Actually the whole point of particle physics is that the same thing _doesn't_ happen every time. Quantum field theory allows us to predict probabilities e.g. of

Actually the whole point of particle physics is that the same thing _doesn't_ happen every time. Quantum field theory allows us to predict probabilities e.g. of a particle decaying to another particle, for a given model. As for doing something 1e4, 1e5 times, at the LHC we collided bunches of 10e10 particles continuously every 50ns for months, and still only produced a few hundred Higgs particles. So these studies of ultra rare processes tend to also have limited statistical power.