Re: A Gambling Math Question

On 23 Jan 2007 09:54:18 -0800, C6L1V@xxxxxxx wrote:
Dave Seaman wrote:
On 23 Jan 2007 08:46:35 -0800, JyBrdnj@xxxxxxxxx wrote:
I was looking over an old post of mine, and I just want to see if
someone can clerify something for me. Someone posted that after 100
trials in a 50/50 game, you would have a return of between -15 and 15,
and after 1,000,000 trials you would have a return of between -1500 and
1500. They said there's a function D that can be applied to the number
of trials to show you how far away you would be from zero, and this
function D is monotonical, or always increasing. My question is why is
there a function D, where did this come from?

Let p be the probability of success and q = 1-p = probability of failure.
If N is the number of trials, the expected number of successes is
obviously N*p. The standard deviation is approximately sqrt(N*p*q).

This is *exact*, not at all an approximation.

Ok, you're right. But the approximation comes in replacing the binomial
distribution with a normal distribution having the same mean and standard
deviation.

This
comes from the well-known normal approximation to the binomial
distribution, which you can easily read about using a Google search.

In the case N=100, p=q=1/2, we get a standard deviation of
sqrt(100*1/2*1/2) = 5, and there is a >99% probability that the observed
number of heads will lie within 3 standard deviations of the mean, or
between 35 and 65.

Agreed. But the OP seems to be saying that getting more than 65 is
impossible. He seems to be mixing up 'impossible' with 'improbable'.

Very likely, he is just repeating what he was told.



If we substitute N=10^6, then the S.D. is sqrt(25*10^4) = 500, and thus
the observed number of heads should lie between 498,500 and 501,500 with
probability >99%.




--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>



--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>
.

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