The card drawing paradox is isomorphic to the old paradox of the game where you double your money each time a coin comes up heads (the paradox being that simplistic theory assigns infinite value to both games). The solution is the same in each case: first, the entity underwriting the game cannot pay out infinite resources, and second, your utility function is not infinitely scalable in whatever resource is being paid.
The card drawing paradox is isomorphic to the old paradox of the game where you double your money each time a coin comes up heads (the paradox being that simplistic theory assigns infinite value to both games). The solution is the same in each case: first, the entity underwriting the game cannot pay out infinite resources, and second, your utility function is not infinitely scalable in whatever resource is being paid.