 Does this solve the St. Petersburg paradox? The answer depends on whether we think a rational agent offered to play the St. Petersburg game has any reason to accept the continuity axiom. A possible view is that anyone who is offered to play the St. Petersburg game has reason to reject the continuity axiom. Because the St. Petersburg game has infinite utility, the agent has no reason to evaluate lotteries in the manner stipulated by this axiom. As explained in Section 3, we can imagine unboundedly valuable payoffs.