 McGee constructs another type of Dutch Book with implications for decision theory. Suppose that an agent’s probability function is not concentrated at finitely many points. Such a state of opinion, in which the agent does not rule out all but a finite number of possibilities, seems both consistent and reasonable, yet assuming that an agent’s utilities are unbounded, McGee shows that there is an infinite series of bets, each with positive expected value, which together assure a loss (McGee 1999). Assuming that it is reasonable to have probabilities that are not concentrated at finitely many points, McGee calls into question the general adequacy of the decision theoretic framework, and in particular the principle of utility maximization that his Dutch Book argument presumes.