  One reason for maximizing expected utility is that it makes for good policy in the long run. Feller (1968) gives a version of this argument. He relies on two mathematical facts about probabilities: the strong and weak laws of large numbers. Both these facts concern sequences of independent, identically distributed trials—the sort of setup that results from repeatedly betting the same way on a sequence of roulette spins or craps games. Both the weak and strong laws of large numbers say, roughly, that over the long run, the average amount of utility gained per trial is overwhelmingly likely to be close to the expected value of an individual trial.