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.
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.
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.
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.
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.
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.
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.
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.
20 thoughts on “Kelly Bet on Everything”
I think there’s an illusion of transparency going on with this particular twitter beef.
To keep it short, my suspicion is that people who say “be risk averse” (I was in that crowd somewhere) really mean something more like:
“Be selective about risk, know your priorities and act ruthlessly risk seeking where the payoff is big, be a risk miser with everything else.”
The goal here is to avoid Talebian ruin (https://medium.com/incerto/how-to-be-rational-about-rationality-432e96dd4d1a), but still go after the stuff that’s important to you. Minimizing your risk on the nonessentials so you can bet big on the important stuff is in fact rational and important. e.g. If you’re devoted to a higher power, a vow of chastity works wonders to disentangle yourself from all sorts of distractions.
I expect that the risk-averse people, while they have a large pool of ‘actual resources’ like money, their pool of ‘risk-available’ resources is much smaller, and that they should determine what the amount of resources they have that is risk-available, and then kelly bet with this amount until it is equal to their actual resources.
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Or if doing this, then bet more than Kelly, for the reason Jacob gives (Kelly assumes log utility).
E.g. I do big stock market bets, using a bankroll of about half my net worth – I’ve ringfenced half so in a catastrophe I won’t go bankrupt. Hence my betting bankroll is surplus cash, so arguably I should place even bigger bets then Kelly, more like maximizing final wealth than Kelly’s log wealth (the latter being equivalent to maximizing average growth rate).
Are you sure that, on average, people don’t account for the Kelly criterion in their decisions? My initial guess would be that it’s at least partially included in the predictive processing – aiming at minimizing surprise. Or maybe rationalists are more anxious and conscientious, which is somehow related to their higher IQ and highly abstract interests?
One alternative explanation might involve the observation that wins and losses have different weights in real life. As the natural selection favored our increased sensitivity to threatening stimuli, it is usually more painful to lose a job, a partner, or resources than it is pleasant to get them. From this perspective, loss aversion might not be a bias, but a reasonable way of avoiding more unpleasantness. For many people, high-variance life is also a significant stressor on its own. It’s an interesting topic, and I hope you’ll explore it even further. :-)
I’m familiar with the world of polyamory (art school), but I don’t understand framing it as a “high-risk, high-reward option” that multiplies both good and bad things. What arguments would support this position? Overall, it seems better for people with flexible forms of attachment, LGBTQ folks, and generally progressive types. I’ve also seen it marketed as a “last resort option” for dispossessed guys who may either stay alone forever or become the secondary, less appreciated partners of poly women. BTW, I don’t know why it’s like that, but poly circles tend to attract really deceptive and unpleasant people. I’m not saying that all, most or even many poly people are bad (you seem like a great person!), just that a lot of objectively bad people are poly.
I assume that loss aversion is an outdated evolutionary hangover. Because presumably it was intended to keep you alive in a near-starvation situation where even a small loss (eg of food, health) was dangerous. This is no longer the case in most countries.
I strongly agree with the call to action(do things! be bold! timidity is causing you to leave money on the table!), but think that the Kelly criterion isn’t the the right tool to think about this.
WARNING: I ran out of brainpower 70% of the way through writing, so it may ramble. sorry.
if you have one bankroll and one currency to maximize, Kelly is a good upper bound of how much to bet. you may want to bet less, as our friend Zvi discusses.
in life, you have a large number of bankrolls and currencies, that often back each other in complex ways. as a result there are at least three big differences: currency != bankroll, total ruin in one currency/bankroll is acceptable, as long as it is backed by another, and lots of “bets” actually have no cost when you lose.
I’ll try to take it one at a time, but the categories bleed into each other quite nicely.
currency != bankroll:
unlike horse races where your bankroll and payout are both money, someones bankroll for making friends could be (social status + niceness + engaging conversationalist + cool cetholopod facts) and the payout could be winning or losing social status. if most of you social desirability comes from status, gambling it all on befriending a celebrity is dumb. if people like you for your cetholopod insight, you might as well see if Nathan Fillion is a fan of the cuttlefish, losing face doesn’t hurt you much, and you could gain a lot of status.
a lot of blog readers have a big bankroll of programming/finance skill so even if you lose all you money, you can still earn more as easily as before. wipeing out your savings means eating cheaper meals and less fancy dates for a while, but leaves your earning ability intact.
