This feature of random distributions is fairly simple to deduce. Since the probability of heads in a single coin toss is , the probability of a run of five heads equals . But a series of 100 coin tosses contains 96 sequences of length five. So there is a strong likelihood that at least one run of five heads (or tails) will occur; in fact, an 81% chance. Analogously, runs of 6 occur with a probability of 55%, runs of 7 with 32% and runs of 8 with 16%.

In this Demonstration, Mathematica's random number generator simulates up to 500 coin tosses. You can generate a new sequence of heads and tails by changing the seed value.

Similarly, every basketball player is likely to experience both "hot" and "cold" shooting streaks, like the runs of heads or tails shown here. This is an unavoidable consequence of the mathematics of statistics. However, many players and coaches refuse to believe this!