If one throws a dice once, it is difficult to predict the outcome, but if one repeats this experiment many times, one will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value.
The notion is used in games of chance, demographic statistics, quality control of a manufacturing process, and in many other parts of our lives.
Observations of this phenomenon provided the initial motivation for the concept of what is now known as frequency probability.
This phenomenon should not be confused with the gambler's fallacy, because regularity only refers to the (possibly very) long run.
The gambler's fallacy does not apply to statistical regularity because the latter considers the whole rather than individual cases.