We consider the problem of encoding the pi-calculus with mixed choice into the asynchronous pi-calculus via a uniform translation while preserving a reasonable semantics. Although it has been shown that this is not possible with an exact encoding, we suggest a randomized approach using a probabilistic extension of the asynchronous pi-calculus, and we show that our solution is correct with probability 1 under any proper adversary wrt a notion of testing semantics. This result establishes the basis for a distributed and symmetric implementation of mixed choice which, differently from previous proposals in literature, does not rely on assumptions on the relative speed of processes and it is robust to attacks of proper adversaries.