Here are the answers for the Qarey Quiz. I'm surprised that none of the theoreticians discerned the nature of the quiz. Far from a random assemblage of third rolls problems with odd match scores, these are rather a carefully crafted collection of common third rolls with precise scores. These problems are intended not only as reference positions but also as reference scores.
Even after 36 units of rollouts (46,656), each play has almost exactly the same equity. So what that means is that whatever play you chose for whatever reason, you were correct! Each problem represents the precise score where the offensive and defensive needs are in prefect balance. Two or three points will usually shift the balance completely to one side or the other so there are a range of scores where either play is acceptable.
I will present the answers two problems at a time and will include the opening 11 point match score for reference. (I have fixed all scores to be inside an 11 point match. Away scores have not changed.)
#1 34Z 61P 41 5 Away - 9 Away
          
 
         
 | | White is Player 2
score: 2
pip: 160 | | 11 point match | pip: 160
score: 6
Blue is Player 1 |
|
| XGID=-b----E-CA--dD---bbe-A--A-:0:0:1:41:6:2:0:11:10 |
| Blue to play 41 |
| 1. | Rollout1 | 9/5 6/5 | eq: +0.0881 |
| Player:
Opponent: | 55.07% (G:17.22% B:1.14%)
44.93% (G:12.19% B:0.46%) | Conf.: ±0.0024 (+0.0857...+0.0905) - [79.5%]
Duration: 2 hours 31 minutes |
|
| 2. | Rollout1 | 24/20 21/20 | eq: +0.0867 (-0.0013) |
| Player:
Opponent: | 53.55% (G:12.74% B:0.47%)
46.45% (G:6.94% B:0.24%) | Conf.: ±0.0021 (+0.0847...+0.0888) - [20.5%]
Duration: 2 hours 50 minutes |
|
| 3. | XG Roller++ | 24/23 13/9 | eq: -0.1503 (-0.2383) |
| Player:
Opponent: | 49.92% (G:12.99% B:0.61%)
50.08% (G:13.76% B:0.48%) | |
|
| 4. | XG Roller++ | 21/20 13/9 | eq: -0.1920 (-0.2801) |
| Player:
Opponent: | 49.05% (G:12.74% B:0.61%)
50.95% (G:14.11% B:0.55%) | |
|
| 5. | XG Roller++ | 13/9 6/5 | eq: -0.1920 (-0.2801) |
| Player:
Opponent: | 49.17% (G:12.83% B:0.63%)
50.83% (G:14.66% B:0.70%) | |
|
| |
1 46656 Games rolled with Variance Reduction.
Dice Seed: 58918962
Moves: 3-ply, cube decisions: 4-ply
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
#1 34Z 61P 41 11 Away - 11 Away
| | White is Player 2
score: 0
pip: 160 | | 11 point match | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-b----E-CA--dD---bbe-A--A-:0:0:1:41:0:0:0:11:10 |
| Blue to play 41 |
| 1. | Rollout1 | 9/5 6/5 | eq: +0.2290 |
| Player:
Opponent: | 55.18% (G:17.01% B:0.79%)
44.82% (G:12.20% B:0.52%) | Conf.: ±0.0088 (+0.2202...+0.2378) - [100.0%]
Duration: 11 minutes 09 seconds |
|
| 2. | Rollout1 | 24/20 21/20 | eq: +0.1929 (-0.0360) |
| Player:
Opponent: | 53.76% (G:12.74% B:0.35%)
46.24% (G:7.19% B:0.26%) | Conf.: ±0.0072 (+0.1858...+0.2001) - [0.0%]
Duration: 12 minutes 30 seconds |
|
| 3. | XG Roller++ | 24/23 13/9 | eq: -0.0125 (-0.2415) |
| Player:
Opponent: | 49.87% (G:12.81% B:0.59%)
50.13% (G:13.59% B:0.47%) | |
|
| 4. | XG Roller++ | 13/9 6/5 | eq: -0.0476 (-0.2766) |
| Player:
Opponent: | 49.04% (G:12.74% B:0.55%)
50.96% (G:14.15% B:0.67%) | |
|
| 5. | XG Roller++ | 21/20 13/9 | eq: -0.0477 (-0.2767) |
| Player:
Opponent: | 48.99% (G:12.42% B:0.57%)
51.01% (G:13.72% B:0.54%) | |
|
| |
1 3888 Games rolled with Variance Reduction.
Dice Seed: 58918962
Moves: 3-ply, cube decisions: 4-ply
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
#2 41S 61P 43 11 Away - 6 Away
 
