Normal game. Blue on roll.
| White | 99 | ||
|---|---|---|---|
                        | |||
| Blue | 117 | ||
| Position ID: 2Z8DABgzuwMCGA Match ID: UQkAAAAAAAAA | |||
Here's the rollout. Note the "cubeless" game results.
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.5535 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | Double, take | +0.9520 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.0000 | +0.0480 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | No double | +0.8409 | -0.1110 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | Redouble, take | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2592 games, Mersenne Twister dice gen. with seed 907323591 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] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
And here are some cubeful statistics, using the Gnubg "show statistics" feature.
Holding a 4-cube, White 32.48% of all games, instead of 28.45%. That's a gain of 4.03%. And White saves some gammons, too, losing 19.09% gammons/backgammons, instead of 19.77%.
White manages to redouble to 8 more than one-third of the time -- 34.45% of all games. 58% of his redoubles get a pass. And that means 20% of all games end in redouble/pass. At the point of redouble/pass, White's cubeless GWC might be anywhere from 75% to 100%. Since almost all of the games White wins with a double/pass are 8-cubes, if we set White's average GWC at the point of double/pass to 80%, that would account for the 4% difference in games won cubeful versus cubeless. Without the cube, White would have lost 20% of those games, that is, instead of winning 20% of all games with the cube, he would have only won 80% of the 20%, or 16%.
Winning games with redouble to 8/pass is one of two reasons that White's cubeful equity is higher than his cubeless equity. The other reason is that White wins a majority of the games in which Blue takes the 8-cube.
If we ignore the final cube value, the cubeful game breakdown for White is
| Win | Win G+BG | Win BG | Lose | Lose G+BG | Lose BG | |
| 32.48 | 2.81 | 0.15 | 67.52 | 19.09 | 0.69 |
which attains an equity of -0.5186, or -1.0372 after the initial double/take. In other words, being able to double Blue out increases White's equity from an estimate -1.1456 cubeless to -1.0372 cubeful. But that's still short of take. White makes up the difference with his performance in the games in which he redoubles the stakes once again by giving an 8-cube that is taken. The cube reaches at least 8 about 14.5% of the time, and White wins 71.5% of those, which is about 10.4% of all games, compared to the 4.1% of all games that White loses whenever the cube reaches 8 or higher. And about 11% of White's 8-cube wins are gammons, so that helps too.