Are you saying the bar is lower than we think for stuff like like… winning karma on lesswrong? (I agree for publishing content in public most people, including myself, probably should just go for it more)
Or are you also saying the bar is lower than we think for really hard things as well like making a scientific breakthrough or getting elected to your county’s parliament or making 100 million dollars?
Maybe it would help if you construct an explicit concrete model? You’re welcome to define what future opportunities will come along after this bet (or even a distribution of possible future opportunities)
Are you claiming that after you build this concrete model—Kelly betting will emerge as the objectively optimal strategy regardless of the agent’s preferences and regardless of whether we add a safety net/income stream into the picture?
Or are you making a softer (seemingly irrelevant) claim about what happens with geometric means/average growth rates when we don’t account for safety nets and income streams?
SimonM’s analysis is great—a hugely important point he covers well is that in the real world you don’t know exactly what your edge is.
And whenever you’re considering betting in a context like a highly liquid prediction market—you’re playing a negative sum game against competent adversaries. So for most people not only are they wrong about the size of their edge, but their edge is actually negative.
By default people have a bias towards risk aversion, which helps cancel out a bias towards overconfidence they can beat the market.
But I think it’s still important to notice that, if you’re someone with a safety net and/or future earnings to look forward to—you should in principle be willing to tolerate very high levels of risk as long as the expected value is positive (while still admitting the EV of day-trading options is negative).
The two world models:
“There’s lots of alpha to be found, but my utility as a function of money is very curved and I’m terrified of losses”
“My utility as a funciton of money is relatively flat given my substantial future earnings and safety net, but I don’t actually have an edge when it comes to financial markets”
Both advise against making reckless bets in financial markets. I claim for most of us number 2 is closer to the truth.
The practical implication—in situations where you get the opportunity to take +EV risks and you’re not subject to adversarial efficient market dynamics—you basically want to load up on risk to a degree way higher than what feels comfortable .
When a game is asymetric, non-zero-sum, and you don’t have competent adversaries trying hard to screw you—you really will find legimitate edges. This is where it’s appropriate to be extremely bold. And most of the time these prosaic “bets” have an inherently capped, relatively small bet size anyway.
Stuff like
Spending money on cleaners/babysitters to free up time to work on speculative on side projects
Hiring a tutor
Spending time+money to attend a networking event
Posting online under your real name
Spend money on products which may or may not work (e.g. a gadget that’s meant to help you sleep)
Asking for more money before accepting a job offer
Asking to pay less money before signing a contract to buy a house
Even mundane stuff like asking for an introduction or telling a joke that might not land
In my view the optimal policy for privlidged young people is usually avoidance of stuff like prediction markets (unless an absurd opportunity arises), while at the same time seeking to take an abmormally high level of +EV risk in positive-sum non-EMH domains.
maximize the chance that I have the most bankroll to spare for any better betting opportunities that come along in the future
What does “most” mean? If you start with W and go all-in on the coin flip game—you end up with 2W with probability
2W is the “most” you can possibly end up with to spare when the next betting opportunity comes along.
So by that framing, going all-in is what maximises the chance you have the most bankroll to spare.
(I’m not pretending that is a good argument I just made—I’m just pointing out that these desiderata we’re trying to express in natural language have lots of room for interpretation when it comes to turning them into math—and the only sensible way to resolve this ambiguitiy is to start with your utility function and derive the risk taking policy from that, not the other way around!)
Yep, you understood correctly!
If you’re 65 years old and already sitting on wealth that’s an order of magnitude more valuable than your future earnings/your safety net—then your utility function plausibly is close to
But for the majority of people who’ll see this post—the value of their safety net and their human capital is substantial compared to their current wealth—so taking this into account pushes them to bet more agressively than Kelly prescribes (which imo is interesting given how agressive Kelly already feels intuitively).
Personally, I’m 33 years old (that still counts as young?), married with 2 kids so far.
And yes, my family and I could probably move in with my sister or my wife’s parents if we were struggling. I agree if I was betting from the NPV of my human capital (rather than just what my wife and I currently own) I wouldn’t go all in on this bet.
What’s your situation and how much would you bet?
You do, however, maximise your long-term growth rate, regardless of any utility function.
When you say “growth rate” you’re picking out one specific metric from an infintie set of other reasonable choices!
Of course if you focus on ratios, you tautologically end up maximising the logarithm!
But you’re still doing a lot of normative work when you make the “rate of growth”, defined as
If you run a bunch of simulations exploring the results achieved by different betting strategies and then compare the average results using the geometric mean then yes, Kelly betting wins.
