Thanks, it didn’t occur to me that “double your money” in the example meant “double your entire bankroll” not “double some amount that you selected to bet”. I think you’re right that that’s what the author meant, but I share Karthik’s concern that you’re then comparing “bet everything” to “do nothing”.
I understand your concerns about the number of coin flips required. I loosely addressed it in my original comment, noting that even with a fixed limit of 20 bets in Exampleville (but with the ability to select bet size), the optimal approach will be clearly be less risky than “always bet everything”.
Furthermore, it’s important to consider that any scenario based on a limited number of bets is only applicable to the real world if the bets in the scenario will be the only positive-EV bets you can make in your entire life, or if the resource you are betting will never have any utility outside of the constrained scenario, or something very strange like that. In the real world, if you encounter a positive-EV bet denominated in USD that you are only able to make a limited number of times, even if you have a salient group of people to aid with the outcome of the bet, you need to consider that you may have other positive-EV bets in your life and you may be able to use the USD to help other people in the future if you manage risk more normally and don’t blow your entire net worth on the first set of positive-EV bets that you encounter.
With respect, it is highly unusual to call full Kelly betting “very conservative risk management”. Most people familiar with the concept consider full Kelly betting to be extremely aggressive.
I definitely wouldn’t call full Kelly “very conservative.” My point was that in Exampleville and other scenarios with a capped best outcome, a very conservative strategy (e.g., 0.001 Kelly) is trivially superior to even merely conservative strategies if there is practically infinite time to flip coins before you need to act, and flipping coins is a costless activity. So the specification of the constraints is what makes the problem interesting (and realistic). The example shows that there are constraints where very agressive betting makes sense; the rest of the post needs to demonstrate how those scenarios—or at least somewhat similar scenarios—might occur in real life.
Bets don’t have to be in USD or anything else that is a store of value. One could imagine that the “currency” was virologists in a rapidly-moving pandemic. You can put them on safe research that will save a modest number of lives or tell them to roll the dice on speculative research with a possible big payoff. You can’t really “store” their labor for a possible better bet that may appear ten years down the road, or use it for something else very effectively.
Thanks, it didn’t occur to me that “double your money” in the example meant “double your entire bankroll” not “double some amount that you selected to bet”. I think you’re right that that’s what the author meant, but I share Karthik’s concern that you’re then comparing “bet everything” to “do nothing”.
I understand your concerns about the number of coin flips required. I loosely addressed it in my original comment, noting that even with a fixed limit of 20 bets in Exampleville (but with the ability to select bet size), the optimal approach will be clearly be less risky than “always bet everything”.
Furthermore, it’s important to consider that any scenario based on a limited number of bets is only applicable to the real world if the bets in the scenario will be the only positive-EV bets you can make in your entire life, or if the resource you are betting will never have any utility outside of the constrained scenario, or something very strange like that. In the real world, if you encounter a positive-EV bet denominated in USD that you are only able to make a limited number of times, even if you have a salient group of people to aid with the outcome of the bet, you need to consider that you may have other positive-EV bets in your life and you may be able to use the USD to help other people in the future if you manage risk more normally and don’t blow your entire net worth on the first set of positive-EV bets that you encounter.
With respect, it is highly unusual to call full Kelly betting “very conservative risk management”. Most people familiar with the concept consider full Kelly betting to be extremely aggressive.
I definitely wouldn’t call full Kelly “very conservative.” My point was that in Exampleville and other scenarios with a capped best outcome, a very conservative strategy (e.g., 0.001 Kelly) is trivially superior to even merely conservative strategies if there is practically infinite time to flip coins before you need to act, and flipping coins is a costless activity. So the specification of the constraints is what makes the problem interesting (and realistic). The example shows that there are constraints where very agressive betting makes sense; the rest of the post needs to demonstrate how those scenarios—or at least somewhat similar scenarios—might occur in real life.
Bets don’t have to be in USD or anything else that is a store of value. One could imagine that the “currency” was virologists in a rapidly-moving pandemic. You can put them on safe research that will save a modest number of lives or tell them to roll the dice on speculative research with a possible big payoff. You can’t really “store” their labor for a possible better bet that may appear ten years down the road, or use it for something else very effectively.