# Kelly Bet on Everything

Cross-posted, as always, from Putanumonit.

It’s a core staple of Putanumonit to apply ideas from math and finance out of context to your everyday life. Finance is about making bets, but so is everything else. And one of the most useful concepts related to making bets is the Kelly criterion.

It states that when facing a series of profitable bets, your wagers should grow proportionally with your bankroll and with your edge on each bet. Specifically, that you should bet a percentage of your bankroll equivalent to your expected edge — if a bet has a 55% chance to go your way your edge is 55%-45%=10% and you should risk 10% of your bankroll on it (assuming equal amounts wagered and won). There could be reasons to avoid betting the full Kelly in practice: you’re not sure what your edge is, your bet size is limited, etc. But it’s a good guide nevertheless.

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. “Exponential” means “fast and crazy”; logarithm is the inverse of that. It’s slow and cautious. If you have \$1,000 and you’d risk no more than \$750 for an equal chance to win \$3,000, you’re logarithmic in dollars and should “bet the Kelly”.

Log scales apply to the difficulty and value you get for most things. Life satisfaction grows with log(money). Making a new friend is probably one tenth as valuable to someone who has 10 friends than to someone who has one, so your social life depends on log(friends). It’s equally hard to double one’s number of blog readers, sexual partners, job offers etc regardless of how many you have, as opposed to incrementing each by a fixed amount. It’s equally valuable too.

And so, for most things, it makes sense to bet the Kelly. You’ll need to find out what bets are available, where your edge is, and what your bankroll is.

## Money

Let’s start with the obvious one. What kind of Kelly bets can you make with money? Investments are the obvious one, and standard investment advice is to switch to high-risk-high-return assets when you have some money to spare.

You can also make bets on your ability to make money: take on a side project, look for a new job, start your own business, ask for a raise. Each one entails a risk and a possible reward. Your bankroll is your literal bankroll, your edge is your ability to make money for yourself or your employer.

People have a tendency to think that if they’re paid \$N a month their value to their employer is something like N and half, but that often way off. Some people are worth less than what they are paid, but are kept around because their boss can’t tell. Some people are worth 10x their salary — an employer has no reason to pay you more if you don’t ask for it. I quit a job once and immediately got offered a 30% raise to come back. I did some math on what I’m worth, gambled on asking for 50%, and got it.

## Friends

When your friendships are few and tenuous, people’s inclination is to play it safe and conform to the crowd. It won’t make you a social star, but it won’t turn people away either. But if you have an edge in popularity and enough close friends to fall back on you can make some bets on your own vision.

When I was younger and struggled to make friends I’d just wait to be invited to parties. When I finally figured it out and acquired a rich social life I started throwing my own events the way I like them: controversial topic parties, naked retreats in the woods, psychedelic rationality workshops. Each one is a gamble — the event could fail or people could just not show up. In either case I’d lose some of the status and goodwill that allowed me to plan those events in the first place. But when it works the payoff is equally great.

## Creative Talent

Whatever creative outlet you have, you get better by getting feedback from the audience. Show people your paintings, read them your poems, invite them to your shows, link them to your blog. This is a gamble — if people don’t like what you’re making you won’t get their attention next time.

When I just arrived in NYC I was doing stand-up and would perform at bringer shows where you get stage time if you bring 3 or 4 paying guests. My ability to do that depended on the number of friends willing to humor me (bankroll) and my humor (edge). By the time I got decent enough to get an invite to a non-bringer show I had just about run out of comedy-tolerating friends to call on.

## Romance

The most obvious way to bet on yourself in romance is to flirt with people “outside of your league”, your bankroll being in part your ability take rejection in stride and stay single for longer. The same applies the other way, with making the bet on breaking up a relationship that is merely OK in hopes of something better.

But you can also bet on an existing relationship. If the person you’re dating just got into a school or job in a faraway city your ability to go long-distance for a while depends a lot on the bankroll of relationship security you have. Ethical non-monogamy is a similar gamble: if you’re don’t have an edge in making your partner happy they may leave you. If you do, their happiness only doubles for their ability to date other people, and polyamory makes you all the more attractive as a partner.

Polyamory makes bad relationships worse and good ones better; if you only know people who opened up when their relationship started deteriorating you’re liable to miss this fact.

## Sanity

Psychedelics can drive you insane. They can also make you saner than you’ve every been. The same applies to meditation, mysticism, esoteric ideologies, and whatever else Bay Area Rationalists are up to. Epistemic Rationality is your bankroll and your edge.

## Reputation

A lot of people are seeing the rise in callout and cancel culture purely as a threat, a reason to go anonymous, lock their accounts, hide in the dark forest of private channels. But where there’s threat there’s also opportunity, and where reputations can be lost they can also be made. Chaos is a ladder.

In 2015 Scott Aaronson’s blog comment went viral and threatened to spark an outrage mob. Aaronson didn’t expect that popular feminist writers would dedicate dozens of pages to calling him an entitled privileged asshole for expression his frustrations with dating as a young nerd. But he also didn’t expect that Scott Alexander would write his most-read blog post of all time in defense of Aaronson, and that the entire Rationalist community would mobilize behind him. This wouldn’t have happened if Aaronson hadn’t proven himself a decent and honest person, writing sensitively about important topics under his real name. Aaronson’s reputation both online and in his career only flourished since.

