Poker Poker Poker!: Re: [vpFREE] Re: Best Randomness Analogy Contest

I believe you and Cogno are both correct, but you're talking about
different things. I'll reduce the problem to a simpler case -- flipping
a fair coin.

Suppose we flip a fair coin 1 million times and record the number
of heads, then repeat this experiment many many times and plot
the results.

The fraction of experiments where the number of heads is exactly
500,000 will be very small. This is what Cogno was talking about.
As the number of flips increase, the probability of having exactly
one half of them come up heads shrinks.

Most of the experiments will result in the number of heads being
near 500,000 (within a few thousand). This is what David is talking
about. As the number of flips increase, the outcome becomes
less likely to deviate far from the mean. Looking at the deviation
can be confusing because the deviation can appear to shrink or
to grow depending on how you look at it. When N coins are flipped,
the absolute deviation increases as sqrt(N), which increases as
N gets larger. Howevery, when you view the deviation as a fraction
the total number of flips, taking sqrt(N)/N gives 1/sqrt(N) which
shrinks as N grows larger. Thus, when you flip a fair coin a million
times, your outcome will usually be within 1000 flips of 500,000
heads, which is one part in 500. If you increase the experiment
to 100 million flips, then the absolute deviation grows to 10,000
flips but this is now one part in 5,000. So, depending on how
you look at it, the deviation is both growing and shrinking!

On Monday 17 January 2011 08:06:10 am you wrote:
> Not according to the Law of Large Numbers.
>
>
>
> To: vpFREE@yahoogroups.com
> From: cognoscienti@hotmail.com
> Date: Mon, 17 Jan 2011 06:56:14 -0800
> Subject: RE: [vpFREE] Re: Best Randomness Analogy Contest
>
>
>
>
>
>
> Not true. The greater the number of rolls, the less likely it becomes that
> the results are exactly the expected value.
>
> Cogno
>
> -----Original Message-----
> From: vpFREE@yahoogroups.com [mailto:vpFREE@yahoogroups.com]
On Behalf Of
> David Silvus
> Sent: Sunday, January 16, 2011 7:58 PM
> To: vpfree@yahoogroups.com
> Subject: RE: [vpFREE] Re: Best Randomness Analogy Contest
>
> True, but as the number of rolls approaches infinity the distribution will
> be exactly that.
>
>
> To: vpFREE@yahoogroups.com
> From: guruperf@att.net
> Date: Fri, 14 Jan 2011 14:11:55 -0800
> Subject: Re: [vpFREE] Re: Best Randomness Analogy Contest
>
> ________________________________
>
> >"Equiprobable & Unpredictable". Everything has an equal chance of
> > occurring
>
> and
>
> >you can't predict it.
> >
> >Toss two fair dice. Everything has an equal chance of occuring and you
>
> can't
>
> >predict it? No, I can predict the follow outcomes:
>
> 2 occurs 1 out of 36
> 3 occurs 2 out of 36
> 4 occurs 3 out of 36
> 5 occurs 4 out of 36
> 6 occurs 5 out of 36
> 7 occurs 6 out of 36
> 8 occurs 5 out of 36
> 9 occurs 4 out of 36
> 10 occurs 3 out of 36
> 11 occurs 2 out of 36
> 12 occurs 1 out of 36
>
> But not in EVERY 36 throws. Any stat-head out there want to calculate
the
> odds
> of that EXACT distribution occurring in one series of 36 throws?
>
> ._,___
>
> [Non-text portions of this message have been removed]
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> [Non-text portions of this message have been removed]
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