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Statistical regularity is a notion in statistics that if we throw a thumbtack onto a table once, we would have a hard time predicting whether the point would touch the surface of the table or not. But if we repeat this experiment many times, we will see that the number of times the point touches the surface divided by the number of throws will eventually stabilize at a specific value.
Similar experiments with coins, dice, and roulette wheels reinforce the main idea. Repeating a series of trials will produce similar, but not identical, results for each series. This phenomenon is called statistical regularity.
Observations of this phenomenon provided the initial motivation for the concept of what is now known as frequency probability.