[Bug-gnubg] Rollout statistics

[Ian Shaw]

We've just been discussing a position at GammOnLine, and I wanted to 
investigate the rollout statistics to see why I might win more games with the 
opponent holding the cube.

They didn't appear to support the reported wins. Could someone check it please.

Here is the position:
    GNU Backgammon  Position ID: OQAAwA0AAAAAAA
                    Match ID   : UQlgAVAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: Leader
OOO | O     O          |   |                  |  5 points
 OO |       O          |   |                  |  
 OO |       O          |   |                  |  
 OO |                  |   |                  |  
 OO |                  |   |                  |  
    |                  |BAR|                  |v 11 point match
 XX |                  |   |                  |  
 XX |                  |   |                  |  
 XX |    X             |   |                  |  
 XX |    X  X          |   |                  |  On roll
 XX |    X  X          |   |                  |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Trailer (Cube: 2)


Cube analysis
Rollout cubeless equity  +0.034 (Money:  +0.034)

Cubeful equities:
1. No double            +0.122
2. Double, pass         +1.000  ( +0.878)
3. Double, take         +0.096  ( -0.025)
Proper cube action: No redouble, take (2.8%)
Rollout details:
Player Trailer owns 2-cube:
  0.517 0.000 0.000 - 0.483 0.000 0.000 CL  +0.034 CF  +0.122
 [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.000 CF  +0.001]
Player Leader owns 4-cube:
  0.522 0.000 0.000 - 0.478 0.000 0.000 CL  +0.153 CF  +0.096
 [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.066 CF  +0.000]
Full cubeful rollout with var.redn.
12960 games, rollout as initial position, seed 1203654912 using quasi-random 
dice and Mersenne Twister
Play and cube: 2-ply cubeful 100% speed [world class]

I can't understand how Trailer wins 0.5% more games by letting the opponent 
hold the cube. If Trailer redoubles, he must lose many games where Leader 
cashes 4 points. I wondered if the rollouts statistics would shed some light.

It took some time to understand the Rollout statistics window, but it broke 
down like this (I can post screen shots if anyone wants to check my breakdown:

                                Total Win   Pass  Lose Win      Cash  Lose  
Leader Trailer    Trailer
                                        @ 2   @ 2   @ 2  @ 4    @ 4   @ 4   
Wins   Wins       Win %
Trailer owns 2-cube     12960   6343    5456    982     0       55      124     
6398     6562           50.633%
Leader owns 4-cube      12960                           3235    3915    5810    
7150     5810           44.830%

(Win & Lose refer to Leader's results with games to completion. 
 Pass refers to Leader passing, Cash refers to Leader Cashing)

Now, I know that the numbers won't match exactly because of the variance 
reduction, but they ought to be similar enough for comparison. When Trailer 
doubles to 4, Leader does indeed get to cash a lot of games,so Trailer only 
wins 44.8% compared to 50.6% if he holds on to the cube. 

--Ian