What does Savage's subjective EUT say?
if (and only if) the decision maker's preferences over bets (not lotteries!) satisfy 7 axioms, then:

Savage's subjective expected utility theory (EUT) states that an individual's decisions under uncertainty should reflect their preferences according to seven axioms. These axioms state that the individual's preferences should be complete (all alternatives are ranked in order of preference), transitive (the individual should not cycle between preferences), continuous (switching between two similar gambles should only yield small changes in decision-making), independent (nothing should be known about the outcome of one bet from knowledge of the outcome of another), span (all gambles should be compared to a standard gamble), and finally, the monotonicity and sure-thing axioms (the desirability of a gamble should not decrease as the probability of success increases). If an individual's preferences satisfy these seven axioms, then Savage's EUT states that the expected utility of a bet should serve as a rational guide for decision-making under uncertainty.