## Children

Having children is a bet that you have enough of an edge on life that you can take care of another human and still do well. The payoff is equally life-changing.

## Risk Averse Irrationalists

I wrote this post because of my endless frustration with my friends who have the most slack in life also being the most risk averse. They have plenty of savings but stay in soul-sucking jobs for years. They complain about the monotony of social life but refuse to instigate a change. They don’t travel, don’t do drugs, don’t pick fights, don’t flirt, don’t express themselves. They don’t want to think about kids because their lives are just so comfortable and why would you mess with that?

They often credit their modest success to their risk-aversion, when it’s entirely due to them being two standard deviations smarter than everyone they grew up with. By refusing to bet on themselves they’re consigned forever to do 20% better than the most average of their peers. To make 20% more money with a 20% nicer boyfriend and 1.2 Twitter followers.

And partly, I wrote this post for me. I spent my twenties making large bets on myself. I moved to the US nine years ago today, all alone and with a net worth of \$0. I found polyamory and the love of my life. I started a blog under my real name, with my real opinions, on real topics.

Now in my mid-thirties my life is comfortable, my slack is growing, and I’m surrounded by younger friends who know all about discretion and little about valor. This post is a reminder to keep looking for my edge and keep pushing the chips in. There’s plenty more to be won.

• On the whole I agree with Raemon’s review, 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.

The post states that you should:

However the correct rule is:

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

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 13rd of your bankroll)

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

• This is a useful clarification. I use “edge” normally to include both the difference in probability of winning and losing and the different payout ratios. I think this usage is intuitive: if you’re betting 5:1 on rolls of a six-sided die, no one would say they have a 66.7% “edge” in guessing that a particular number will NOT come up 56 of the time — it’s clear that the payout ratio offsets the probability ratio.

Anyway, I don’t want to clunk up the explanation so I just added a link to the precise formula on Wikipedia. If this essay gets selected on condition that I clarify the math, I’ll make whatever edits are needed.

• So there’s a technical definition of edge which is your expected gain for every unit that you bet, given your own probability and the bet odds.

I agree that not clumping up the post is probably best but to make the post correct I suggest adding the underlined text into the definition in case people don’t click the link.

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

• 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.

• 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.

• This might not be for you, but I found http://​​mindingourway.com/​​ to be very helpful in terms of finding motivation.

The other main thing I’d target would be to spend time around people who make you feel excited about stuff. Don’t try to do it alone.

• I think a big part is I just don’t really trust there to be payoff.

I’m curious how you/​your System I responds to high-risk/​high-reward ideas. Startups are what come to my mind first: eg. startup ideas that maybe you think are unlikely to succeed, but would be billion dollar companies if successful.

• I just don’t feel anything. I do have a certain logical appreciation that if I made a billion dollar company it would be impressive, I’d probably improve people’s lives with it, and I could buy more stuff (mostly donate I guess? I don’t have much else I need...) but I don’t feel anything. Those are the words I feel flowing through my head but I don’t feel any of the wordless feelings that make up my system 1.

Hell, I don’t even feel anything thinking about the pleasure I’d get from getting a peach from my kitchen and there’s a 95% chance the peach is good and ripe today. I just do it because I know I’ll have good feels once I actually have the peach. Which is enough to make me do something low effort like get a peach but not start a company.

Edit: If anyone was curious, the peach was indeed delicious

• I am not an expert, but this sounds to me like depression. Maybe there is a pill for that?

Or maybe peer pressure if you could find the right group of peers which would push you in the direction you want to go anyway. (I wonder if you could rent such group. Maybe this is a business opportunity.)

• Ah, I see.

• 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.

• 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.

• 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?

• Nitpick: Kelly betting does not ever go bankrupt, at all. Unless the probability is exactly 1 or 0 (which is bad) the Kelly bet will always be less than the total amount of money you have right now—meaning that you can never lose all of your money on a Kelly bet.

That said, the code you linked is systematically losing money over time (though never actually hitting zero) because this line is backwards:

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

When dice < pwin, that should be a win (assuming that pwin is supposed to be the probability of winning), so the bet resolution should be positive in that case, not negative. With that fixed, wealth shoots up at a pretty quick exponential clip, eventually passes max double (~10^308) and becomes infinity, and then becomes NaN.

• 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 5050 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.

• Manipulating one’s own utility functions is supposed to be hard? That would be news to me. I’ve never found it problematic, once I’ve either learned new information that led me to update it, or become aware of a pre-existing inconsistency. For example, loss aversion is something I probably had until it was pointed out to me, but not after that. The only exception to this would be things one easily attaches to emotionally, such as pets, to which I’ve learned to simply not allow myself to become so attached. Otherwise, could you please explain why you make the claim that such traits are not readily editable in a more general capacity?

• 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.