Sorry you feel that it’s dumb, because it’s not so much a formula as the basic concept (in words) of a expected value, which is perhaps the most fundamental con

Sorry you feel that it’s dumb, because it’s not so much a formula as the basic concept (in words) of a expected value, which is perhaps the most fundamental concept in statistics, ML, decision theory, game theory, economics, medical decision and more. As I mentioned, the application of this concept gets much spicier (and more useful) once you start accounting for random variables, priors, model assumptions, etc. There are centuries of academic and practical thought devoted to these topics. The “definition” of risk that I gave is a useful heuristic, even for my cat. He seems to calculate the probability of being caught on the kitchen counters, conditional on the number of people home and the time of day. He knows that he may get spritzed for violations and can balance this against the reward (simply chillin’ = stern warning; eviscerating a briefly undefended loaf of fresh challah = direct barrage from the water bottle). Clearly, this shrewd exploitation of Lady Luck is a learned behavior. (Whether is consciously strategic behavior or just serendipitously adaptive cat programming is actually immaterial in the game theoretic sense—mixed strategy Nash equilibria that result from evolutionary dynamics are equivalent to those that arise from strategic deduction). Anyways, you’re right that the original motivation for probability theory and expected value was to “get money” (via gambling): https://en.m.wikipedia.org/wiki/Problem_of_points https://en.m.wikipedia.org/wiki/Problem_of_points