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Alternative(s) to XGR++ for cube decisions

Posted By: Daniel Murphy
Date: Tuesday, 24 January 2012, at 2:28 a.m.

In Response To: Alternative(s) to XGR++ for cube decisions (Neil Robins)

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?

White59

2O3X5X2O4X3X ' ' ' ' ' '

 '1O2O2O2O2O1O ' ' ' ' '
Blue160
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
WinW gW bg LoseL gL bgCubelessCubeful
Centered 1-cube0.66770.47400.2122-0.33230.00020.0000 +0.7860 +0.8816
Standard error0.00180.00220.0057-0.00180.00010.0000 0.0065 0.0114
Player Blue owns 2-cube0.66520.46570.3368-0.33480.00020.0000 +1.3156 +0.8719
Standard error0.00190.00250.0068-0.00190.00060.0001 0.0103 0.0144
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]

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:

WGBGLLGLBG
XG "cubeless" No double 67.0647.3314.9732.0400.0100.00
Gnubg "cubeless" No double 66.7747.4021.2233.2300.0200.00
Gnubg actual No double 69.1532.5002.2030.8500.0000.00
XG "cubeless" Double 66.1746.2925.4333.8300.0100.00
Gnubg "cubeless" Double 66.5246.5733.6833.4800.0200.00
Gnubg actual Double 64.3534.6500.0035.6500.0000.00

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 nowYou 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% --

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