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## Re: [Bug-gnubg] Re: The importance of METs

 From: nis Subject: Re: [Bug-gnubg] Re: The importance of METs Date: Tue, 2 Sep 2003 00:57:01 +0200 (CEST)

```On Sat, 30 Aug 2003, Joseph Heled wrote:

> Well, those are matches, not games. They are played in pairs, with
> matching (swapped) dice, on a per game basis. How much this reduces the
> STD I have no idea.

If you have the results still around, it would be interesting to know how
many pairs of matches were won by the "inferior" table. This is the only
number needed to calculate the confidence interval(s).

In your case, you are performing 250.000 experiments with three possible
outcomes: E1: (MET1 > MET2), E2: (MET1 < MET2) and E3: (MET1 = MET2). The
outcomes are assigned the values 2, -2 and 0.

It is expected that p1 (=P(E1)) and p2 are (very) small compared to p3.
The stddev of the distribution is

2 * sqrt(p1 + p2 - (p2 - p1)^2)

This we plug into the normal formula for confidence intervals - for 95%
confidence interval we have

Avg +- 1.96 * stddev/sqrt(numtrials)

For instance, if p1 = 0.0062 and p2 = 0.0038 (random guesses), we get

1.96 * 2 * sqrt(0.01 - 0.0024^2)/sqrt(250.000) = 0.000078 =
0.0078%

for the experiment of playing a pair of 2 matches, and thus a
confidenceinterval of 50.12% +- 0.0039% for the outcome of a single match.

This is definitely significant - but unfortunately it is based on my
random guess of the value of p1 and p2 :-)

--
Nis
Live from Hoofddorp

```

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