 
| | White is Player 2
score: 5
pip: 164 | | 11 point match | pip: 162
score: 0
Blue is Player 1 |
|
| XGID=-aa---E-CA--dDa--c-e---AA-:0:0:1:43:0:5:0:11:10 |
| Blue to play 43 |
| 1. | Rollout1 | 24/20 23/20 | eq: +0.3287 |
| Player:
Opponent: | 55.65% (G:14.18% B:0.46%)
44.35% (G:8.77% B:0.41%) | Conf.: ±0.0024 (+0.3263...+0.3311) - [67.1%]
Duration: 2 hours 50 minutes |
|
| 2. | Rollout1 | 9/5 8/5 | eq: +0.3279 (-0.0008) |
| Player:
Opponent: | 54.89% (G:17.71% B:0.71%)
45.11% (G:12.01% B:0.65%) | Conf.: ±0.0025 (+0.3254...+0.3304) - [32.9%]
Duration: 2 hours 08 minutes |
|
| 3. | XG Roller++ | 24/21 13/9 | eq: +0.1884 (-0.1403) |
| Player:
Opponent: | 52.17% (G:13.38% B:0.57%)
47.83% (G:12.20% B:0.46%) | |
|
| 4. | XG Roller++ | 23/20 13/9 | eq: +0.1630 (-0.1657) |
| Player:
Opponent: | 51.33% (G:13.47% B:0.60%)
48.67% (G:12.57% B:0.48%) | |
|
| 5. | XG Roller++ | 13/10 13/9 | eq: +0.1090 (-0.2196) |
| Player:
Opponent: | 49.69% (G:13.96% B:0.62%)
50.31% (G:13.59% B:0.64%) | |
|
| |
1 46656 Games rolled with Variance Reduction.
Dice Seed: 58918962
Moves: 3-ply, cube decisions: 4-ply
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
#2 41S 61P 43 11 Away - 11 Away
| | White is Player 2
score: 0
pip: 160 | | 11 point match | pip: 162
score: 0
Blue is Player 1 |
|
| XGID=-b----E-CA--dD---bbe---AA-:0:0:1:43:0:0:0:11:10 |
| Blue to play 43 |
| 1. | XG Roller++ | 24/20 23/20 | eq: +0.1798 |
| Player:
Opponent: | 53.49% (G:12.10% B:0.34%)
46.51% (G:7.07% B:0.22%) | |
|
| 2. | XG Roller++ | 9/5 8/5 | eq: +0.1062 (-0.0736) |
| Player:
Opponent: | 51.92% (G:15.74% B:0.64%)
48.08% (G:12.54% B:0.47%) | |
|
| 3. | XG Roller++ | 24/21 13/9 | eq: -0.0125 (-0.1922) |
| Player:
Opponent: | 49.87% (G:12.81% B:0.59%)
50.13% (G:13.59% B:0.47%) | |
|
| 4. | XG Roller++ | 23/20 13/9 | eq: -0.0477 (-0.2274) |
| Player:
Opponent: | 48.99% (G:12.42% B:0.57%)
51.01% (G:13.72% B:0.54%) | |
|
| 5. | XG Roller++ | 13/10 13/9 | eq: -0.0705 (-0.2503) |
| Player:
Opponent: | 48.09% (G:13.97% B:0.65%)
51.91% (G:14.91% B:0.69%) | |
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2