The first sentence of your post, while technically true, misses the point. This misunderstanding undermines many of your other points.
The kelly criterion happens to be optimal with respect to log wealth but that's not the main reason why it's interesting. Many explanations, including the original post, make this mistake. Maybe because 'maximizing expected utility' is a more common idea.
The first sentence of the wikipedia article:
"In probability theory and intertemporal portfolio choice, the Kelly criterion (or Kelly strategy or Kelly bet), also known as the scientific gambling method, is a formula for bet sizing that leads almost surely (under the assumption of known expected returns) to higher wealth compared to any other strategy in the long run".
In other words, pick a strategy. I'll pick the kelly strategy. There will be some point in time, after which I will have more money than you, and you will never overtake me. No logarithms involved. This is something you can easily check by simulation, but requires some heavier math to formulate precisely and prove.
See also posts by spekcular and rssoconnor elsewhere in this thread.
If it's a mistake, it's a charitable one. Picking log utility is at least somewhat principled, trying to lead almost surely to higher wealth is way more arbitrary.
At no point in time does Kelly give you more wealth with probability 1, and there is no reason to care about "more wealth with high probability", that's not even a transitive comparison function.
The kelly criterion happens to be optimal with respect to log wealth but that's not the main reason why it's interesting. Many explanations, including the original post, make this mistake. Maybe because 'maximizing expected utility' is a more common idea.
The first sentence of the wikipedia article:
"In probability theory and intertemporal portfolio choice, the Kelly criterion (or Kelly strategy or Kelly bet), also known as the scientific gambling method, is a formula for bet sizing that leads almost surely (under the assumption of known expected returns) to higher wealth compared to any other strategy in the long run".
In other words, pick a strategy. I'll pick the kelly strategy. There will be some point in time, after which I will have more money than you, and you will never overtake me. No logarithms involved. This is something you can easily check by simulation, but requires some heavier math to formulate precisely and prove.
See also posts by spekcular and rssoconnor elsewhere in this thread.