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A better approch? [LONG]

Posted By: MaX
Date: Monday, 9 November 2009, at 12:39 p.m.

In Response To: A better approch? [LONG] (Maik Stiebler)

I'll see if we can easily plug thins into gnubg.

Concerning your example where minCI is misleading, here's what I did.

Let's take 0.5 as our base equity. After 1000 trials the stdev is 00158. Hence our top play will have an equity of 0.5 + 2.5*0.158 = 0.5395.

Now I run my test program with the following settings: 1000 trials, 1001 discrete points for bayes estimation, 100K MonteCarlo samples. Equities are [0.5395 0.5] (N=1 in your example), [0.5395 0.5 0.5] (N=2), ... [0.5395 0.5 ... 0.5] (N=6).

Here's what I get:

N | Pbayes | Pmc | CI_LB | CI_UB

1 | 98.806 | 98.885 | 98.878 | 98.878

2 | 98.390 | 98.457 | 98.412 | 98.878

3 | 98.056 | 98.089 | 98.006 | 98.878

4 | 94.786 | 95.138 | 94.408 | 96.329

5 | 92.873 | 93.216 | 91.845 | 96.329

6 | 92.692 | 93.029 | 91.466 | 96.329

So, first of all, I don't get the same numbers you get: can you tell me the exact figures you run (equities, stdevs, number of MC trials)?

Second, Pbayes and Pmc more or less agree, and they go down with increasing N, that's OK.

Third, my last column (which is the minCI thing) has a jump on N=4, but that's probably due to different random samples (if I fix the sample equal for all the plays, this should no longer appear). otherwise, the PminCI is constant, as expected. however, the 3rd column (which is the lower bound computed as simple product of the minCIs of p1 vs p2, p1 vs p3 etc.) goes down with N.

I would say that knowing column 3 and 4 is more or less equivalent to knowing column 1 or 2: it's enough to say you trust or not the rollout result. Which is our question: I'm not sure we want to know the exact probability of p1 being best, we just want something the lets us say 'OK, that's enough'.

If that's true, we could go for a stopping criteria using minCI upper andlower bounds (maybe lower bound only is just enough) and a posteriori MC integration for the "true" number.

MaX.

P.S. A few experiments with the size of the bayes discretization seems to indicate that increasing the number of points drives Pbayes to Pmc. I guess that there's a direct way to link the expected stdevs of the plays and the bayes discretization size, I'm just too lazy to work it out (maybe Tim can do it).

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