more if I only had $100k
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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 ]
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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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Good point should have been
lim t --> inf EV[ (W_{t}/W_0)^(1/t) ]
With your equation the limit does t matter it's the same value at all times
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yeah if you define it that way, then you're trying to max log growth.
but you could also look at other metrics! you could do EV(W_t - W_0)/ t, or EV(W_t+1/W/t), or EV(w_t+1)/EV(W_t), you'll get a different predicted strategy.
idk which is right, it depends on the situation