> 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!)
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
Ok I understand what you’re saying now. My reaction is that we should just add the expected current value of all the money you will make in the future (maybe discounted and also conditional on you making the bet), to your current wealth and then kelly as if you have that much money. This seems like a valid critique of how people Kelly bet currently, but I still disagree the correct response to this hypothetical is “we should consider our utility functions as being way less curved than a logarithm”. I think people do genuinely value wealth roughly logarithmically so if you don’t make any money in the future then Kelly is correct.
I do understand “if you have an anual salary of 100k you shoudln’t trust kelly anywhere below like 500k” now and I agree.
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
Not making a real money bet because it seems difficult to operationalize / flush out the details enough that I would think I have enough edge. People imo will correctly give a more conservative number if they think the question is realistic, and they will give closer to 50% if they think it is an idealized scenario where all they have is money. But I will say 30% of people would give >=50% if they understand the scenario as mathematical.
Also, I was saying something weaker. I disagreed on “This strikes most people as being insanely agressive”. I am saying that people would, after being told the correct answer (i.e. in retrospect), think/tell you that the mathematically correct answer is not insanely aggressive. Even if 50% is higher than what they said would personally bet, I think most people would not say and would disagree that it is insanely aggressive.
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.
> 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!)
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
Ok I understand what you’re saying now. My reaction is that we should just add the expected current value of all the money you will make in the future (maybe discounted and also conditional on you making the bet), to your current wealth and then kelly as if you have that much money. This seems like a valid critique of how people Kelly bet currently, but I still disagree the correct response to this hypothetical is “we should consider our utility functions as being way less curved than a logarithm”. I think people do genuinely value wealth roughly logarithmically so if you don’t make any money in the future then Kelly is correct.
I do understand “if you have an anual salary of 100k you shoudln’t trust kelly anywhere below like 500k” now and I agree.
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
Not making a real money bet because it seems difficult to operationalize / flush out the details enough that I would think I have enough edge. People imo will correctly give a more conservative number if they think the question is realistic, and they will give closer to 50% if they think it is an idealized scenario where all they have is money. But I will say 30% of people would give >=50% if they understand the scenario as mathematical.
Also, I was saying something weaker. I disagreed on “This strikes most people as being insanely agressive”. I am saying that people would, after being told the correct answer (i.e. in retrospect), think/tell you that the mathematically correct answer is not insanely aggressive. Even if 50% is higher than what they said would personally bet, I think most people would not say and would disagree that it is insanely aggressive.
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.
Yeah, I’m thinking about stuff like “do I sell my house and my two dogs to make this bet?”