Yes, I agree. In other problems, your "probabilities" are going to not be statistically independent from basic facts of mathematics. I myself posted a top level comment with regards to ultimate futility of 'probabilistic' approach. Probability is not just like logic. If you have graph with loops or cycles, it is incredibly expensive. It isn't some reals flowing through network of tubes, sides of a loop are not statistically independent. It doesn't cut down your time at all, except in extreme examples (I once implemented a cryptographic algorithm dependent on Miller–Rabin primality test, which is "probabilistic", and my understanding is that this is common in cryptography and is used by your browser any time you establish a SSL connection)