Power law

Video is here: https://www.youtube.com/watch?v=HBluLfX2F_k

At table number one you get 100 tosses of a coin, each time you flip and it lands on heads, you win $1. How much would you be prepared to pay to play this game? Expected value is $50.

At table number two you get 100 tosses of a coin, but this time instead of potentially winning a dollar on each flip, your winnings are multiplied by some factor. So you start out with $1 and then every time you toss a head, you multiply your winnings by 1.1. If you toss tails you multiply your winnings by 0.9. How much would you pay to play this game? Expected value is 1.1 + 0.9 / 2 = $1. But this doesn't take into account the distribution, you could potentially win big with $1 * 1.1¹⁰⁰ = $13,780.

At table three you start out with $1 and the payout doubles each time you toss the coin and you keep tossing until you get heads, then the game ends. How much would you pay to play this game? The expected value of this game is infinite. This is the St. Petersburg Paradox.