Good quiz and comments!
Below are XGR++ results for Stick's variants. When I first saw the Counter Quiz, I misinterpreted the significance of variants #3 and #5. Still, I'm fairly happy with my own answers except for my decision to pass (original) #2.
In #1, I am also a little surprised at the magnitude of the equity difference of 24/23, but it's pretty clear that you don't want to be splitting when White has ten checkers in the zone and more attacking potential than priming potential.
In #5, I'd be a little cautious of generalizing too hastily. I believe that lifting the blot will be a mistake, perhaps even a whopper, in many seemingly similar positions. For example, backgammon wins don't matter ATS whereas they might at other scores. The fact that White has made her ace point probably also makes a difference, making her hits slightly more dangerous. This is not to say that lifting the blot isn't right when there's little or nothing to gain and a lot to lose, but here there are several non-lifting plays that do gain something, so it's a pretty subtle fact that lifting comes out on top of the rollout.
#1
          
 
         
 | | White is Player 2
score: 6
pip: 152 | | 9 point match | pip: 160
score: 5
Blue is Player 1 |
|
| XGID=-b----EBB---cD--ac-d-b--B-:0:0:1:21:5:6:0:9:10 |
| Blue to play 21 |
| 1. | XG Roller++ | 13/11 6/5 | eq: -0.049 |
| Player:
Opponent: | 46.92% (G:12.63% B:0.61%)
53.08% (G:19.03% B:1.61%) | |
|
| 2. | XG Roller++ | 7/5 6/5 | eq: -0.057 (-0.008) |
| Player:
Opponent: | 46.20% (G:13.38% B:0.62%)
53.80% (G:18.33% B:1.35%) | |
|
| 3. | XG Roller++ | 13/10 | eq: -0.219 (-0.170) |
| Player:
Opponent: | 43.20% (G:11.56% B:0.54%)
56.80% (G:19.38% B:1.32%) | |
|
| 4. | XG Roller++ | 24/23 13/11 | eq: -0.224 (-0.175) |
| Player:
Opponent: | 43.63% (G:11.22% B:0.54%)
56.37% (G:20.59% B:0.98%) | |
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
#2
   
  
| | White is Player 2
score: 0
pip: 103 | | Unlimited Game | pip: 116
score: 0
Blue is Player 1 |
|
| XGID=-bB-CBBBA--A----aa-cAbbbbA:0:0:1:00:0:0:0:0:10 |
| Blue on roll, cube action? |
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 63.84% (G:16.46% B:0.95%) | 63.99% (G:16.62% B:0.95%) |
| Opponent Winning Chances: | 36.16% (G:21.63% B:1.77%) | 36.01% (G:21.72% B:1.77%) |
| Cubeless Equities | +0.217 | +0.441 |
| Cubeful Equities |
| No double: | +0.318 | |
| Double/Take: | +0.254 (-0.063) | |
| Double/Pass: | +1.000 (+0.682) |
| |
| Best Cube action: No double / Take |
| Percentage of wrong pass needed to make the double decision right: 7.8% |
eXtreme Gammon Version: 2.10
#3
 
 
| | White is Player 2
score: 0
pip: 153 | | Unlimited Game | pip: 133
score: 0
Blue is Player 1 |
|
| XGID=-B-B-aDb----cE-A-c-dbA----:0:0:1:63:0:0:0:0:10 |
| Blue to play 63 |
| 1. | XG Roller++ | 21/15 6/3 | eq: -0.052 |
| Player:
Opponent: | 49.27% (G:12.92% B:0.21%)
50.73% (G:15.31% B:0.45%) | |
|
| 2. | XG Roller++ | 21/15 13/10 | eq: -0.078 (-0.027) |
| Player:
Opponent: | 48.14% (G:13.14% B:0.25%)
51.86% (G:14.46% B:0.53%) | |
|
| 3. | XG Roller++ | 15/6 | eq: -0.165 (-0.114) |
| Player:
Opponent: | 45.22% (G:15.20% B:0.28%)
54.78% (G:16.26% B:0.48%) | |
|
eXtreme Gammon Version: 2.10
#4
  
| | White is Player 2
score: 4
pip: 117 | 5 point match
Crawford | pip: 82
score: 0
Blue is Player 1 |
|
| XGID=--bCBCCB-B--a-----bcbbba--:0:0:1:34:0:4:1:5:10 |
| Blue to play 34 |
| 1. | XG Roller++ | 9/6 9/5 | eq: +0.797 |
| Player:
Opponent: | 89.36% (G:8.95% B:0.21%)
10.64% (G:0.25% B:0.01%) | |
|
| 2. | XG Roller++ | 7/4 7/3 | eq: +0.783 (-0.014) |
| Player:
Opponent: | 88.60% (G:10.34% B:0.25%)
11.40% (G:0.39% B:0.01%) | |
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
#5
  
 
| | White is Player 2
score: 4
pip: 145 | | 5 point match | pip: 110
score: 1
Blue is Player 1 |
|
| XGID=c-BBABBAA----C---cbeA---b-:1:-1:1:61:1:4:0:5:10 |
| Blue to play 61 |
| 1. | XG Roller++ | 13/6 | eq: +2.158 |
| Player:
Opponent: | 89.35% (G:65.34% B:4.26%)
10.65% (G:2.00% B:0.12%) | |
|
| 2. | XG Roller++ | 13/7 4/3 | eq: +2.156 (-0.002) |
| Player:
Opponent: | 89.52% (G:65.08% B:3.69%)
10.48% (G:1.69% B:0.11%) | |
|
| 3. | XG Roller++ | 20/14 4/3 | eq: +2.124 (-0.034) |
| Player:
Opponent: | 89.40% (G:63.66% B:3.67%)
10.60% (G:1.64% B:0.09%) | |
|
| 4. | XG Roller++ | 13/12 13/7 | eq: +2.123 (-0.035) |
| Player:
Opponent: | 89.00% (G:64.02% B:4.26%)
11.00% (G:2.28% B:0.19%) | |
|
| 5. | XG Roller++ | 13/7 5/4 | eq: +2.119 (-0.039) |
| Player:
Opponent: | 89.23% (G:63.57% B:4.12%)
10.77% (G:1.76% B:0.09%) | |
|
| 6. | XG Roller++ | 20/14 13/12 | eq: +2.092 (-0.066) |
| Player:
Opponent: | 88.74% (G:62.77% B:4.14%)
11.26% (G:2.57% B:0.24%) | |
|
| 7. | XG Roller++ | 20/14 7/6 | eq: +2.091 (-0.067) |
| Player:
Opponent: | 88.86% (G:62.60% B:4.12%)
11.14% (G:2.11% B:0.11%) | |
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2