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BGonline.org Forums
Got Variance? I did that test
Posted By: eXtreme Gammon In Response To: Got Variance? (bob koca)
Date: Monday, 24 May 2010, at 12:00 a.m.
A few weeks ago a position was posted by Neil Robins
is Player 2
score: 1
pip: 1537 point match pip: 161
score: 0
is Player 1XGID=--aBa-D-BA--dC---bbbc-BA--:0:0:1:63:0:1:0:7:10 to play 63
1. Rollout1 13/4* eq: -0.657
Player:
Opponent:34.46% (G:10.28% B:0.87%)
65.54% (G:21.00% B:1.31%)Conf: ± 0.033 (-0.690...-0.624)
Duration: 3 minutes 00 second1 648 Games rolled with Variance Reduction.
Dice Seed: 31247
Moves and cube decisions: 3 plyeXtreme Gammon Version: 1.14, MET: Rockwell-Kazaross
Using seed 31247 his 674 game rollout was way off the final RO CI.So I decided to investigate that. Lastweek end I rolled the position 648 times using all seed from 1 to 200 (I modified my work version of XG so it could do that in one batch overnight).
I surely have the same effect than him on the 31247 seed (using 648 rather than 674 game and R/K met) the aggregate value of the position over the 200 seed is 0.699 +/- 0.0009. Neil's Seed gives 0.657 +/- 0.033.
The odd of Neil rollout to be that off are about 1%.
So here are the result of the distribution of these 200 seeds:
CI at % of RO outside the CI Theoretical value 99.9% 0.0% 0.1% 99.5% 1.0% 0.5% 99.0% 2.0% 1.0% 98.0% 3.5% 2.0% 95.0% 7.5% 5.0% 90.0% 10.5% 10.0% 80.0% 18.0% 20.0% 50.0% 48.0% 50.0% 200 values is not enough to get a good picture but the data seems reasonable.
seed 12 was the lowest: -0.750 +/- 0.045
seed 152 was the highest: -0.643 +/- 0.046 (0.15% chances so one out of 667)
Maybe when I've more time, I will extend that study and write a little article with the link to the actual data (right now I've that in a huge XL spreadsheet).
Note about the 129600 samples
- average = -0.699
- median = -0.678
- std dev = 0.464
- skewness = -0.0307
- kurtosis = 17.365
So it's not really a normal distribution, but a very peaked one. My gut felling is that the large number of dice sequence that lead to a D/D is creating that effect.
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