 The analysis should be careful not to prove too much; for some departures from theory are inevitable, and some even laudable. For example, a person required to risk money on a remote digit of \(\pi\) would, in order to comply fully with the theory, 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 implication of all that you know. Is it possible to improve the theory in this respect, making allowances within it for the cost of thinking, or would that entail paradox, as I am inclined to believe but unable to demonstrate? (Savage 1967 excerpted from Savage’s prepublished draft; see notes in Seidenfeld et al. 2012)