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Random number generation produces values intended to follow a prescribed probability distribution. A physical source uses a measured uncertain process; a pseudorandom number generator deterministically expands a seed into a reproducible sequence. For a uniform integer on $\{0,\dots ,m-1\}$, reducing a uniform $b$-bit integer modulo $m$ is biased unless $m$ divides $2^b$. Rejection sampling fixes this by accepting only values below $m\lfloor 2^b/m\rfloor$ before taking the remainder. For $b=3,m=3$, accept $0,\dots ,5$: each residue then has exactly two preimages.

A random number generation technique that retains the unused equally likely outcomes after a rejected trial in rejection sampling. Instead of discarding those outcomes, it uses their conditional probability to obtain a new uniform distribution on a finite set for the input state of the next trial.