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[Bug-gnubg] Rollout statistics
From: |
Ian Shaw |
Subject: |
[Bug-gnubg] Rollout statistics |
Date: |
Thu, 10 Apr 2003 12:01:12 +0100 |
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
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