The machine itself is exactly the word RAM of Lax67; randomness is input, not a new primitive instruction. A random tape of length $r$ is a function $Fin r → Bool$, encoded in index order by the words zero and one. There are exactly $2 ^ r$ such tapes. For a rational success threshold $q$, the inequality $q · 2^r ≤ |good tapes|$ states the probability bound without introducing a measure-theoretic representation of a finite experiment. The Welzl-order theorem instantiates $q$ with $2/3$.

The definition separates total running time from success: every tape must halt within the bound, while a bad tape may return any output. The accepting condition is a relation on output words because a search algorithm may return any one of many correct witnesses. Supplying more bits than a program reads does not alter the success fraction—each used prefix has equally many extensions—so a theorem may use its time bound itself as a uniform tape length without exposing an implementation-specific random-bit count.