6 ms·

How should you bet if you're not comfortable with variance? I tried the "autobetter" simulation at the bottom of the page, always clicking heads, and it took 15

by gfd 5y ago

How should you bet if you're not comfortable with variance? I tried the "autobetter" simulation at the bottom of the page, always clicking heads, and it took 150 tries to max out. For most of the time it was way below the initial $25 investment: https://imgur.com/a/HKKHMRL https://imgur.com/a/HKKHMRL

krajzeg 5y ago
If you're not comfortable with variance, you should bet 0$ each time. This is only partially tongue-in-cheek, since the only way to reduce variance is to bet lower amounts, but this will also reduce your expected return, all the way to zero at 0$ bets.
alisonkisk 5y ago
contravariant 5y ago
A simple way would be to pick a strategy with a slightly different utility function from Kelly's (which implicitly uses log as the utility function). The downside of this is that Kelly's utility function has some very nice properties. In particular the total utility of a sequence of bets will turn into a sum which means you can ignore dependencies between events. Note for instance that the argument in this article still holds even if you've got very strong dependencies between coin flips, it could repeat the pattern HTHTH forever and the Kelly criterion would still give the same optimal proportion, though obviously there are better strategies if you don't restrict yourself to blindly betting on heads.
ojbyrne 5y ago
Not to mention that in real life, there is probably a minimum bet.
cevi 5y ago
If you bet with the -1/x utility function, then the optimal strategy is to always bet about 10.1% of your money. I find this to give a good tradeoff between the variance and the rate of exponential growth.
kqr 5y ago
The way to reduce variance is to keep some of your wealth out of the equation. In other words, put half of your money to the side, and then apply the Kelly criterion to that which remains. This is a "fractional Kelly" strategy, which optimises growth under the condition that you want to reduce variance.
- joosters 5y ago
  Yes. The 'fully Kelly' betting is the fastest growth, but the variance is sky-high in practice. If I remember the math right, while betting using full Kelly stakes, you will have a 50% chance of losing half of your current bank at some point in the future. Most people (rightly or wrongly) don't have the stomach for such wild swings in fortune, and so using reduced stakes will lead to less variance while still being profitable. Also, in the real world, you never accurately know how big your % edge actually is, so there's a real chance that you are over-betting when using Kelly stakes. Using reduced stakes is a way to compensate for this.

by gfd 5y ago

krajzeg 5y ago

If you're not comfortable with variance, you should bet 0$ each time. This is only partially tongue-in-cheek, since the only way to reduce variance is to bet lower amounts, but this will also reduce your expected return, all the way to zero at 0$ bets.

alisonkisk 5y ago

contravariant 5y ago

A simple way would be to pick a strategy with a slightly different utility function from Kelly's (which implicitly uses log as the utility function). The downside of this is that Kelly's utility function has some very nice properties. In particular the total utility of a sequence of bets will turn into a sum which means you can ignore dependencies between events. Note for instance that the argument in this article still holds even if you've got very strong dependencies between coin flips, it could repeat the pattern HTHTH forever and the Kelly criterion would still give the same optimal proportion, though obviously there are better strategies if you don't restrict yourself to blindly betting on heads.

ojbyrne 5y ago

Not to mention that in real life, there is probably a minimum bet.

cevi 5y ago

If you bet with the -1/x utility function, then the optimal strategy is to always bet about 10.1% of your money. I find this to give a good tradeoff between the variance and the rate of exponential growth.

kqr 5y ago

The way to reduce variance is to keep some of your wealth out of the equation. In other words, put half of your money to the side, and then apply the Kelly criterion to that which remains. This is a "fractional Kelly" strategy, which optimises growth under the condition that you want to reduce variance.

joosters 5y ago
Yes. The 'fully Kelly' betting is the fastest growth, but the variance is sky-high in practice. If I remember the math right, while betting using full Kelly stakes, you will have a 50% chance of losing half of your current bank at some point in the future. Most people (rightly or wrongly) don't have the stomach for such wild swings in fortune, and so using reduced stakes will lead to less variance while still being profitable. Also, in the real world, you never accurately know how big your % edge actually is, so there's a real chance that you are over-betting when using Kelly stakes. Using reduced stakes is a way to compensate for this.