Uniform random character from a stream in one pass

A file holds an unknown number of characters. Reading it only once and without knowing its length in advance, how can you select one character so that every character is equally likely to be chosen?

Reservoir sampling: when reading the $k$th character, replace the current pick with it with probability $1/k$. A character at position $k$ survives to the end of an $n$-character file with probability $\tfrac1k\cdot\tfrac{k}{k+1}\cdots\tfrac{n-1}{n}=\tfrac1n$. This uses $O(1)$ memory and one pass.