Code I wrote for this video: https://github.com/manforowicz/Manim-Videos/blob/main/kelly_criterion.pyGreat ergodicity economics blog post by Jason Collins: h...
Because if you gamble in small increments the odds are in your favor. If you gamble your entire wealth then you’ll likely lose.
Lets say you’re gambling in $5 increments. The odds are 50/50, if you lose then you’ll have $2.5, and if you win you’ll have $9. That’s a 50% chance to lose $2.5 and a 50% chance to gain $4, the actual risk is if you lose too many times in a row that you don’t have enough money to gamble with. Otherwise, you’ll slowly gain money.
Because if you gamble in small increments the odds are in your favor. If you gamble your entire wealth then you’ll likely lose.
Lets say you’re gambling in $5 increments. The odds are 50/50, if you lose then you’ll have $2.5, and if you win you’ll have $9. That’s a 50% chance to lose $2.5 and a 50% chance to gain $4, the actual risk is if you lose too many times in a row that you don’t have enough money to gamble with. Otherwise, you’ll slowly gain money.
Ah, I was assuming that the premise was all-in on each gamble. It’s true that it will work with small increment gambles.