10) What about a wackier bet? How about you only win 10% of the time, but if you do you get paid out 10,000x your bet size? (For now, let’s assume you only get to do this bet once.)
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Are you saying you would bet more if you only ha $100,000? or you would bet more because you do have more than $100,000 to start?
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You do realize the reason you shouldn't bet more than $10,000 is the same reason you gave for not betting it all in #22? You need funding to provide value with future opportunities.
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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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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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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 ]
or, really, lim t --> inf [EV W_{t+1}]/EV[W_t] if you don't want to worry about div0
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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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