Room for ChanceThe science of chance

Free interactive tool

Coin Sequence and Runs Explorer

Generate a reproducible coin sequence or inspect your own, counting heads, runs and the longest repeated block.

Inputs and results stay in this page. These tools set no cookies, save no browser preferences and send no input data to our server. A CSV downloads only when you request it. Displayed probabilities are rounded; combination counts use exact integer arithmetic.

Understand the result

What Does a Random Sequence Look Like? The Appearance Trap explains the derivation and common interpretation errors. Compare it with the published 1-2-3 versus 2-6-9: exact enumeration and one million draws.

Exact enumeration of all 64 six-toss strings. The 20 green cells contain three heads and three tails. Each individual cell still has probability 1/64 under independent fair tosses.
Figure 1. Exact enumeration of all 64 six-toss strings. The 20 green cells contain three heads and three tails. Each individual cell still has probability 1/64 under independent fair tosses.
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