Slightly More Realistic Personal Probability

Abstract

A person required to risk money on a remote digit of π would, in order to comply fully with the theory [of personal probability] have to compute that digit, though this would really be wasteful if the cost of computation were more than the prize involved. For the postulates of the theory imply that you should behave in accordance with the logical implications of all that you know. Is it possible to improve the theory in this respect, making allowance within it for the cost of thinking, or would that entail paradox?