eribosot, (edited ) 
A group of 100 players are playing a game of chance. All players start with $100. All players play 500 turns of the game.
Each turn, a player must bet half of their money or, if they're down to their last dollar or less, all of their money.
During each turn, they have 51% chance of winning. If they win, they double their bet amount back; if they lose, they get nothing back.
After 500 rounds, how much money does the most successful player have?