total ruin in one currency/bankroll is acceptable:
you can afford to lose your (friends/money/lovers/gigs/free time/status/job) for a while, as long as the most of other items are in solid shape. friends will let you couch surf, free time will let you make new friends, savings will help if you lose your job, and friends and status will help you find a new job, status will help you date more easily, ect. wipeing out in one or two categories is acceptable if you are very robust, and the more bets you make, the better you’ll do(and the more robust you can become)
also, many skills are fixed, programming/flirting/kindness skills aren’t something you “lose”, no matter what you bet, and provide healthy amounts of money/dates/friendship
many “bets” actually have no cost when you lose:
this one is especially true socially in large cities like NYC, and less true in the 30-person tribes of you ancestors. you instincts will deceive you, do not trust them.
inviting an interesting stranger over for dinner(or to go pigeon-catching) won’t damage your status if they say no(cities are big, you’ll never see them again). be honest and bold, but not unkind. with an infinite pool of potential friends, where the failure mode is just talking to the next person, maximize variance. if you aren’t compatible with someone, find out fast and move on, instead of fearing failure.
also, often time the failure of a plan is a little embarrassment and a good story. get over the former, and get excited about the latter(it’s another form of bankroll)
Taleb’s advice of making large numbers of very risky high expected-value bets with uncorrelated outcomes works well here, especially if you are robust.
take big romantic risks, you’ll still have companionship and love from your friends either way, spend time learning weird skills that might be useless, you bank account is untouched either way, take social risks and risk weirding someone out, if you are a kind/friendly/gregarious personality there are lots of other folks eager to befriend you.
in a one-currency betting game, bet Kelly.
in life, as long as your bets are numerous and multidimensional and your risks uncorrelated, take almost any bet with positive expected value, and have fun doing it. seems like Kelly should be the lower bound for how much you should bet. maybe you should bet Kelly, maybe you should bet more than Kelly, but if you are less than Kelly you aren’t being bold enough.
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Re living in New York, presumably this is one reason (aside from network effects and specialisation) why cities are prosperous and innovative compared with villages. Because their size and rapid turnover of people means they are relatively anonymous; so people aren’t so dependent on reputation, and hence can take big business/career and social risks. They can just move on if they fail – by physically moving, or just starting up again with a different set of people in the same place.
Interesting idea but I suspect this is equivalent or similar to saying that people’s capital has various parts, each of which you can lose but you usually don’t lose them all. E.g. you maybe be risking your career by some manoeuvre, but your career is only say 30% of your total capital, so you can still recover via friends etc.
Two counterexamples to the idea that you can’t ruin all aspects at once are (a) death, (b) prison (especially life sentence). E.g. if you’re a married teacher who gets convicted of paedophilia you’ll probably lose your career, marriage, friends, home, maybe your money (on legal bills or something), reputation, happiness and maybe health.
Thoroughly like + endorse this.
These are excellent points for young, talented, upper-middle-class or higher men (such as yourself). You probably know a lot of smart guys who are too risk averse and could stand to take a few more risks.
The catch, of course, is that the Kelly criterion is that you should bet proportional to your bankroll and your edge. This may apply in terms of the stock market, which over the long term has gone up more than down. But what if your edge is negative (as in a casino game)? In that case you should walk away from the bet.
In work, many young people today are stuck doing lousy jobs with few opportunities to find new ones. The expected value of their new job should they quite should well be less than their current one (taking into account the possibility of long-term unemployment).
Controversial topic parties and naked parties in the woods? Seems like they’d both get many people in trouble with HR should someone at work who doesn’t like you find out about it. A lot of people more autistic than you are going to have a lot of problems taking any social risks at all, because the chance of blowing it in that circle is much higher. I’ve long since mentally calculated that any unscripted social interaction–for me–carries a 1% chance of significant negative effects.
Creative talent, well, if you start anonymously to avoid getting cancelled if someone finds your work objectionable I guess you’re OK.
As for romance, flirting with someone outside of your league can lead to them telling all their friends what a creep you are, and possibly even to getting #MeTooed in the current year (hah!). As for the polyamory bit…if you’re in a stable marriage the risk of inducing a divorce probably far outweighs any additional spice you may add, not to mention that women have a much easier time finding casual partners than men.
