Assuming fixed, measurable edge, which is better >2.00 (+100): fixed unit stake / fixed win (to win) stake / something inbetween / kelly (derivative) / other?

By better, I mean optimal in terms of absolute profits. Would also be interested to hear thoughts on other pros/cons of each if anyone has a strong opinion.

100% of BR on highest ROI bet. Everything else is wrong.

Your question is terrible. No one cares about the answer to that.

Come on, surely you can do better than that? I know you have, like literally, nothing left to learn in regards to sports betting and bazillion-dollar bankrolls, but there are likely other people out there that, like me, are open to learning, discussing and sharing and not spending the majority of their time acting the keyboard warrior.

He answered your question, peasant.

Then either he is trolling or broke. Since he claims to have a bazillion-dollar bankroll, then it must be the former. I will respectfully decline from responding to trolling

While it is literally impossible to discuss this with you, what do you think is the correct answer? Or why do you think my answer is incorrect? (Both are useful, despite what many thing.)

I don't know what the correct answer is, which is why I was posting, but I guess I would be leaning toward some variation of Kelly (as edge is known). I think your answer is incorrect as staking 100% of bankroll on highest ROI bet would result on you going broke after first loser.

That's on the same level as saying martingale works if you have an infinite bankroll.

Sure. Problem is in the formulation of the question (only an idiot would choose to maximize EV).

Sure, that's one problem. But your solution only maximizes EV under circumstances ranging from the very extreme (a small series of bets) to the absurd (you can bet infinite). For most cases, bankroll preservation would play a factor.

Sure. But Kelly doesn't concern itself with future possibilities. In those scenarios you also need to make some attempt to model what options will exist in the future. If we're gonna start talking about series of bets (independent of course, dependent can become intractably complex extremely quickly), we need to make some arbitrary simplifying assumptions to even make the ad hoc solutions we do use fit perfectly.

Kelly most certainly does concern itself with future possibilities. According to our friends at Wikipedia: "In probability theory and intertemporal portfolio choice, the Kelly criterion, Kelly strategy, Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets." The whole concept of maximizing bankroll growth makes little sense when looking at one bet in isolation.

Sure, assumptions need to be made but that's life. See https://en.wikipedia.org/wiki/Proebs...dox#Resolution for one example of how inaccurate estimates of the future can lead to ruin when using Kelly.

Is this where Mihkel05 throws his toys out of his pram and then Iowa! comes in as his bazillionaire backup (again)?

I phrased that incorrectly. I should say unknowable future betting opportunities. It is clearly applicable for a series of independent bets, but is poorly suited for questions like "Do I double down on this HT that also affects my futures portfolio?" (complexity)

I think Brown's solution to the second paradox clarifies an issue that exists with using pure Kelly. (And where some knowledge of the subject beyond "bet Kelly" is necessary)

For an example, lets say our Kelly roll is 1m, we have 250k available and we are offered a bet of 1% edge that takes a year to resolve. How does Kelly actually weigh that against the possibility of more valuable bets occurring in the interim? (aside from the obvious time value adjusted Kelly)

I'm pretty sure n00b has enough math and money to argue against both Iowa! and me.

Questions regarding opportunity cost can't really be answered unless we know what the roll's owner's bet frequency and perceived edge is, iyam.

e.g. if the bettor normally has a perceived edge of 0.5% in markets where bets are freely available throughout a year, the decision to lock up a sufficient portion of the roll for a year would be a -EV decision even if Kelly tells us that it's sound to invest n% of the roll (in the bet with 1% edge).