Re: Dice
Re: Dice
- Subject: Re: Dice
- From: Bill Briggs <email@hidden>
- Date: Tue, 26 Oct 2004 17:56:32 -0300
At 2:39 PM -0500 10/26/04, John C. Welch wrote:
On 10/26/2004 13:28, "Graff" <email@hidden> wrote:
So no, it doesn't seem to be perfect but it's probably good enough
for most applications.
Out of curiosity, what would the std deviation be if the random was
perfect?
A perfectly even distribution would be for every value to show up the
same number of times. In that case the std deviation would be 0.
However, a perfectly even distribution is not, by definition, perfectly
random, or even close.
Actually, this notion of a perfectly even "distribution" is a bit of
semantic confusion introduced into what is a very clearly understood
and tractable bit of mathematics. It makes no sense at all, at least
in reference to the code the original poster was running in
AppleScript.
In reference to the generation of events (an event being the
occurrence of a number 1 through 6) as is under discussion here, the
distribution of the event count, which is what this is
1 161
2 167
3 173
4 170
5 169
6 160
the only distribution it makes any sense to talk about is the
probability distribution, that is, the probability that any
particular event of the six will happen. It makes no sense whatever
to talk about the distribution of event counts.
In this case, you want the probability of each event to be 1/6. But
to think that at any time you will get the "same count of events" for
each of the possible outcomes is absurd. Because this is a discrete
random variable, it could at best only be achieved each time the
number of events hit a multiple of 6 (was n*6 where n = 1, 2, ... N),
and furthermore, each six events would have to proceed as selections
from the six possible outcomes without replacement. As a consequence
of this you'd never be able to have the same outcome twice in a row
in any round of 6 throws. This kind of behaviour would require some
bastardized approach to selection rules, having them vary between
random selection from the 6 possibilities, to selection without
replacement until all 6 had been "used up", then back to random from
the pool again, and so on.
Just because the probabilities are equal for each outcome in a
series of events, the event count histogram for those outcomes over
repeated events DOES NOT have to show similar values in any finite
number of repetitions. To assume so is to be completely misguided. To
use the term "even distribution" is to describe some desired equality
of the event counts (it's a semantic trap), not a mathematical
property of a series of independent random events, which is what you
get when you execute the code to generate the above numbers. It's the
PROBABILITY DISTRIBUTION that is even, i.e., the outcome of an event
is equally likely to be any of the six. That's the only thing that is
even, and the count for each of the possible outcomes will manifestly
NOT be "equal" even if you generate a hundred million events. And the
fact that they are not the same gives you no information about the
real probability attached to this process in the machine generating
the outcomes. There IS a way to determine whether or not the process
could involve identical event probabilities, and that is to test the
variance against what could be expected for a particular number of
events. This can be done. I'd have to look up the calculation.
Deivy, where the hell are you? You should be all over this like a
starving squirrel on a peanut. And you probably have the variance
test in your head. Don't make me go look it up.
Okay, I've got to go to dinner.
- web
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