If you plot some simulations on a chart and make your y-axis logarithmic then yes, the chart seems to show how Kelly beats everything almost always. But by doing the analysis this way you’ve already baked in the conclusion.
In an analogous way to how odds ratios are isomorphic to probabilities—but in some cases cause less confusion when we try reason about them—I think it’s way more productive to reason about your utility function than it is to talk about growth rates
When we start to talk along the lines of “Yeah this maximises expected utility—but” this is a sign that there’s a type error somewhere. There is no but—your utility function is definitionally the thing you want to maximise the expected value of.
I don’t mind whether we frame it as utility curves being flatter than logarithmic, or as logarithmic curves but shiffted to the left - both are approximation of the real function regardless. (And mathematically I don’t think there’s even a difference… The slope of ln(x) is 1/x so shifting it left does make it flatter)
The high level point is that both framings seem to imply we should bet far more aggressively that how Kelly Criterion is typically applied
There are different ways to exactly define “growing your bankroll the fastest without going bust”. Making that your goal and then choosing the one specific mathematical instantiation of the concept that leads to Kelly betting—is equivalent to declaring you have log utility.
If you have any utility function other than log(W) then you don’t maximize your expected utility by Kelly betting—even if there’s many repeated bets.
I think if you start asking people this question, even educated people, you’ll be supprised!
While the scenario is idalized in the sense of you can know the payoffs and odds with certianty—there’s no need to stipulate “all they have is money”—they can have a complex utility function involving a thousand inputs, as long as the only input that changes based on the bet they make is money.
In response to “Why” reacts:
Let’s think about another hypothetical. Say you were forced to choose between 2 bad options:
Option 1: You lose all your wealth save for $10,000
Option 2: We flip a coin, heads you lose all your wealth save for $100 dollars, tails you lose all your wealth save for 1 million dollars (and if you currently are worth less than a million you actually recieve money to get your net worth up to this figure)
We’re not leaning on the singularity at 0 here.
Log utility says these options have the same value. But obviously someone with a safety net and healthy future earning potential should way prefer option 2
> I don’t think so. ~Everyone can see this is super obviously a good deal
There’s a difference between thinking it’s a good deal and being willing to bet 50% of your net worth on it. Do you think if we polled a bunch of people, almost everyone would say they’d bet at least as agressivlely as Kelly prescribes? (If you do, want to make a meta-bet about this? :P )
I pointed out the negative infinity thing not just to make fun of the singualarity at 0, but to gesture at the fact that in general we should consider our utility functions as being way less curved than a logarithm.
In similar vein to how log utility treats the difference between being flat out broke and only having $100 as infinite, wheras to you the difference is negligible—it’s also wildly exagerating the difference between 100 and 1,000, and 1,000 vs 10,000.
It’s not just below $100 that you souldn’t trust kelly. If you have an anual salary of 100k you shoudln’t trust kelly anywhere below like 500k!
You’re right that the issue is that in the real world it’s very easy to be wrong about the size of your edge and most of the time any major edge comes along with a capped bet size. But distinguishing between “I’m very risk averse” and “I’m not very risk averse but it’s very hard to eek out big edges” is useful—and does have practical implications in some cases (going to write about this in future post!)
What if people are required to try a tiny bit of each before deciding which one they want a full helping of? In that setup I’m still extremely confident the ice cream wins—it would be crazy imo for anyone to update meaningfully due to this survey.
Of course, as we dive more into the nitty gritty of the setup it becomes relevant how the product/stunt is positioned etc. - but the fact that there are all these considerations that need to be made serves to further reinforce the point that it’s hard to predict human preferences!
Ironically—it’s hard know whether to take your survey results at face value given the complexity of human motivations (if it wasn’t for the meme, would people’s reaction be different?).
If we ran an experiement where there were 2 stalls set up in public (ideally not in SF, thus almost nobody is in on the joke), and each offers free food—one serving the best ice cream available and one serving the bear fat + salt + honey mixture—which do you think will draw longer lines?
(If anyone is persuaded by this post that the bear fat would win and is willing to wager, perhaps we can run it for real!)
I think an important consideration being overlooked is how comptetntly a centralised project would actually be managed.
In one of your charts, you suggest worlds where there is a single project will make progress faster due to “speedup from compute almagamation”. This is not necessarily true. It’s very possible that different teams would be able to make progress at very different rates even if both given identical compute resources.
At a boots-on-the-ground level, the speed of progress an AI project makes will be influenced by thosands of tiny decisions about how to:
Manage people
Collect training data
Prioritize research direcitons
Debug training runs
Decide who to hire
Assess people’s perfomance and decide to should be promoted to more influential positions
Manage code quality/technical debt
Design+run evals
Transfer knowledge between teams
Retain key personnel
Document findings
Decide what internal tools to use/build
Handle data pipeline bottlenecks
Coordinate between engineers/researchers/infrastructure teams
Make sure operations run smoothly
The list goes on!
