The score is 0-0/3. Blue on roll, cube decision?
| White | 97 | ||
|---|---|---|---|
                        | |||
| Blue | 102 | ||
| Position ID: 1zFzAEBz2wQBAw Match ID: cAlgAAAAAAAE | |||
I've rolled this out with Gnubg's "show statistics" feature in order to show more clearly why this position is Too Good to Double. Glaze your eyes over the table below:
| Blue Wins | White Wins | CL | CF | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Wins | Single | Gammon | BG | Wins | Single | Gammon | BG | |||
| 83.32% | 58.68% | 24.25% | 00.39% | 16.68% | 14.03% | 2.57% | 0.08% | +1.0038 | +1.1364 | |
| 59.94% | 61.25% | |||||||||
| Blue Wins | White Wins | |||||||||
| Cube | Wins | Single | Gammon | BG | Wins | Single | Gammon | BG | ||
| 1-cube | 82.44% | 66.00% | 16.29% | 0.15% | 2.62% | 2.40% | 0.22% | 0.00% | ||
| 2-cube | 7.83% | 5.90% | 1.93% | 0.00% | 3.59% | 3.28% | 0.31% | 0.00% | ||
| 4-cube | 1.30% | 1.30% | 0.00% | 0.00% | 2.22% | 2.22% | 0.00% | 0.00% | ||
| Total | 91.57% | 73.20% | 18.22% | 0.15% | 8.43% | 7.90% | 0.53% | 0.00% | ||
| Blue Cubes | White Cubes | |||||||||
| Cube | D/T | D/P | D/T | D/P | ||||||
| 2-cube | 12.17% | 66.00% | 2.77% | 2.40% | ||||||
| 4-cube | 0.43% | 0.62% | 3.09% | 1.78% | ||||||
The table has three parts. The first part is what the rollout reports -- the "cubeless" results that the bot estimates would occur if the game was always played to the end. The second part is what actually happens in the rollout after No Double now -- how often Blue and White actually win single games and gammons, and the cube level that each trial ends on. The third part shows how often -- after No Double now -- Blue or White double later to 2 and to 4, and how often White or Blue takes or passes.
The point is:
The rollout result may lead you to believe that by playing on Blue is risking 16.68% wins in order to win 24.25% gammons. That's not true. It would be true if Blue never doubled and all games had to be played to the end. But after No Double now Blue will reconsider cube action on every subsequent turn.
78.17% of the time, Blue will eventually double to two. 66% of the time, White will pass that double. 12.17% of the time, White will take. 5.17% of the time, Blue's game will become so bad that White will make the double to two, and Blue will have to pass about half of these cubes.
After No Double now, 66% of all games will eventually end with Blue doubling White out (and 2.4% will end with White doubling Blue out). 14.94% of the time, one or the other player will give a takable 2-cube. 3.52% of the time, there will be a takable 4-cube. 16.44% of the time, Blue never doubles and goes on to win a gammon or backgammon on a 1-cube.
Which means that by not cashing now Blue is not risking 16.68% wins to gain 24.25% gammons. Blue risks only 8.43% wins to gain 18.22% gammons.
• Blue doubles
Alert: wrong double ( -1.351%)! [very bad]
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless MWC | 59.937% | (Money: +0.8895) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | 61.250% | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, take | 71.265% | 10.015% | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, pass | 59.899% | -1.351% | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | Too good to double, pass (11.9%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 10000 games, Mersenne Twister dice gen. with seed 910356710 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skip pruning for 1-ply moves. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||