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Deriving the Kelly Criterion to Maximise Profits

(obrhubr.org)
50 points obrhubr | 4 comments | 12 Oct 24 21:16 UTC | HN request time: 0.636s | source
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roenxi ◴[18 Oct 24 00:16 UTC] No.41875153[source]▶
A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy.

[0] https://en.wikipedia.org/wiki/Ergodic_process

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1. diab0lic ◴[18 Oct 24 01:15 UTC] No.41875506[source]▶
An example that may be useful to aid in understanding… Casinos are non ergodic.

A million players each placing a single bet will have an expectation of losing the house edge.

A single player placing a million bets has an expectation of $0.

The fact that the aggregate and the single entity Experience different expectations despite both placing a million bets is what makes this ergodic.

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2. ◴[18 Oct 24 01:30 UTC] No.41875567[source]▶
3. ◴[18 Oct 24 05:56 UTC] No.41876691[source]▶
4. diab0lic ◴[19 Oct 24 13:03 UTC] No.41887536[source]▶
Errr that last sentence should end with “is what makes this non-ergodic.”