←back to thread

Kelly Can't Fail

(win-vector.com)
389 points jmount | 3 comments | 19 Dec 24 23:07 UTC | HN request time: 0.602s | source
Show context
hawkjo ◴[20 Dec 24 00:12 UTC] No.42467116[source]▶
Very cool to see no variance in the outcome. But that also makes it feel like there should be a strategy with better expected return due to the unique problem structure. Do we know if the Kelly strategy is optimal here?
replies(6): >>42467134 #>>42467239 #>>42467299 #>>42468243 #>>42468284 #>>42469751 #
1. rahimnathwani ◴[20 Dec 24 00:40 UTC] No.42467239[source]▶

  Do we know if the Kelly strategy is optimal here?
What do you mean by optimal? Do you mean you're willing to risk going bankrupt, if it means a higher expected value?
replies(1): >>42467969 #
2. scotty79 ◴[20 Dec 24 03:18 UTC] No.42467969[source]▶
Surely there's some space between risking to go bankrupt and risking of getting less than 9.08 return guaranteed by Kelly strategy.

If you are willing to take some risk in exchange for possibility of higher payout just bet a bit more then Kelly recommends. That's your "optimal" strategy for the amount of risk you are willing to take. I imagine it's expected return is the same as Kelly and calculating it's variance is left as the exercise for the reader.

replies(1): >>42469364 #
3. rahimnathwani ◴[20 Dec 24 08:52 UTC] No.42469364[source]▶

  I imagine it's expected return is the same as Kelly
Given two options with the same expected return, most people would prefer the lower variance.

Accepting higher variance with no increase in expected return has a name: gambling.