A Gnubg 2-ply rollout gets a similar result -- a smallish no-double:
The score (after 0 games) is: White 4, Blue 1 (match to 7 points)
Move number 2: White on roll, cube decision?
| White | 59 | ||
|---|---|---|---|
                       | |||
| Blue | 160 | ||
| Position ID: 2rYAwFju8w4AAA Match ID: MAHgAEAACAAE | |||
• White doubles
Alert: wrong double ( -0.0096)!
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.7860 | (Money: +1.0214) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.8816 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.0000 | +0.1184 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.8719 | -0.0096 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No double, take (7.5%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2000 games, Mersenne Twister dice gen. with seed 911 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] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Annotation
2-ply cubeless equity +0.9402 (Money: +0.8279)
0.6478 0.4547 0.0781 - 0.3522 0.0005 0.0000
Cubeful equities:
1. No double +0.8652
2. Double, pass +1.0000 ( +0.1348)
3. Double, take +0.8519 ( -0.0133)
Proper cube action: No double, take (9.0%)
4-ply cubeless equity +0.9792 (Money: +0.8633)
0.6572 0.4678 0.0812 - 0.3428 0.0002 0.0000
Cubeful equities:
1. Double, take +0.9050
2. Double, pass +1.0000 ( +0.0950)
3. No double +0.9050 ( -0.0000)
Proper cube action: Double, take [by 0.000011, i.e., optional double to 4 decimal places]
0.6478 0.4547 0.0781 - 0.3522 0.0005 0.0000
Cubeful equities:
1. No double +0.8652
2. Double, pass +1.0000 ( +0.1348)
3. Double, take +0.8519 ( -0.0133)
Proper cube action: No double, take (9.0%)
4-ply cubeless equity +0.9792 (Money: +0.8633)
0.6572 0.4678 0.0812 - 0.3428 0.0002 0.0000
Cubeful equities:
1. Double, take +0.9050
2. Double, pass +1.0000 ( +0.0950)
3. No double +0.9050 ( -0.0000)
Proper cube action: Double, take [by 0.000011, i.e., optional double to 4 decimal places]
Gnubg's "show statistics" feature generates all sorts of data. Among the more interesting, I think, are the actual number of games, gammons and backgammons won, in comparison to the "cubeless" numbers:
| W | G | BG | L | LG | LBG | |
|---|---|---|---|---|---|---|
| XG "cubeless" No double | 67.06 | 47.33 | 14.97 | 32.04 | 00.01 | 00.00 |
| Gnubg "cubeless" No double | 66.77 | 47.40 | 21.22 | 33.23 | 00.02 | 00.00 |
| Gnubg actual No double | 69.15 | 32.50 | 02.20 | 30.85 | 00.00 | 00.00 |
| XG "cubeless" Double | 66.17 | 46.29 | 25.43 | 33.83 | 00.01 | 00.00 |
| Gnubg "cubeless" Double | 66.52 | 46.57 | 33.68 | 33.48 | 00.02 | 00.00 |
| Gnubg actual Double | 64.35 | 34.65 | 00.00 | 35.65 | 00.00 | 00.00 |
Above, "W" includes "G" and "BG," and "G" includes "BG."
The reason for the difference between actual and "cubeless" gammons and backgammons is that actual gammons only occur when the cube is centered or on 2, and actual backgammons only occur when the cube is centered.
What, if any, of the following data of what actually happened in the rollout is of interest in this position or generally?
