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...
How is this video calculating that a 50% chance of 80% gain and a 50% chance of 50% loss yields a positive expected gain? An alternating string of heads and tails will drive your money to zero - a 50% loss (1/2) would be balanced by a 100% gain (2/1) in a fair system.
This is true if you’re betting everything you have. By not having shrinking bets after losses you can tap into the net gains. Compare 1 win followed by 1 loss with $100 start:
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.
How is this video calculating that a 50% chance of 80% gain and a 50% chance of 50% loss yields a positive expected gain? An alternating string of heads and tails will drive your money to zero - a 50% loss (1/2) would be balanced by a 100% gain (2/1) in a fair system.
This is true if you’re betting everything you have. By not having shrinking bets after losses you can tap into the net gains. Compare 1 win followed by 1 loss with $100 start:
Win is $100+$80 = $180
Loss is $180-$90 = $90
Compare with fixed bets of $50 with bank of $100:
Win is $100+$40 = $140
Loss is $140-$25 = $115
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.