It's easy to miss this one OtB, and QF puts it into focus. But I don't think you need QF to see the right play if you properly value the various assets.
Here, blue has a solid five prime with none of white's five checkers at the edge. This is very strong, and as Tim points out the only way to preserve the five prime is to make the banana split play. Not hitting is not an option
I hypothesized that white's weak board and three blots on her side of the board would tip the balance in favor of the banana split, but in the first variant I've cleaned up the blots and strengthened the board, and it's an even bigger error to make the four vs slotting the four and five (and worse than not hitting). The right idea is to keep the five prime, hits be damned.
In the second variant, I've moved blue's blot up to the 21 to see what happens not hitting while preserving the five prime was an option. Hitting is still correct according to XGR+++, but slotting the five is not necessary.
        
 
           
 | | White is Player 2
score: 0
pip: 187 | | Unlimited Game | pip: 128
score: 0
Blue is Player 1 |
|
| XGID=-b-ba-EBCBB-b--a-a-cb-Aa--:1:-1:1:32:0:0:0:0:10 |
| Blue to play 32 |
| 1. | Rollout1 | 8/5 6/4* | eq: +0.452 |
| Player:
Opponent: | 66.99% (G:29.18% B:2.39%)
33.01% (G:6.38% B:0.39%) | Conf.: ± 0.016 (+0.436...+0.468) - [100.0%]
Duration: 6 minutes 35 seconds |
|
| 2. | Rollout1 | 7/4* 6/4 | eq: +0.350 (-0.102) |
| Player:
Opponent: | 61.33% (G:30.76% B:4.57%)
38.67% (G:5.74% B:0.25%) | Conf.: ± 0.015 (+0.336...+0.365) - [0.0%]
Duration: 5 minutes 59 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
Variant 1:
 
| | White is Player 2
score: 0
pip: 180 | | Unlimited Game | pip: 128
score: 0
Blue is Player 1 |
|
| XGID=-b-ba-EBCBB-b------ccbA---:1:-1:1:32:0:0:0:0:10 |
| Blue to play 32 |
| 1. | XG Roller++ | 8/5 6/4* | eq: +0.311 |
| Player:
Opponent: | 64.65% (G:23.20% B:1.74%)
35.35% (G:9.82% B:0.45%) | |
|
| 2. | XG Roller++ | 10/8 10/7 | eq: +0.103 (-0.208) |
| Player:
Opponent: | 57.44% (G:20.10% B:1.35%)
42.56% (G:9.43% B:0.34%) | |
|
| 3. | XG Roller++ | 7/4* 6/4 | eq: +0.072 (-0.239) |
| Player:
Opponent: | 55.57% (G:22.30% B:2.15%)
44.43% (G:11.24% B:0.45%) | |
|
eXtreme Gammon Version: 2.10
Variant 2:
| | White is Player 2
score: 0
pip: 187 | | Unlimited Game | pip: 127
score: 0
Blue is Player 1 |
|
| XGID=-b-ba-EBCBB-b--a-a-cbA-a--:1:-1:1:32:0:0:0:0:10 |
| Blue to play 32 |
| 1. | XG Roller++ | 21/18 6/4* | eq: +0.479 |
| Player:
Opponent: | 66.82% (G:29.94% B:2.85%)
33.18% (G:4.90% B:0.19%) | |
|
| 2. | XG Roller++ | 8/5 6/4* | eq: +0.456 (-0.024) |
| Player:
Opponent: | 66.75% (G:29.17% B:2.71%)
33.25% (G:6.65% B:0.29%) | |
|
| 3. | XG Roller++ | 21/16 | eq: +0.393 (-0.086) |
| Player:
Opponent: | 65.80% (G:25.66% B:1.60%)
34.20% (G:5.49% B:0.22%) | |
|
eXtreme Gammon Version: 2.10