| You don't double now | You do double now | |
|---|---|---|
| You cash 1 point | 18.50% | 00.00% |
| You win 2-point gammon with a centered cube | 11.90% | 00.00% |
| You win 3-point backgammon with centered cube | 02.20% | 00.00% |
| You double to 2, win single (2 points) | 07.90% | 11.40% |
| You double to 2, win gammon (3 points) | 18.40% | 34.65% |
| The cube gets to 4, you win 3 points | 09.95% | 18.30% |
| You are redoubled to 8, win 3 points | 00.30% | 00.00% |
| Opponent cashes 1 point | 03.30% | 00.00% |
| You double to 2, pass the redouble to 4,losing 2 points | 11.90% | 06.55% |
| The cube gets to 4, you lose 4 points | 15.60% | 29.10% |
| You are redouble to 8, lose 6 points | 00.10% | 00.00% |
| No one ever doubles | 14.10% | 00.00% |
| You make the initial double, Opponent drops | 18.50% | 00.00% |
| You make the initial double, Opponent takes | 54.35% | 100.00% |
| Percent of initial doubles by you dropped | 25.39% | 00.00% |
| Percent of initial doubles by you taken | 74.60% | 100.00% |
| Opponent redoubles to 4, you drop | 03.90% | 06.40% |
| Opponent redoubles to 4, you take | 25.35% | 47.40% |
| Percent of redoubles to 4 by Opponent dropped | 13.33% | 11.89% |
| Percent of redoubles to 4 by Opponent taken | 86.66% | 88.10% |
| Opponent makes the initial double, you drop | 03.30% | 00.00% |
| Opponent makes the initial double, you take | 09.75% | 00.00% |
| Percent of initial doubles by Opponent dropped | 25.28% | -- |
| Percent of initial doubles by Opponent taken | 74.71% | -- |
| You redouble to 4, Opponent drops | 00.80% | 00.00% |
| You redouble to 4, Opponent takes | 00.55% | 00.00% |
| Percent of redoubles to 4 by you dropped | 59.26% | -- |
| Percent of redoubles to 4 by you taken | 40.74% | -- |
| Opponent redoubles to 8 and you take | 00.35% | 00.00% |
| Percent of redoubles to 8 by Opponent dropped | 00.00% | -- |
| Percent of redoubles to 0 by Opponent taken | 100.00% | -- |
| You win | 69.15% | 64.35% |
| You win 1 point | 18.50% | 00.00% |
| You win 2 points | 19.80% | 11.40% |
| You win 3 points | 30.85% | 52.95% |
| You win single | 36.65% | 29.70% |
| You win single (1 point) | 18.50% | 00.00% |
| You win single (2 points) | 07.90% | 11.40% |
| You win single (3 points) | 10.25% | 18.30% |
| You win gammon | 30.30% | 34.65% |
| you win gammon (2 points) | 11.90% | 00.00% |
| You win gammon (3 points) | 18.40% | 34.65% |
| You win backgammon (3 points) | 02.20% | 00.00% |
| You win gammon (2 or 3 points) or backgammon (3 points) | 32.50% | 34.65% |
| You lose | 30.85% | 35.65% |
| You lose 1 point | 03.30% | 00.00% |
| You lose 2 points | 11.90% | 06.55% |
| You lose 4 points | 15.60% | 29.10% |
| You lose 6 points | 00.10% | 00.00% |
| Percent of your wins that are 1 point wins | 26.75% | 00.00% |
| Percent of your wins that are 2 point wins | 28.63% | 17.71% |
| Percent of your wins that are 3 point wins | 44.61% | 82.28% |
| Percent of your wins that are single wins | 53.00% | 46.15% |
| Percent of your wins that are gammons | 43.81% | 53.84% |
| Percent of your wins that are backgammons | 03.18% | 00.00% |
| Percent of your wins that are gammons or backgammons | 47.00% | 53.84% |
| Percent of your losses that are 1 point losses | 10.70% | 00.00% |
| Percent of your losses that are 2 point losses | 38.57% | 18.37% |
| Percent of your losses that are 4 point losses | 50.56% | 81.635 |
| Percent of your losses that are 6 point losses | 00.32% | 00.00% |
| No double by anyone | 14.10% | 00.00% |
| Initial double by someone | 85.90% | 100.00% |
| Initial double by you | 72.85% | 100.00% |
| Initial double by Opponent | 13.05% | 00.00% |
| Double to 2 by you | 72.85% | 100.00% |
| Double to 2 by you, pass | 18.50% | 00.00% |
| Double to 2 by you, take | 54.35% | 100.00% |
| Percent of your doubles to 2 redoubled to 4 | 53.81% | 53.80% |
| Double to 4 by opponent | 29.25% | 53.80% |
| Double to 4 by opponent, pass | 03.90% | 06.40% |
| Double to 4 by opponent, take | 25.35% | 47.40% |
| Percent of Opponent's doubles to 4 redoubled to 8 | 00.00% | 00.00% |
| Double to 8 by you | 00.00% | 00.00% |
| Double to 2 by opponent | 13.05% | -- |
| Double to 2 by opponent, pass | 03.30% | -- |
| Double to 2 by opponent, take | 09.75% | -- |
| Percent of Opponent's doubles to 2 redoubled to 4 | 10.34%% | -- |
| Double to 4 by you | 01.35% | -- |
| Double to 4 by you, pass | 00.80% | -- |
| Double to 4 by you take | 00.55% | -- |
| Percent of your doubles to 4 redoubled to 8 | 25.92% | -- |
| Double to 8 by opponent | 00.35% | -- |
| Double to 8 by opponent, pass | 00.00% | -- |
| Double to 8 by opponent, take | 00.35% | -- |