Suppose you have a crooked coin. It lands heads with a probability $p$ that you do not know, perhaps $0.7$, perhaps $0.55$. Can you use it for a perfectly fair, fifty-fifty draw? In the same 1951 paper in which he spoke of the “state of sin” of those who manufacture random numbers, von Neumann gave a short and surprising answer. The trick Toss the coin twice: if it comes up heads, tails, say “heads”; if it comes up tails, heads, say “tails”; if it comes up heads, heads or tails, tails, forget it and toss twice more. Why is it fair? The two tosses are independent, so