A third argument tries to add rigor by considering monetary payoffs. If Beauty's bets about the coin get paid out once per experiment, some argue that she will do best by acting as if the probability is one half.half (while others argue that probability one third gives the correct result if decision theory is correctly applied). If instead the bets get paid out once per awakening, one can again argue about whether or not acting as if the probability is one third has the best expected value.
A third argument tries to add rigor by considering monetary payoffs. If Beauty's bets about the coin get paid out once per experiment, some argue that she will do best by acting as if the probability is one
half.half (while others argue that probability one third gives the correct result if decision theory is correctly applied). If instead the bets get paid out once per awakening, one can again argue about whether or not acting as if the probability is one third has the best expected value.