Below is the variant demonstrating what I believe John said, that when we don't own the cube sometimes we are more apt to make bigger/bolder plays in order to kill the opp's recube efficiency. While the correct play remains the same, the difference from the correct play to the second best play is cut to almost a third.
Also below that is a variant showing the opponent not only without the blotted inner board, but another point made and it's still correct to make the big play.

              
 
              
 | | White is Player 2
score: 0 pip: 112 | Unlimited Game Jacoby Beaver | pip: 124 score: 0
Blue is Player 1 | |
| XGID=--BBaBC--B--cB----bccB-ba-:1:-1:1:21:0:0:3:0:10 |
| Blue to play 21 |
| 1. | Rollout1 | 9/8 6/4* | eq: +0.247 |
| Player: Opponent: | 63.77% (G:23.96% B:0.48%) 36.23% (G:13.81% B:0.42%) | Conf.: ± 0.007 (+0.240...+0.255) - [100.0%] Duration: 19.6 seconds |
|
| 2. | Rollout1 | 6/4* 5/4 | eq: +0.152 (-0.096) |
| Player: Opponent: | 59.82% (G:21.64% B:0.43%) 40.18% (G:10.69% B:0.32%) | Conf.: ± 0.009 (+0.142...+0.161) - [0.0%] Duration: 22.3 seconds |
|
| 3. | Rollout1 | 6/4* 4/3 | eq: +0.066 (-0.181) |
| Player: Opponent: | 57.13% (G:17.34% B:0.34%) 42.87% (G:9.15% B:0.35%) | Conf.: ± 0.007 (+0.059...+0.074) - [0.0%] Duration: 21.4 seconds |
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| |
1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller
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Variant - Owning the cube

              
 
              
 | | White is Player 2
score: 0 pip: 112 | Unlimited Game Jacoby Beaver | pip: 124 score: 0
Blue is Player 1 | |
| XGID=--BBaBC--B--cB----bcbBbb--:1:1:1:21:0:0:3:0:10 |
| Blue to play 21 |
| 1. | XG Roller++ | 9/8 6/4* | eq: +0.315 |
| Player: Opponent: | 54.78% (G:16.76% B:0.19%) 45.22% (G:17.06% B:0.48%) | |
|
| 2. | XG Roller++ | 6/4* 4/3 | eq: +0.282 (-0.033) |
| Player: Opponent: | 52.48% (G:13.60% B:0.20%) 47.52% (G:9.49% B:0.28%) | |
|
| 3. | XG Roller++ | 6/4* 5/4 | eq: +0.265 (-0.049) |
| Player: Opponent: | 51.10% (G:14.92% B:0.19%) 48.90% (G:11.25% B:0.29%) | |
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Variant - Four point board

              
 
              
 | | White is Player 2
score: 0 pip: 112 | Unlimited Game Jacoby Beaver | pip: 124 score: 0
Blue is Player 1 | |
| XGID=--BBaBC--B--cB----bcbBbb--:1:-1:1:21:0:0:3:0:10 |
| Blue to play 21 |
| 1. | Rollout1 | 9/8 6/4* | eq: -0.010 |
| Player: Opponent: | 55.60% (G:18.43% B:0.34%) 44.40% (G:16.89% B:0.55%) | Conf.: ± 0.008 (-0.019...-0.002) - [100.0%] Duration: 27.7 seconds |
|
| 2. | Rollout1 | 6/4* 4/3 | eq: -0.071 (-0.060) |
| Player: Opponent: | 52.91% (G:14.41% B:0.25%) 47.09% (G:10.05% B:0.41%) | Conf.: ± 0.008 (-0.078...-0.063) - [0.0%] Duration: 26.3 seconds |
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1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller
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