First I want to mention that from a practical point of view, if you're in time trouble, then I believe that the decision to keep a closed board is the right one. Regardless of what the bot says, you probably don't want to be hit, because it will extend the game with a lot of complicated decisions.
Now for the variants and analysis. Everything below is at DMP for simplicity and to avoid potential cube errors by XG. With an extra White checker on her 2pt, the decision is closer. Note that if Blue plays 7/6 2/off 1/off and White rolls 11, Blue still gets a shot from the bar.
      
 
        
 | | White is Player 2
score: 0
pip: 34 | | 1 point match | pip: 57
score: 0
Blue is Player 1 |
|
| XGID=aBCBBBCA---------------da-:0:0:1:11:0:0:0:1:10 |
| Blue to play 11 |
| 1. | Rollout1 | 7/6 2/Off 1/Off | eq: -0.008 |
| Player:
Opponent: | 49.59% (G:0.00% B:0.00%)
50.41% (G:0.00% B:0.00%) | Conf.: ± 0.003 (-0.011...-0.005) - [100.0%]
Duration: 57 minutes 08 seconds |
|
| 2. | Rollout1 | 7/5 2/Off | eq: -0.019 (-0.011) |
| Player:
Opponent: | 49.06% (G:0.00% B:0.00%)
50.94% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.021...-0.017) - [0.0%]
Duration: 13 minutes 55 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Huge
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
With two extra checkers the top two plays exchange places in the rollout, and are not close.
 
| | White is Player 2
score: 0
pip: 36 | | 1 point match | pip: 57
score: 0
Blue is Player 1 |
|
| XGID=aBCBBBCA---------------ea-:0:0:1:11:0:0:0:1:10 |
| Blue to play 11 |
| 1. | Rollout1 | 7/5 2/Off | eq: +0.171 |
| Player:
Opponent: | 58.53% (G:0.00% B:0.00%)
41.47% (G:0.00% B:0.00%) | Conf.: ± 0.002 (+0.168...+0.173) - [100.0%]
Duration: 10.1 seconds |
|
| 2. | Rollout1 | 7/6 2/Off 1/Off | eq: +0.122 (-0.049) |
| Player:
Opponent: | 56.08% (G:0.00% B:0.00%)
43.92% (G:0.00% B:0.00%) | Conf.: ± 0.003 (+0.118...+0.125) - [0.0%]
Duration: 33.8 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Let's verify that with four checkers on her 2pt, White prefers not to have to hit the blot that Blue volunteers, at least if the other half of her roll is blocked.
 
| | White is Player 2
score: 0
pip: 34 | | 1 point match | pip: 53
score: 0
Blue is Player 1 |
|
| XGID=aABBBBD----------------da-:0:0:-1:21:0:0:0:1:10 |
| White to play 21 |
| 1. | Rollout1 | Bar/24* | eq: -0.078 |
| Player:
Opponent: | 46.11% (G:0.00% B:0.00%)
53.89% (G:0.00% B:0.00%) | Conf.: ± 0.005 (-0.083...-0.073)
Duration: 1 minute 32 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
| | White is Player 2
score: 0
pip: 34 | | 1 point match | pip: 53
score: 0
Blue is Player 1 |
|
| XGID=aABBBBD----------------da-:0:0:-1:22:0:0:0:1:10 |
| White to play 22 |
| 1. | Rollout1 | Cannot Move | eq: +0.012 |
| Player:
Opponent: | 50.60% (G:0.00% B:0.00%)
49.40% (G:0.00% B:0.00%) | Conf.: ± 0.003 (+0.009...+0.015)
Duration: 21.5 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
By comparing with the equity after 7/5 2/off in the first rollout above, we see that White's GWC after a dance are essentially the same, regardless of which of the two candidate plays Blue chooses to make. That means that the relevant tradeoff is just between White's "good" hits and her "bad" hits (61 and 11 versus the rest).
Let's go back to three checkers on White's 3pt, but suppose Blue plays 7/5 2/off. Does Blue still want to volunteer a blot on his 1pt? If his next roll is 41, then XG prefers not to volunteer a blot. However, with other rolls involving a 1 (not shown), XG strongly prefers to volunteer a blot on the 1pt.
 