I won’t comment on psychedelics. I don’t speak of what I know nothing of, even if I am on the Internet. ;)
Aaronson got away with it, yes. But he had just the right combination of sympathy from the right and some people on the left, coming off as just enough of a feminist to get the more moderate ones on his side (something that might not happen again in our current era of even greater polarization), not to mention being an acknowledged brilliant computer scientist which might have gotten him another job in a company outside of the limelight. He also wrote pretty damn well for a science guy. For every Aaronson there are 100 people who lost their job when they said something on Facebook their boss didn’t like. They’re not even all on the right.
And long as we’re talking rationalists, how about that other Scott A, who killed his blog to avoid getting doxxed by the NYT and wound up having it happen anyway? (His real name’s much more searchable now, though I won’t give any details because I don’t want to make him any easier to find–I am firmly on Scott’s side on this one and have switched to other news sources to avoid giving the NYT any clicks.)
Children–well, this has been described much better by sociologists than me, but it’s well known family formation decreases in bad economic times, largely for the reasons you cite.
Your ability to take risks decreases as you get older, as you have less time to recover from any setbacks. It’s harder to get hired after 40 (or younger in many tech jobs), and after 50 it’s almost impossible in most industries. If you have children, you might feel comfortable risking your welfare, but not theirs. And women have to pop out a baby by 40, preferably 35, if they want one.
I’m not saying many people aren’t too risk-averse. But for much of humanity, that actually is rational. You’re bright, young, talented, and likely wealthy as a result. I don’t believe in telling people to ‘check your privilege’, because that’s an annoying thing leftists do to shut down debate. But in this case the expected value function looks very different for other people than it does for you. It may even have a different sign. For many people, to quote an old movie, the only winning move is not to play.
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Re “Your ability to take risks decreases as you get older, as you have less time to recover from any setbacks”
Incidentally this is the reason pensions tend to invest in higher-risk assets in your younger years and gradually shift to lower-risk ones as you get older. Because if your pension performs poorly when you’re young, then in principle you can top it up by working harder. When you’re older you have fewer opportunities or ability to earn more at will.
Do you think the measurability of each possible bet could be a determining factor in how rationally people approach it? Monetary bankroll seems to be the most measurable, followed by reputation, friendship-volume, romance-volume, skill-volume in that order I’d think
And that ranking seems to correspond with how rationally people gamble on each domain
“Friends who have the most slack in life [and] the most risk averse” is noticably vague as to the source of these slack / risk assessments. I would expect that it is hard to tell from the outside how much “bankroll” of any kind any other person actually has, and that on most axes this is much easier to overestimate than underestimate. People tend to project positive aspects in their life more than negative ones.
This is a very interesting topic really, and I for a fleeting moment thought of illustrating the questions it raises with aspects of my own life; but these are not actually topics I am inclined to open up to and take any concrete advice on from online randos. Not even from relatively casual friends really, a very close confidant would be needed to productively discuss the topic at all. So case examples will continue to not be forthcoming…
Minor math nitpick:
If I have a sequence of bets where half the time I divide my wealth by 4, and half the time multiply my wealth by 3.25 ($1000 – $750 + $3000), eventually I will have almost no money.
I’m pretty sure Jacob means a bet where half the time you lose $750 (so you end up with $250, quartering your money) and half the time you gain £3000 (so you end up with $4000, quadrupling your money). “Risk $750″, not “pay $750″.
I don’t think using your current net worth as the “bankroll” input number is quite right for Kelly betting purposes. Instead, you should use something that’s more like (your expected remaining lifetime earnings) + (your current net worth) as the “bankroll” input, and bet some fraction of that.
As a concrete example, if you just graduated college, have zero savings, and find that you’re the kind of software engineer who can get a job at Google, I think it’s fairly safe to assume that your future working life is convertible into at least $5 million. So an opportunity that’s 55% likely to double your money should see you plunking down 10% * $5e6 = $500,000, presumably via loans since you have no savings. Or about 2-3 years of your early career, since that’s about the same opportunity cost.
I think this generalizes to the other examples you named – in early life, Kelly-betting using only your current savings/friends/reputation as your bankroll is not aggressive enough.
An excellent & thought-provoking post. One little point to add re taking higher risks in life than most people do – I think it was Eliezer who said re failure that if you’re not regularly failing, you’re not trying hard enough things (i.e. ones with high reward as well as high risk).