“You are playing a game where you and another person roll a 100-sided die. Whoever rolls the highest number receives $1 from the house, not the opponent. If you tie, you get nothing. You are given the option to double the number of your roll for $0.2. How often do you double your roll?”
I’d be inclined to double the number every time. Assuming there’s no limit to when the game ends, and that numbers can exceed 100 when doubled, you automatically win on 49 of 100 possible numbers, and have greatly increased odds in every roll below that. Even if the numbers max out at 100 there’s a 1 in 100 chance that you don’t make money for anything above 49.
Returns per game obviously go down but you can just play more games and make more money in the long run.
Is there something I’m missing? Is that why Jane Street wouldn’t hire me
I say this assuming that my opponent is not given the opportunity to double. That’s a different story, but I’d probably still double it every time because every time I don’t do it, my odds are worse than a regular roll because there’s the chance that my opponent doubles their roll too, which would nullify my chances. If they have the option too it’s just the same game as before but with a 20 cent buy-in
Not sure about the odds of any of this, but if there’s a ‘house’ paying out winnings, you have to believe that the odds are skewed in a way that you won’t make money from a strategy as simple as that. The house always wins
