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Can someone please explain how to apply this first and an ELI5 second?
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this post was submitted on 24 Oct 2023
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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.
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.
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