  Second, the argument relies on two independence assumptions, one or both of which may fail. One assumption holds that the probabilities of the different trials are independent. This is true of casino gambles, but not true of other choices where we wish to use decision theory—e.g., choices about medical treatment.  My remaining sick after one course of antibiotics makes it more likely I will remain sick after the next course, since it increases the chance that antibiotic-resistant bacteria will spread through my body. The argument also requires that the utilities of different trials be independent, so that winning a prize on one trial makes the same contribution to the decision-maker's overall utility no matter what she wins on other trials. But this assumption is violated in many real-world cases. Due to the diminishing marginal utility of money, winning $10 million on ten games of roulette is not worth ten times as much as winning $1 million on one game of roulette.