Kelly isn't (just) about logarithmic utility

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.

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.

Calculating Kelly

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

Your Cheerful Price

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.

Your Cheerful Price

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.

Lessons from “The Book of My Life”

Memorizing ancient philosophers was key to intellectual status

Cardano's accounting of these incidents sounds almost exactly like

Catching the Spark

‘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).

D&D.Sci II Evaluation and Ruleset

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

Pseudorandomness contest: prizes, results, and analysis

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.

D&D.Sci II: The Sorceror's Personal Shopper


Blue Pendant of Hope, Blue Hammer of Capability, Yellow Plough of Plenty, Yellow Warhammer of Justice +1, gaining 124+ mana for 145gp.

Do not gamble with green items or the red pendant of truth; the value of a good, lucrative client with a somewhat useful sensing device and your own credibility is worth much more than some gold pieces today.

okay, lemme read:

Regularities found:

  • blue items register +/- 1 on the thaugister, except jewelry gets a +22
  • weapon mana is at least 10x the bonus and no more than 10(x+1) the bonus
  • (axes and hammers are tools, not weapons)
  • yellow items yield 18-21 mana
  • green items are capped at 40 mana and their thauyard readings seem very uncorrelated
  • actually all jewelry gets a +22 to its thaudout
  • jewelry-adjusted blue-adjusted thaulues are at most 60
  • red mana is always some product of 2s, 3s, and 5s
  • green items always yield an even amount of mana
  • non-blue items have thauras whose only prime factors are 2, 3, 5, or 7
  • green items yield mana whose prime factorization's non-2 exponents sum to at most 2, and only if exactly 1 from bases greater than 5
  • some identical red and green items have wildly different mana/thauata
Longsword of Wounding +2Red1466gp

20, 24

Warhammer of Justice +1Yellow541gp


Hammer of CapabilityBlue3535gp

34, 36

Pendant of TruthRed4038gp

2^a x 3^b x 5^c

Ring of Joy +5Blue2932gp

6, 8

Warhammer of Flame +2Yellow4865gp


Battleaxe of GloryBlue723gp

6, 8

Plough of PlentyYellow1235gp


Saw of Capability +1Green1635gp

2 x A

Amulet of Wounding +2Green5035gp

2 x B

Pendant of HopeBlue7734gp

54, 56

Pendant of Joy +4Green4239gp

2 x C

200gp, 120m? We can get that with Blue Pendant of Hope, Blue Hammer of Capability, Yellow Plough of Plenty, Yellow Warhammer of Justice +1, gaining 124+ mana for 145gp. Definitely take the job, and try to figure out on the road what's up with the Red Pendant of Truth and all the Green items. A good Green item saves ~30gp, but if we can know the Red Pendant of Truth is great we could save even more.

Crucially, no probabilistic choices should be made, for three reasons:

  • You have no guarantee about the distribution of item stats presented. They are very likely not uniform random. In fact meta-you suspects that there was once a list of 1000 items and 164 got filtered out.
  • You have a good client who is handing you 55gp for a day's work. This is an excellent situation. It is far better to keep this client than to try to eke out additional gold for this particular job.
  • Further, you have valuable information. You know what the client's thaudget does with jewelry and items with a blue glow, and you know how weapon mana and bonuses are related, and you know the yield of items with a yellow glow, and you know the maximum yield of items with a green glow. You can use this information in future deals with the client, or, if you can arrange a more profitable deal for the information itself, perhaps land a major score. But this second possibility is far, far less likely if you accidentally damage your credibility by supplying less than 120 mana.
Pseudorandomness contest, Round 2

I submitted an answer. It took me longer than I expected or originally wanted, but the side effects were pleasant.

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