The theory of independent experiments is the analytically simplest and most advanced part of probability theory. - William Feller

The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts.

In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions.

The fact that the mean recurrence time is infinite implies that the chance fluctuations in an individual prolonged coin-tossing game are far removed from the familiar pattern governed by the normal distribution.