> Monte-Carlo can and should be deterministic and repeatable.

That's a nitpick, but if the computation is executed in parallel threads (e.g. on multicore, or on a multicomputer), and individual terms are, for example, summed in a random order, caused by the non-determinism introduced by the parallel computation, then the result is not strictly deterministic. This is a property of floating-point computation, more specifically, the finite accuracy of real floating-point implementations.

So, it is not deterministic, but that should not cause large qualitative differences.