Good point, this combines the iteratability justification for EV plus the fact that we have finite resources with which to bet. But doesn’t this break down if you are unsure how much wealth you have (particularly if the “wealth” being gambled is non-monetary, for example years of life)? Suppose the devil comes to you and says “if you take my bet you can live out your full lifespan, but there will be a 1 in 1 million chance I will send you to Hell at the end for 100 billion years. If you refuse, you will cease to exist right now.” Well, the wealth you are gambling with is years of life, but it’s unclear how many you have to gamble with. We could use whatever our expected number of years is (conditional on taking the bet) but of course, then we run back into the problem that our expectations can be dominated by tiny probabilities of extreme outcomes. This isn’t just a thought experiment since we all make gambles that may affect our lifespan, and yet we don’t know how long we would have lived by default.
Edit: realized that the devil example has the obvious flaw that as the expected default lifespan increases, so does the amount of years that you’re wagering, so you should always take the bet based on Kelly betting, but this point is more salient with less Pascalian lifespan-affecting gambles. I guess the question that remains is that the gamble is all or nothing, so what do we do if Kelly betting says we should wager 5% of our lifespan? Maybe the answer is: bet your life 5% of the time, or make gambles that will end your life with no more than 5% probability.
The uncertainties that will always be present for a real gamble make the Kelly bet rash, uncertainties about not only the numbers, but about whether the preconditions for the criterion obtain.
Because of this, Zvi recommends that Kelly is the right way to think, and you should evaluate the Kelly recommendation as best you can, but you should then bet no more than 25% to 50% of that amount. Further elaboration here.
Good point, this combines the iteratability justification for EV plus the fact that we have finite resources with which to bet. But doesn’t this break down if you are unsure how much wealth you have (particularly if the “wealth” being gambled is non-monetary, for example years of life)?
Suppose the devil comes to you and says “if you take my bet you can live out your full lifespan, but there will be a 1 in 1 million chance I will send you to Hell at the end for 100 billion years. If you refuse, you will cease to exist right now.” Well, the wealth you are gambling with is years of life, but it’s unclear how many you have to gamble with.We could use whatever our expected number of years is (conditional on taking the bet) but of course, then we run back into the problem that our expectations can be dominated by tiny probabilities of extreme outcomes. This isn’t just a thought experiment since we all make gambles that may affect our lifespan, and yet we don’t know how long we would have lived by default.Edit: realized that the devil example has the obvious flaw that as the expected default lifespan increases, so does the amount of years that you’re wagering, so you should always take the bet based on Kelly betting, but this point is more salient with less Pascalian lifespan-affecting gambles. I guess the question that remains is that the gamble is all or nothing, so what do we do if Kelly betting says we should wager 5% of our lifespan? Maybe the answer is: bet your life 5% of the time, or make gambles that will end your life with no more than 5% probability.
The uncertainties that will always be present for a real gamble make the Kelly bet rash, uncertainties about not only the numbers, but about whether the preconditions for the criterion obtain.
Because of this, Zvi recommends that Kelly is the right way to think, and you should evaluate the Kelly recommendation as best you can, but you should then bet no more than 25% to 50% of that amount. Further elaboration here.