutes 07 seconds |
|
2. | Rollout1 | 6/2 | eq: -1.091 (-0.028) |
| Player: Opponent: | 4.15% (G:0.25% B:0.00%) 95.85% (G:18.06% B:0.74%) | Conf.: ± 0.004 (-1.095...-1.087) - [0.0%] Duration: 3 minutes 05 seconds |
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1 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10