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Old 08-27-2005, 12:39 AM
BruceZ BruceZ is offline
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Join Date: Sep 2002
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Default Re: Question for BruceZ (or others) regarding streaks

[ QUOTE ]
Change the situation around a little bit.

Say a computer generates a random number from 1-17. What's the chance that you would guess the number (with 1 guess each round) 14 times in a span of 100 guesses. This is really the same thing as the pocket pair question.

Seems to me like binomial theorem would work.

100c14*100c86*(1/17)^14*(16-17)^86

It's been a while since I took probability, so there may be a 1 - something in there somewhere, but is there any reason binomial therom doesn't work here?

[/ QUOTE ]

The probability that you guess it exactly 14 times out of 100 is just

C(100,14)*(1/17)^14*(16/17)^86

or in Excel, =Binomdist(14,100,1/17,false).

For the probability that you guess it 14 times or more, you would take 1 minus the sum of C(100,k)*(1/17)^k*(16/17)^(100-k) for k = 0 to 13. This is the same as =1 - Binomdist(13,100,1/17,true).

This isn't the question that the OP asked. He wants to know the probability of 14 or more out of 100 hands for some consecutive 100 hands within 1000 hands. The binomial distribution is just used to get the initial conditions for the first 100 hands.
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