I would first try to test the deterministic components as much as possible in isolation. Then, for the stochastic part, if you really run enough tests and/or your tolerance is large enough, you can be reasonably sure that the tests will "virtually never" fail. For example, if you expect 80,000 out of 100,000, I would estimate a standard deviation of about 120 (assuming independent random events with p=0.8). That means that you will very rarely see deviations greater than 400, and virtually never greater than 1000 (which is half of the sample tolerance you gave).