 However, Duff 1986 and Hájek 2003 argue that the argument is in fact invalid. Their point is that there are strategies besides wagering for God that also have infinite expectation—namely, mixed strategies, whereby you do not wager for or against God outright, but rather choose which of these actions to perform on the basis of the outcome of some chance device. Consider the mixed strategy: “Toss a fair coin: heads, you wager for God; tails, you wager against God”. By Pascal’s lights, with probability 1/2 your expectation will be infinite, and with probability 1/2 it will be finite. The expectation of the entire strategy is: