You're absolutely right! I think I have a true intuition I'm trying to communicate, and will continue to think about it and see, but it might turn out that the entirety of the intuition can be summarized as "actually the utility is nonlinear in money".

This post makes some good points, too strongly. I will now proceed to make some good points, too rambly.

F=ma is a fantastically useful concept, even if in practice the scenario is always more complicated than just "apply this formula and you win". It's short and intuitive and ports the right ideas about energy and mass and stuff into your brain.

Maximizing expected value is a fantastically useful concept.

Maximizing expected value at a time t after many repeated choices is a fantastically useful concept.

(Edit: see comments, there are false statements incoming. Leaving it all up for posterity.) It turns out that maximizing expected magnitude of value at every choice is very close to the optimal way to maximize your expected value at a time t after many repeated choices. Kelly is a nice, intuitive, easy heuristic for doing so.

So yes, what you really want to do is maximize something like "your total wealth at times t0 and t1 and t2 and t3 and... weighted by how much you care about having wealth at those times, or something" and the way to do that is to implement a function which knows there will be choices in the future and remembers to take into account now, on this choice having the power to maximally exploit those future choices, aka think about repeated bets. But also the simple general way to do something very close to that maximization is just "maximize magnitude of wealth", and the intuitions you get from thinking "maximize magnitude of wealth" are more easily ported than the intuitions you get from thinking "I have a universe of future decisions with some distribution and I will think about all of them and determine the slightly-different-from-maximize-log-wealth way to maximize my finnicky weighted average over future selves' wealth".

Do you need to think about whether you should use your naive estimate of the probability you win this bet, when plugging into Kelly to get an idea of what to do? Absolutely. If you're not sure of the ball's starting location, substituting a point estimate with wide variance into the calculation which eventually feeds into F=ma will do bad things and you should figure out what those things are. But starting from F=ma is still the nice, simple concept which will be super helpful to your brain.

Kelly is about one frictionless sphere approximation to [the frictionless sphere approximation which is maximizing magnitude of wealth]. Bits that were rubbed off to form the spheres involve repeated bets, for sure.

This kind of synthesis, boiling down an expression to a very few, very human components, is incredibly valuable to me. Thank you.

Other examples I learned from this community:

lnO(A|B) = lnO(A) + lnL(A|B)

(U(X)-U(Y)) / (U(Z)-U(Y)) = (V(X)-V(Y)) / (V(Z)-V(Y)) when U and V are isomorphic utility functions

I was referring to me! I thought back over my most aversive things and I believe a life coach would have helped me get through all but two with relative ease. Not like butterflies and rainbows, but enough that for an aversive thing now I'd be quite happy to make it happen given, y'know, lots of cash. To be clear, I'm not talking about a once-a-week therapy session, I'm talking about someone sitting with me 8 hours a day.

At a high enough price I would be ecstatic to subcontract to a life coach who will work with me to get it done with a minimum of aversion.

Memorizing ancient philosophers was key to intellectual status

Cardano's accounting of these incidents sounds almost exactly like https://www.google.com/search?q=and+then+everyone+clapped+meme

‘What feels important or exciting but also daunting/confusing/impossible?’

Merely reading this question, inline with everything else, no special pauses or anything, caused me to feel like I do when I recall some of my favorite music swells. Chest grows suddenly warm, and feels heavy-with-significance (not heavy with dread, the good kind of heavy).

It was very obvious upon filtering to just-hammer or just-axe that the abstractions were suspiciously limited.

I enjoyed this! I performed really poorly!

So after an enjoyable evening of coding up some heuristics and then having very little clue of how to combine and then translate them into probabilities, I realized that my only chance to win was to hope that the data set was in some ways easy, meaning that most participants would get almost everything "right", and the winner might be determined by who was overconfident enough.

Don't get me wrong, my heuristics didn't perform all that well, but I do wonder how much of the "overconfidence" we see is a result of actual miscalibration versus strategic. If you think your discrimination is working really well, you probably want to gamble that it's working better than everyone else's, but if you think it's not working so well, it does seem like the only chance you have of winning is overconfidence plus luck.

tl;dr:

okay, lemme read: