Kelly Bet on Everything

I feel like one of the people you're writing this for.  25.  900k NW yet still working a boring programming job for one of the top tech companies that I don't care about.  Last time I seriously tried at Tinder I had 5 dates planned in the first weekend and 112 matches in the first week yet I'm spending my time with a casual partner I'm lukewarm about.  Every time I start a side project I go two days and then think "eh, I bet nobody will care about it" and stop.  Besides the job the only reason to stay where I am is I like the swing dancing scene here but that's closed with covid and I don't like much else about here.  In my hobbies I'll get bored right before I'm impressive. Leaving just before world finals in ICPC. Switching to be more casual about my lifting a few pounds short of a state record.

I don't need to start making Kelly Bets, I just need to start making bets period.  I don't know what it would take for me to start doing that.  I have a friend who makes big bets and I look up to him but I don't copy him.  I think a big part is I just don't really trust there to be payoff.  I don't feel like I'll be much happier.  I don't expect any of my side project ideas will be that useful to people.  Or maybe that's just an excuse.  I mostly feel blankness when I try and think of the tradeoffs so maybe there's some emotional block about my inability to take risks?  I'm not even sure where it would come from.  Most of my problems I have an obvious source of trauma to blame it on but not here.

On the whole I agree with Raemon’s review [LW(p) · GW(p)], particularly the first paragraph.

A further thing I would want to add (which would be relatively easy to fix) is that the description and math of the Kelly criterion is misleading / wrong [LW(p) · GW(p)].

The post states that you should:

bet a percentage of your bankroll equivalent to your expected edge

However the correct rule is:

bet such that you are trying to win a percentage of your bankroll equal to your percent edge.

(emphasis added)

The 2 definitions give the same results for 1:1 bets but will give strongly diverging results with other odds.

In addition the post gives a method of calculating one’s edge which gives correct results for 1:1 bets. It is not entirely clear how one would use the formula for non 1:1 bets but it doesn’t seem to indicate a calculation which would give one’s edge correctly. (55%-45%=10% doesn’t seem to readily generalise correctly in the same way that (55%-50%)/50%=10% does).

The post never states that the definition is only for 1:1 bets so the impression given by the post is that these formulae can be used in the cases given in the post. However there are no guarantees that any of the examples in the post are 1:1 bets.

(The post does mention that the example is based on 1:1 bets but it doesn’t imply that the calculation as given only works for such bets.)

As a result the post effectively ends up recommending making incorrectly sized bets. For non 1:1 bets it is possible to calculate recommended bet sizes which have an expected negative impact on the logarithm of ones bankroll and as such actively makes one’s life worse.

(e.g. the bet odds are at 25% but you believe there’s a 50% chance that it will resolve true then your edge is 100% (calculated properly, not using the method in the post as I’m not sure how to use that) and the post would suggest betting your entire bankroll. The correct Kelly calculation gives 1/3^rd of your bankroll)

Without this correction I would strongly recommend against including this post in the review.

The _vast_ majority of interesting decisions are uncertain and have multidimensional risks and payouts that defy such calculation. Even something as trivial as "how much to pay for a residence" has massive variance in the monetary outcome _and_ unknown impact on quality of life, ease of social experiences, what work options there are, etc.

Sure, if you see a 3:1 chance to get paid even money, you should bet half your resources on it (that's not your current net worth, actually - it's the discounted value of your future cash flows, independent of this bet. For young folks, it's likely a large multiple of your current net worth). But you will _never_ see such an opportunity.

On one hand, AFAICT the math here is pretty fuzzy, and one could have written this post without it, instead just using the same examples to say "you should probably be less risk averse." I think, in practice for most people, the math is a vague tribal signifier that you can trust the post, to help the advice go down.

But, I see this post in a similar reference class to Bayes' Theorem. I think most people don't actually need to know Bayes Theorem. They need to remember a few useful heuristics like "remember the base rates, not just the salient evidence you came across", and "think about relative likelihood ratios between multiple hypothesis."

Nonetheless, an important aspect of The LessWrong Project™ is building a unified worldmap, looking to understand the lawfulness that underlies our heuristics, and when our cleanest laws don't quite apply to our messy situations, keeping an eye out for how we could someday later better integrate everything into a single unified model.

My understanding of the Kelly Criterion makes it something like "idealized Bayes Theorem but for instrumental rationality instead of epistemic."

I'd kinda like there to be a version of this post that's more rigorous, that attempts to take some of Jacob's fuzzy examples and do more math to them (maybe just a couple, to fully illustrate the idea). I confess this is the sort of thing I don't expect to really be directly helpful to anyone – probably most people read this post, absorb the general lesson of "you should be less risk averse" and move on with their day. But it's nice to have more details available when you peer under the hood.

The description of the Kelly’s Criterion here seems like it is for the specific case where the house odds (as it were) are 1:1?

People’s intuition is usually that Kelly bets are too aggressive, that betting half of everything you have a on 75%-25% bet is too wild. But the Kelly criterion is actually quite conservative in that it maximizes not the expected size of your bankroll but it’s expected logarithm

This is actually a misunderstanding of Kelly's criterion. Log(x) is monotonically increasing in x. The reason we use logarithms at all in the Kelly criterion derivation, is that it allows us to conveniently move the exponent. The Kelly criterion maximizes your return assuming you may play a number of rounds approaching infinity. If you're only playing fewer than infinity rounds, your expected value increases if you bet a larger percentage of your pot size.

reference: https://explore.paulbutler.org/bet/

I'm running simulations to get a feel for what "betting Kelly" would mean in specific contexts. See code here: https://jsfiddle.net/se56Luva/ . I observe, that given a uniform distribution of probabilities 0-1, if the maximum odds ratio is less than 40/1, this algo has a high chance of going bankrupt within 50-100 bets. Any thoughts on why that should be?

let betres = (dice < pwin) ? (-frbet) : (frbet * odds);

Saying that people would be better off taking more risks under a particular model elides the question of why they don't take those risks to begin with, and how we can change that. If its desirable to do so. 

The psychological impact of a loss of x is generally higher than that of a corresponding gain. So if I know I will feel worse from losing $10 than I will feel good from gaining $100, then its entirely rational in my utility function to not take a 50/50 bet between those two outcomes.  Maybe I would be better off overall if I didn't over weight losses, but utility functions aren't easily rewritable by humans. The closest you could come is some kind of exposure therapy to losses. 

only doubles

Only?

Sanity

That one could have used more explaining. It's a bit harder to grasp that one.

Children

...

The payoff is equally life-changing.

And probably deserving of its own post.

Nice post. I might try to use this idea to force myself to make more bet socially. I'm risk taking in terms of ideas and creation and jobs, but not enough in terms of talking to new people and flirting. Forcing myself to start a conversation with a stranger everyday is one way I'm trying to solve that; thinking about the rationality of the bet might become another.