Jeff Crowell wrote:


While each throw is statistically independent (assuming honest dice,
naturally), the fact that they are honest dice requires that the most
common throw be a seven. The more consecutive boxcars you
throw, the higher the probability that the next throw will NOT be
a 12. Boxcards is not a statistically likely event. Each throw **is**
an independent event, but the total population of throws is governed
by the overall statistical distribution.

The total distribution is not "governed" by anything you can name,
except in hindsight, and is therefor no governance at all.

You must make up your mind -- either each roll is an independent event
or it is not.

In aviation, designers refer to "a wing of infinite length" when
analyzing and describing airfoils. In a sample of "an infinite number of
rolls of the dice" it is perhaps easier for you to see that you have no
basis for your claim of governance according to "statistical
distribution", and each roll must have the same probabilities as the
previous roll and the following roll.

It is necessary for statisticians to understand before they can explain.
Unfortunately for many, circular argument is as much a fallacy in the
use of statistics as it is everywhere else.


Jack