You don’t literally multiply 0 by infinity, of course, you take the limit of (payoff of N)*probability(you actually get that payoff) as N goes to infinity. If that limit blows up, there’s something wrong with either your probabilities or your utilities. Bounding the utility is one approach; bounding the probability is another.
Because otherwise you get mugged.
You don’t literally multiply 0 by infinity, of course, you take the limit of (payoff of N)*probability(you actually get that payoff) as N goes to infinity. If that limit blows up, there’s something wrong with either your probabilities or your utilities. Bounding the utility is one approach; bounding the probability is another.