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
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