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Kelly Can't Fail

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389 points jmount | 8 comments | 19 Dec 24 23:07 UTC | HN request time: 0s | source | bottom
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JohnMakin ◴[20 Dec 24 02:50 UTC] No.42467834[source]▶
Kelly criterion is one of my favorite game theory concepts that is used heavily in bankroll management of professional gamblers, particularly poker players. It is a good way to help someone understand how you can manage your finances and stakes in a way that allows you to climb steadily forward without risking too much or any ruin, but is frequently misapplied in that space. The problem is kelly deals with binary results, and often situations in which this is applied where the results are not binary (a criteria for applying this) you can see skewed results that look almost right but not quite so, depending on how you view the math
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1. peter_retief ◴[20 Dec 24 05:35 UTC] No.42468559[source]▶
Could this work with roulette betting on color? Seems like you could spend a lot of time not winning or losing
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2. plorkyeran ◴[20 Dec 24 06:15 UTC] No.42468729[source]▶
Roulette results are uncorrelated and you have the exact same chance of winning each time, so the Kelly criterion isn’t applicable. Betting on a color has a negative edge and you don’t have the option of taking the house’s side, so it just tells you the obvious thing that you should bet zero.
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3. dmurray ◴[20 Dec 24 08:42 UTC] No.42469336[source]▶
> exact same chance of winning each time, so the Kelly criterion isn’t applicable.

Actually, the main assumption that leads to the Kelly criterion is that you will have future opportunities to bet with the same edge, not constrained by the amount.

For example, if you knew this was your last profitable betting opportunity, to maximise your expected value you should bet your entire stake.

I'm slightly surprised it leads to such a nice result for this game - I don't see a claim that this is the optimal strategy for maximizing EV zero variance is great, but having more money is also great.

Of course you are right about roulette and, if you are playing standard casino roulette against the house, the optimal strategy is not to play. But that's not because bets are uncorrelated, it's because they are all negative value.

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4. Tepix ◴[20 Dec 24 09:24 UTC] No.42469476[source]▶
What makes 0 better than the other numbers?
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5. Vecr ◴[20 Dec 24 10:23 UTC] No.42469805{3}[source]▶
Can't bet negative in that kind of game. If a game is expected to lose you money, don't play.
6. ◴[20 Dec 24 20:29 UTC] No.42474719{3}[source]▶
7. lupire ◴[20 Dec 24 21:30 UTC] No.42475245{3}[source]▶
$0, not 0 on the wheel.
8. kqr ◴[21 Dec 24 13:38 UTC] No.42479595{3}[source]▶
> Actually, the main assumption that leads to the Kelly criterion is that you will have future opportunities to bet with the same edge, not constrained by the amount.

Not the same edge -- any edge! And this condition of new betting opportunities arriving every now and then is a fairly accurate description of life, even if you walk out of the casino.