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eh they're to different degrees; losing 10% of your wealth is a lot less likely to cripple your opportunity to do future things than losing > 50%. life isn't exactly a game of iterated "exactly the same bet". And in practice it matters a lot roughly how much $ you'll need!

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and

The Kelly criteria isn't about iterating the exact same bet either. It's about maximizing your long term growth rate in games of random chance. The bet can change each time and you still shouldn't bet above the Kelly value.

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long term *geometric* growth rate, not long term growth rate all-in maximizes long term growth rate

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and

Absolutely not. All long term growth rates are geometric. There is no other kind.

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uhhhh how are you defining growth rate? "Growth rates refer to the percentage change of a specific variable within a specific time period" from the first link: investopedia.com/terms/g/growth I'd interpret that as lim t --> inf EV[ W_{t+1}/W_t ]

investopedia.com

Growth Rates: Formula, How to Calculate, and Definition

Growth rates are the percent change of a variable over time. It can be applied to GDP, corporate revenue, or an investment portfolio. Here's how to calculate growth rates.

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and

That isn't a rate. it's the total growth. You have to scale it a period of time to make it a rate: lim t --> inf EV[ (W_{t+1}/W_t)^(1/t) ] That formula is the geometric return.

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why exactly are you raising it to the 1/t power? you're not taking W_{t+1}/W_0 there so I'm not sure why you should be raising to the 1/t, you're still just looking at growth in one time period!

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and

anyway, whatever, we're just fighting over how to define words now

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and

Were not there is an enormous difference between the two

breakingthemarket.com

The Arithmetic Return Doesn’t Exist

The Arithmetic Return Doesn't Exist. It's a dream that isn't real.Like waves crashing against an ocean cliff, the relentlessness of time simply overwhelms the arithmetic return.In th

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unlikely =!= irrelevant

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and

If you really believe this, though...... say you have 2 choices. (a) doubles every year (b) triples every year; but with probability 1/10^t each year causes 20^t torture to everyone on earth which would you choose?

5:06 PM · Dec 14, 2020Twitter Web App

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and

That's quite an example. Are you trying to put a value on torture? A.

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But note that (b) has this property you've been talking about--it maximizes long-run geometric growth rate no matter how much of a hit you put for the unlikely torture; this is the symmetric scenario to the classic kelly one, where you ignore unlikely outcomes with large effects

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