Even seemingly minor decisions like coding standards, meeting structures and reporting processes might compound over time to create massive differences in research velocity. A poorly run organization with 10x the budget might make substantially less progress than a well-run one.
If there was only one major AI project underway it would probably be managed less well than the overall best-run project selected from a diverse set of competing companies.
Unlike the Manhattan project—there’s already sufficently strong commercial incentives for private companies to focus on the problem, it’s not already clear exactly how the first AGI system will work, and capital markets today are more mature and capable of funding projects at much larger scales. My gut feeling is if AI was fully consolidated tomorrow—this is more likely to slow things down than speed them up.
Yes that’s true that beginning almost any form of exercise will deliver most of the benefits compared to what an optimal rountine would! But your post is all about trying to be as time efficient as possible (e.g you also discussed the potential to use drop sets to go even beyond failure!).
For vast majority of people reading this post—if their goal is to get the greatest possible benefit from resistance training in shortest amount of time—the biggest mistake they’re making right now is not having their sets be difficult enough. You’re right that you don’t need to go to failure to get most of the benefits, but if time efficiency is the goal, spending that extra 15 seconds to add those two final pre-failure reps to a set is the first thing I’d reccomend.
(This comment is directed more at the rest of the audience who I think are likely to take the wrong lessons from this post, rather than OP who I don’t doubt knows what they are talking about and has found success following their own advice)
[For supersets] the main downside being that the overall greater work packed in to a smaller amount of time being somewhat more motivationally taxing.
At least for me personally, this is an overwhelmingly important consideration! There’s no way in hell I could go to failure on both ends of a superset at once without throwing up.
(I just go 1 or two reps shy of failure and don’t worry too much about perfect weight selection to hit the same rep ranges all the time). Studies have found even 2 sets to failure once a week to be sufficient for maintenance if you are super strapped for time. I normally do this twice a week.
This might work for OP, but I don’t think it’s good advice for most readers (80% of whom I’d bet have never actually pushed a weight lifting set to failure and will be mistaken about where their failure point actually is).
If you aren’t tracking your lifts exactly, reccording them each time, and forcing yourself to do more than the previous time every time you return to the gym, it’s very hard to know for sure that you were actually 2 reps shy of failure.
We can experience a lot of discomfort/panic before the point at which we actually fail - (for most weight exercises if you’re not involuntarily making loud yelling noises during the last couple reps, you’re probably not anywhere close to true failure).
If you’re reading this, and you don’t already have a book/app where you write down exactly how much weight you lifted and are progressively increasing that, do this first!
I hear you that teenagers spending hours computing hundreds of analytic derivatives or writing a bunch of essays is a pretty sad time waste… But if incentives shifted so instead that time got spent perfecting a starcraft build order against the AI a hundred times or grinding for years to pull off carpetless star in SM64, this might be one of the few ways to make that time spent even more pointless… (And for most people the latter is no more fun than the former)
You might be right that the concept only applies to specific subcultures (in my case, educated relatively well-off Australians).
Maybe another test could be—can you think of someone you’ve met in the past who a critic might describe as “rude/loud/obnoxious” but despite this, they seem to draw in lots of friends and you have a lot of fun whenever you hang out with them?
I think it’s worth clarifying—what were these acomplishments? Were they easy things or hard things? If they are genuinely hard things then this is a very interesting observation.
I totally buy that someone might have a weird idea for a party game that they were scared to try—but then they tried anyway and it killed. I totally buy that the only thing standing in the way of us writing a decent blog post or cooking a delicious meal could be not realising how low the bar is.
But I don’t think this insight generalizes well to difficult endevours. For something really hard which requires sustained commitment and sacrifice in order to pull off—the initial push to “just go for it” is only a tiny component of the total investment required.
Even for things that are only a little bit difficult, but require sustained effort—like losing weight without drugs—almost everyone overweight attempts this and most don’t succeed. The bar was higher than they thought. When you say “I have a ~25% chance of making a great scientific discovery if I made it my full time job” that’s meaningless conditional if you’re not actually capable of willing yourself to devote your life to it. It’s akin to the observation “I’d have a 99+% chance of achieving an amazing physique if I exercised and dieted better”
For a really ambitious goal like building a billion dollar buisness or winning a Grammy Award—my impression is the bar is higher than people think and I don’t think people should try it more!
My crappy title for the version of this post I’d agree with would be “the bar height as a function of your goal has a lot more variance than you think”. Easy things are easier than we think, hard things are harder