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A study: How confident can we be of the confidence interval!

Posted By: eXtreme Gammon
Date: Sunday, 21 November 2010, at 2:44 a.m.

In Response To: 4-ply queue, Nov 20 update (eXtreme Gammon)

Ah.. i found the data.

I actually made 1068 3-ply Rollout of 1296 games using different seed.

conf	theo	actual
99.90%	0.10%	0.09%
99.50%	0.50%	0.37%
99.00%	1.00%	0.94%
98.00%	2.00%	1.69%
97.00%	3.00%	2.81%
96.00%	4.00%	4.03%
95.00%	5.00%	4.68%
90.00%	10.00%	9.64%
80.00%	20.00%	17.98%
70.00%	30.00%	28.93%
60.00%	40.00%	39.33%
50.00%	50.00%	48.60%
25.00%	75.00%	74.34%
10.00%	90.00%	89.89%

Conf is the confidence interval

Theo is the percentage of RO which CI should not include the actual value of the RO (as determined by the overall 1068x1296=316,128 games [CI is +/- 0.001])

is the actual number of RO which did not include the actual value of the RO

Graphically here is how it looks:

Obviously for large CI (99% and more) I probably need more data, but overall results fit the theory. Also this study was mode on one single position:

	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.	Rollout1	13/4*	eq: -0.700
	Player: Opponent: 34.07% (G:10.03% B:0.61%) 65.93% (G:21.21% B:1.44%) Conf: ± 0.002 (-0.702...-0.698) Duration: 15 hours 22 minutes
1 206853 Games rolled with Variance Reduction. Dice Seed: 801 Moves and cube decisions: 3 ply

eXtreme Gammon Version: 2.00.150.alpha, MET: Rockwell-Kazaross

Comments are welcomed.

Xavier Dufaure de Citres

Messages In This Thread

• 4-ply queue, Nov 20 update
  Nack Ballard -- Saturday, 20 November 2010, at 6:29 p.m.
  • 4-ply queue, Nov 20 update
    mtuhtan -- Saturday, 20 November 2010, at 7:17 p.m.
    • Criteria for extensions
      Nack Ballard -- Saturday, 20 November 2010, at 9:51 p.m.
    • 4-ply queue, Nov 20 update
      eXtreme Gammon -- Sunday, 21 November 2010, at 2:04 a.m.
      • A study: How confident can we be of the confidence interval!
        eXtreme Gammon -- Sunday, 21 November 2010, at 2:44 a.m.
        • A study: How confident can we be of the confidence interval!
          Bob Koca -- Sunday, 21 November 2010, at 3:39 a.m.
          • A study: How confident can we be of the confidence interval!
            eXtreme Gammon -- Sunday, 21 November 2010, at 4:50 a.m.
            • A study: How confident can we be of the confidence interval!
              Maik Stiebler -- Sunday, 21 November 2010, at 7:23 a.m.
          • A study: How confident can we be of the confidence interval!
            eXtreme Gammon -- Sunday, 21 November 2010, at 5:09 a.m.
  • 64R-32 started
    mtuhtan -- Monday, 22 November 2010, at 10:40 p.m.
    • 64R-32 started
      Nack Ballard -- Monday, 22 November 2010, at 11:07 p.m.
      • 64R-32 started
        mtuhtan -- Monday, 29 November 2010, at 2:06 p.m.