Consider a sequence of numbers of the form %5En), where n are natural numbers. Each number in the sequence is rational, the limit of the sequence is not.
Consider your opening question. Assume that your utility is linear in money or that the magical casino offers to triple your utility directly. Each step in the sequence of rounds is rational, the limit itself is not.
Consider a sequence of numbers of the form
%5En), where n are natural numbers. Each number in the sequence is rational, the limit of the sequence is not.
Consider your opening question. Assume that your utility is linear in money or that the magical casino offers to triple your utility directly. Each step in the sequence of rounds is rational, the limit itself is not.
Infinities are weird.