(7) If you (as Blue, for money) are permitted to turn the cube and then play as many aces as you like, how many should you play?
I thought 36 aces to be optimal, but XGR++ thinks 37 aces is slightly better. XGR++ evals are below. I suppose the 37-ace position does better with double 2s, but what about double 4s? So, I still wonder. If anyone cares to do a pair of rollouts, have at it!
          
 
       
 | | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 111
score: 0
Blue is Player 1 |
|
| XGID=cBBBBB-----bBA--aabbbbB---:1:-1:1:00:0:0:3:0:10 |
| 36 aces |
| Analyzed in XG Roller++ | No redouble | Redouble/Take |
| Player Winning Chances: | 89.37% (G:83.06% B:18.35%) | 89.37% (G:83.06% B:18.35%) |
| Opponent Winning Chances: | 10.63% (G:1.12% B:0.04%) | 10.63% (G:1.12% B:0.04%) |
| Cubeless Equities | +1.790 | +3.580 |
| Cubeful Equities |
| No redouble: | +1.752 | |
| Redouble/Take: | +3.505 (+1.752) | |
| Redouble/Pass: | +1.000 (-0.752) |
| |
| Best Cube action: Too good to redouble / Pass |
| Percentage of wrong take needed to make the double decision right: 30.0% |
eXtreme Gammon Version: 2.02
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 110
score: 0
Blue is Player 1 |
|
| XGID=cBBBBB-----bC---aabbbbB---:1:-1:1:00:0:0:3:0:10 |
| 37 aces |
| Analyzed in XG Roller++ | No redouble | Redouble/Take |
| Player Winning Chances: | 89.59% (G:82.87% B:18.93%) | 89.59% (G:82.87% B:18.93%) |
| Opponent Winning Chances: | 10.41% (G:1.09% B:0.04%) | 10.41% (G:1.09% B:0.04%) |
| Cubeless Equities | +1.798 | +3.597 |
| Cubeful Equities |
| No redouble: | +1.762 | |
| Redouble/Take: | +3.524 (+1.762) | |
| Redouble/Pass: | +1.000 (-0.762) |
| |
| Best Cube action: Too good to redouble / Pass |
| Percentage of wrong take needed to make the double decision right: 30.2% |
eXtreme Gammon Version: 2.02
Nack
