This comment sounds so confused that I have to break it down into parts. Maybe I have just misunderstood you.
> I wonder how professional gamblers approach bet sizing.
Some variation of the Kelly criterion, whether they admit it or not. Any time you make a decision with the goal of maximising your growth of wealth relative to a level of risk, you're using the Kelly criterion.
> The utility of money is asymmetric; gaining $25000 is worse than not losing $25000.
Right. Not only is it asymmetric -- it is concave. Just like Bernoulli realised when he invented the proto-Kelly criterion. The Kelly criterion can be interpreted as incorporating an asymmetric, concave utility of wealth. (It's not assuming such a utility -- it's just that log utility happens to maximise long-run growth and be asymmetric and concave.)
But critically, it depends on the size of your bankroll. When you are talking about small stakes compared to your wealth, maximising expected value (i.e. running the risk of losing your entire wager) is the growth optimal choice, because in a local enough region, any continuous utility is linear.
> Relatedly, most actual gamblers want to ensure good returns while not going broke, so minimizing risk of ruin is often more important than maximizing return rate.
This is exactly what the Kelly criterion does. It sacrifices expected value in every gamble for larger long-run growth (which requires also that you don't go bust, or lose too much too quickly.)
> Further complicating the matter is that in real life you don't know your actual probability of success, but you may have an estimation.
But decomplicating the matter is that the Kelly criterion is very forgiving of estimation error, as long as you make your errors intelligently. The optimal bet sizing under the Kelly criterion tends to look like a quadratic function. This means that there is almost a plateau around the optimal bet size where small amounts of misestimation does not actually make your growth much different from the optimal growth. (And if you're worried about large amounts of misestimation, the linear combination of keeping money in your wallet and the full Kelly bet form a sort of "efficient frontier" (to borrow MPT terminology) of risk--growth tradeoffs. Meaning you can always bet less than the full Kelly bet, and get an optimal growth for the risk level that corresponds to. Hence the popularity of half-Kelly and similar variants.)
In the end, estimating the joint distribution of outcomes for the Kelly criterion is a far more forgiving requirement than e.g. estimating the parameters needed for modern portfolio theory type analysis.
> And finally, though this is less commonly significant, your rate of return in a given game might depend on your the amount you bet.
A fact also easily plugged into the Kelly criterion. It might make the search for optimality harder than setting a derivative to zero, but we have computers for numerical optimisation!
> I wonder how professional gamblers approach bet sizing.
Some variation of the Kelly criterion, whether they admit it or not. Any time you make a decision with the goal of maximising your growth of wealth relative to a level of risk, you're using the Kelly criterion.
> The utility of money is asymmetric; gaining $25000 is worse than not losing $25000.
Right. Not only is it asymmetric -- it is concave. Just like Bernoulli realised when he invented the proto-Kelly criterion. The Kelly criterion can be interpreted as incorporating an asymmetric, concave utility of wealth. (It's not assuming such a utility -- it's just that log utility happens to maximise long-run growth and be asymmetric and concave.)
But critically, it depends on the size of your bankroll. When you are talking about small stakes compared to your wealth, maximising expected value (i.e. running the risk of losing your entire wager) is the growth optimal choice, because in a local enough region, any continuous utility is linear.
> Relatedly, most actual gamblers want to ensure good returns while not going broke, so minimizing risk of ruin is often more important than maximizing return rate.
This is exactly what the Kelly criterion does. It sacrifices expected value in every gamble for larger long-run growth (which requires also that you don't go bust, or lose too much too quickly.)
> Further complicating the matter is that in real life you don't know your actual probability of success, but you may have an estimation.
But decomplicating the matter is that the Kelly criterion is very forgiving of estimation error, as long as you make your errors intelligently. The optimal bet sizing under the Kelly criterion tends to look like a quadratic function. This means that there is almost a plateau around the optimal bet size where small amounts of misestimation does not actually make your growth much different from the optimal growth. (And if you're worried about large amounts of misestimation, the linear combination of keeping money in your wallet and the full Kelly bet form a sort of "efficient frontier" (to borrow MPT terminology) of risk--growth tradeoffs. Meaning you can always bet less than the full Kelly bet, and get an optimal growth for the risk level that corresponds to. Hence the popularity of half-Kelly and similar variants.)
In the end, estimating the joint distribution of outcomes for the Kelly criterion is a far more forgiving requirement than e.g. estimating the parameters needed for modern portfolio theory type analysis.
> And finally, though this is less commonly significant, your rate of return in a given game might depend on your the amount you bet.
A fact also easily plugged into the Kelly criterion. It might make the search for optimality harder than setting a derivative to zero, but we have computers for numerical optimisation!