Not a list, but a street fighting tactic is to apply this to finding counterexamples. Don't know whether a thing is true or false? Generate a bunch of random examples and check whether they all agree. Do this before you commit any energy to theoretical analysis. Obviously not a proof, but possibly gives a counterexample faster than you can think of one.

On the other hand, if you find yourself running 1hour+ numpy simulations for days on end you might want to consider an analytical approach.