 
| | White is Player 2
score: 0
pip: 32 | | 1 point match | pip: 53
score: 0
Blue is Player 1 |
|
| XGID=aBBBBCC----------------ca-:0:0:1:41:0:0:0:1:10 |
| Blue to play 41 |
| 1. | Rollout1 | 5/Off | eq: -0.223 |
| Player:
Opponent: | 38.86% (G:0.00% B:0.00%)
61.14% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.225...-0.220) - [100.0%]
Duration: 3 minutes 04 seconds |
|
| 2. | Rollout1 | 6/2 1/Off | eq: -0.242 (-0.019) |
| Player:
Opponent: | 37.92% (G:0.00% B:0.00%)
62.08% (G:0.00% B:0.00%) | Conf.: ± 0.003 (-0.245...-0.239) - [0.0%]
Duration: 5 minutes 36 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: 4-ply
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
White's 1pt blot is of course crucial. If we vary the position by covering it (not shown), then 7/5 2/off is clear. Now my suggested variant (of shifting Blue's spare from the 2pt to the 1pt) becomes more interesting:
 
| | White is Player 2
score: 0
pip: 31 | | 1 point match | pip: 56
score: 0
Blue is Player 1 |
|
| XGID=aCBBBBCA---------------bb-:0:0:1:11:0:0:0:1:10 |
| Blue to play 11 |
| 1. | Rollout1 | 7/4 1/Off | eq: -0.346 |
| Player:
Opponent: | 32.69% (G:0.00% B:0.00%)
67.31% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.348...-0.344) - [99.9%]
Duration: 7 minutes 00 second |
|
| 2. | Rollout1 | 7/6 1/Off(3) | eq: -0.352 (-0.005) |
| Player:
Opponent: | 32.42% (G:0.00% B:0.00%)
67.58% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.354...-0.349) - [0.1%]
Duration: 14 minutes 38 seconds |
|
| 3. | Rollout1 | 7/5 6/5 1/Off | eq: -0.370 (-0.024) |
| Player:
Opponent: | 31.48% (G:0.00% B:0.00%)
68.52% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.372...-0.368) - [0.0%]
Duration: 5 minutes 17 seconds |
|
| 4. | Rollout1 | 7/5 1/Off(2) | eq: -0.375 (-0.029) |
| Player:
Opponent: | 31.24% (G:0.00% B:0.00%)
68.76% (G:0.00% B:0.00%) | Conf.: ± 0.003 (-0.378...-0.373) - [0.0%]
Duration: 34 minutes 38 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Huge
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Finally, for the second position, it looks like 4/off is indicated even if we cover White's blot.
| | White is Player 2
score: 0
pip: 31 | | 1 point match | pip: 44
score: 0
Blue is Player 1 |
|
| XGID=aBCBBBB----------------bb-:0:0:1:31:0:0:0:1:10 |
| Blue to play 31 |
| 1. | Rollout1 | 4/Off | eq: -0.460 |
| Player:
Opponent: | 26.98% (G:0.00% B:0.00%)
73.02% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.462...-0.459) - [96.5%]
Duration: 1 minute 48 seconds |
|
| 2. | Rollout1 | 3/Off 2/1 | eq: -0.463 (-0.003) |
| Player:
Opponent: | 26.85% (G:0.00% B:0.00%)
73.15% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.465...-0.461) - [3.5%]
Duration: 2 minutes 13 seconds |
|
| 3. | Rollout1 | 3/2 3/Off | eq: -0.475 (-0.015) |
| Player:
Opponent: | 26.23% (G:0.00% B:0.00%)
73.77% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.477...-0.473) - [0.0%]
Duration: 1 minute 03 seconds |
|
| 4. | Rollout1 | 6/5 6/3 | eq: -0.480 (-0.020) |
| Player:
Opponent: | 25.98% (G:0.00% B:0.00%)
74.02% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.482...-0.479) - [0.0%]
Duration: 17.1 seconds |
|
| 5. | Rollout1 | 6/3 2/1 | eq: -0.498 (-0.037) |
| Player:
Opponent: | 25.12% (G:0.00% B:0.00%)
74.88% (G:0.00% B:0.00%) | Conf.: ± 0.002 (-0.499...-0.496) - [0.0%]
Duration: 37.0 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: 4-ply
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2