  A third problem is that the strong and weak laws of large numbers are modally weak. Neither law entails that if a gamble were repeated indefinitely (under the appropriate assumptions), the average utility gain per trial would be close to the game's expected utility. They establish only that the average utility gain per trial would with high probability be close to the game's expected utility. But high probability—even probability 1—is not certainty. (Standard probability theory rejects Cournot's Principle, which says events with low or zero probability will not happen.  But see Shafer (2005) for a defense of Cournot's Principle.) For any sequence of independent, identically distributed trials, it is possible for the average utility payoff per trial to diverge arbitrarily far from the expected utility of an individual trial.