The rational price of the Pasadena and Altadena games, introduced by Nover and Hajek (2004), has been the subject of considerable discussion. Easwaran (2008) has suggested that weak expectations-the value to which the average payoffs converge in probability-can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders the problem more realistic and accounts for the role of weak expectations. In particular, we demonstrate that in a bounded utility framework, all agents, even if they have different value functions and disagree on the price of an individual game, will finally agree on the rational price of a repeated, averaged game. Thus, we explain the intuitive appeal of weak expectations, while avoiding both trivialization of the original paradox and the drawbacks of previous approaches.