We distinguish deterministic algorithms from randomized algorithms with two-sided error at most $1/3$ and a worst-case running-time bound. For a computation of at most $t$ steps, all $2^t$ strings of independent fair bits are equally likely. Every string must lead to termination; at least two thirds must give a correct answer. Unused bits are ignored.

Both machine models below have finite programs. In deterministic mode the program cannot use randomness. The hypotheses themselves are propositions, available as explicit premises in later theorems.