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.
In Exampleville (parasite example), if money is infinitely divisible, Kelly betting will save everyone with probability 1.
If bets must be an integral number of coins (and you start with only one coin, a very inconvenient world!), the strategy of "bet the highest amount not more than Kelly, except always bet at least one coin and never bet more than necessary to reach 1024", will save everyone with probability of approximately 0.038, or about 1 in 26, which is significantly better than 1 in 840.
In an intermediate scenario where gold coins are divisible into 100 smaller units for betting purposes, the probability for an analogous strategy will exceed 0.94.
While these strategies do involve betting higher than Kelly in the sole situation that you bet your last betting unit instead of giving up, in general it is fair to call them Kelly variants in contrast to "always bet everything".
The reason that Kelly variants are vastly superior to always betting everything is that the terms of your hypothetical are that "You can play as many times as you like." It is difficult to conceive of why anyone would risk more than Kelly with this allowance (again with exceptions for your last betting unit).
You can salvage the example by saying that you are limited to 10 bets.
However, if you are limited to, for example, 20 bets, then the best strategy will be some intermediate that is riskier than Kelly but definitely less risky than "always bet everything".
My advice to readers is that betting more than Kelly is usually a terrible idea and if you think it's a good idea, you're probably making a mistake. The fact that a thought experiment, in an intelligently written article, went awry and gave an example where risk neutral betting is worse than Kelly variants when it was supposed to do the opposite, is a great example of the danger.
Nonetheless, I concede that for small and medium donors, betting 100% of your funds-to-be-donated on a 51% coin flip is fine if it is genuinely limited to your personal donation. However, the reason for this concession is not that I endorse risk-neutral betting for EA, but rather that the correct way to look at the bet in this scenario, when the funds are already "to be donated", is not as part of your personal bankroll, but rather as part of the bankroll of the cause for which you intend to donate them. Since any individual small or medium donor will in all likelihood represent less than 0.1% of the bankroll of the cause, such an individual betting such funds in isolation is in practice never exceeding Kelly betting.
I would still caution against 51% coin flips in a scenario where a large fraction of the EA community coordinates, spreads news of "an opportunity", etc., such that a large fraction of EA funds are risked on highly correlated 51% coin flips, for reasons which are hopefully quite obvious.
I thought that Sam Trabucco was not EA, but rather someone that SBF knew from math camp and MIT.
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.
In Exampleville (parasite example), if money is infinitely divisible, Kelly betting will save everyone with probability 1.
If bets must be an integral number of coins (and you start with only one coin, a very inconvenient world!), the strategy of "bet the highest amount not more than Kelly, except always bet at least one coin and never bet more than necessary to reach 1024", will save everyone with probability of approximately 0.038, or about 1 in 26, which is significantly better than 1 in 840.
In an intermediate scenario where gold coins are divisible into 100 smaller units for betting purposes, the probability for an analogous strategy will exceed 0.94.
While these strategies do involve betting higher than Kelly in the sole situation that you bet your last betting unit instead of giving up, in general it is fair to call them Kelly variants in contrast to "always bet everything".
The reason that Kelly variants are vastly superior to always betting everything is that the terms of your hypothetical are that "You can play as many times as you like." It is difficult to conceive of why anyone would risk more than Kelly with this allowance (again with exceptions for your last betting unit).
You can salvage the example by saying that you are limited to 10 bets.
However, if you are limited to, for example, 20 bets, then the best strategy will be some intermediate that is riskier than Kelly but definitely less risky than "always bet everything".
My advice to readers is that betting more than Kelly is usually a terrible idea and if you think it's a good idea, you're probably making a mistake. The fact that a thought experiment, in an intelligently written article, went awry and gave an example where risk neutral betting is worse than Kelly variants when it was supposed to do the opposite, is a great example of the danger.
Nonetheless, I concede that for small and medium donors, betting 100% of your funds-to-be-donated on a 51% coin flip is fine if it is genuinely limited to your personal donation. However, the reason for this concession is not that I endorse risk-neutral betting for EA, but rather that the correct way to look at the bet in this scenario, when the funds are already "to be donated", is not as part of your personal bankroll, but rather as part of the bankroll of the cause for which you intend to donate them. Since any individual small or medium donor will in all likelihood represent less than 0.1% of the bankroll of the cause, such an individual betting such funds in isolation is in practice never exceeding Kelly betting.
I would still caution against 51% coin flips in a scenario where a large fraction of the EA community coordinates, spreads news of "an opportunity", etc., such that a large fraction of EA funds are risked on highly correlated 51% coin flips, for reasons which are hopefully quite obvious.