That is correct. My earlier e-mail should have read "but as the number of rolls approaches infinity the distribution will tends toward that" instead of "but as the number of rolls approaches infinity the distribution will be exactly that.". Sloppiness on my part.
The most likely single distribution would be the probability, although the likelihood of that particular exact distribution is extremely small.
Back to the "topic" (although I must admit I am not exactly sure what the origin topic was), there is a "pattern" that will develop as the number of rolls gets larger and larger. The total of the roll of 2 dice isn't entirely random since certain totals of the 2 dice are far more probable than others. The precise combination (4-3, 3-4, 5-2, etc.) is, however, completely random.
That said, the pattern does not change the discrete nature of each roll of the dice though. The probabilities never change -- a number is never "due" or "not due" on a particular roll due to the previous X number of outcomes. In that sense the total of the roll of 2 dice is random.
> To: vpFREE@yahoogroups.com
> From: jacobs@xmission.com
> Date: Mon, 17 Jan 2011 08:35:00 -0700
> Subject: 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]
> >
> >
> >
> > [Non-text portions of this message have been removed]
> >
> > ------------------------------------
> >
> > vpFREE Links: http://members.cox.net/vpfree/Links.htm
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
> > ------------------------------------
> >
> > vpFREE Links: http://members.cox.net/vpfree/Links.htm
> >
> > Yahoo! Groups Links
> >
> >
> >
>
>
> ------------------------------------
>
> vpFREE Links: http://members.cox.net/vpfree/Links.htm
>
> Yahoo! Groups Links
>
>
>
[Non-text portions of this message have been removed]
