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Subject: Re: Bernoulli trials, Binomial and Trinomial Distribution Formulae ?!

Author: Robert Pawlak

Date: 18:50:09 04/25/01

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On April 25, 2001 at 14:30:55, Uri Blass wrote:

>On April 25, 2001 at 13:46:22, guy haworth wrote:
>
>>A game of chess is a 'Bernoulli trial' in a sequence of say 'n' trials.
>>
>>One side's score after 'n' trials is a random-variable X.
>>
>>If chess was a win/lose 2-outcome trial, one could dial straight into the theory
>>of binomial and normal distributions and pick up info about the variance of the
>>score after 'n' trials.
>>
>>Unfortunately, it is a three-outcome trial ... win/draw/lose ...
>>
>>Question is ... is there an equivalent neat formula about the variance of the
>>score after 'n' trials ... assuming 1 for win, 0.5 for draw, 0 for loss of
>>course.

To the best of my knowledge, the answer is no. Although one good source of info
is the two volume Kendall stats reference.

>
>Assumptions:
>1)There is a match between 2 opponents J and F.
>1)The results of different games independent events.

Not valid with book learning.

>2)The results of different games when J is white have the same distribution.

Not true, once again, there is book learning and probably other factors to deal
with also.

>3)The result of different game when F is white have the same distribution
>
>

See above.

Now, I do realize that you are not saying these are true. I'm just pointing out
a few things.

If you want to find the resulting multinomial distribution after N trial, you
just have to perform N-1 convolutions. Any computer will do this very quickly.
The problem is that is doesn't mean anything for the commercial programs.

Bob



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