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Right. So each bet can be maximized using Kelly and betting higher than this value leads risk of ruin to converge to 1 in an infinite series of bets. Is this a false statement?

SBF

@SBF_FTX

Dec 14, 2020

Replying to

@ysoh

and

@tbr90

1) I don't care about an infinite series of bets, we only have finite series of bets 2) do you not care that upside and expected wealth converge to infinity quickly in those cases? Are you approximating X*Y where x --> inf and y --> 0 as 0?

Replying to

and

Hm, yes, I don't care if my expected wealth converges to infinity in those cases, I'm only interested in finding appropriate bet sizes to maximize my EV per event while avoiding ruin. If you tell me there's a better equation for that than Kelly, I'm all ears.

Replying to

and

er yeah there totally is being a bit more aggressive (but not *too much more*) will have higher EV per event, and will avoid ruin

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and

Kelly maximizes a *very specific thing*! Unless you care about exactly that very specific thing, Kelly might or might not be right for you.

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and

E.g. $1k bankroll, 1:1 payout, 60% of winning each one. Kelly says bet 20%. But if you bet 20.5%, you'll: a) have higher EV b) almost certainly not end in ruin

Replying to

and

At the risk of beating a dead horse: If you bet 20.5% over a significant sample (or infinity!), you go broke faster than 20%. Even if this exact scenario isn't stretched to infinity, you still get a series of different betting events where your EV is tied to your bankroll.

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and

I don't know what you mean by "go broke faster" neither go broke! They both converge to infinite wealth with probability approaching 100%!

9:15 AM · Dec 14, 2020Twitter Web App

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and

**more often. Kelly slightly reaches infinite wealth more often than the other :), or my understanding of Kelly is incorrect.

Replying to

and

uh sorta, in that both do it 100% of the time, but kelly is even closer to 100% than the other strategy is but like that's a massively weaker statement than the ones you were making