In a two people's game, you start with one dollar and you are betting 1 dollar coin at the very start of the game, then if you win you have double amount of money and you can choose of choose not to continue to bet all your money, if you lose, you lose all the money you own. This game is a fair game with the follwing rule, when the typical coin is tossed head you win and if you tossed tail you lose, the question is what is the expected return when played on the best strategy of this game?
But when i calculate the answer as follow when played this game infinite numbers of times, something is weird:
expected return = 1*(1/2)+2*(1/4)+4*(1/8)+...= infinity
is this a famous paradox?