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Got Variance? I did that test

Posted By: eXtreme Gammon
Date: Monday, 24 May 2010, at 12:00 a.m.

In Response To: Got Variance? (bob koca)

A few weeks ago a position was posted by Neil Robins





is Player 2

score: 1
pip: 153
7 point match
pip: 161
score: 0

is Player 1
XGID=--aBa-D-BA--dC---bbbc-BA--:0:0:1:63:0:1:0:7:10
to play 63

1.Rollout113/4* 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 second
1 648 Games rolled with Variance Reduction.
Dice Seed: 31247
Moves and cube decisions: 3 ply

eXtreme 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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