Math Problem Solver

You are at a casino, playing a game where your goal is to maximize your return from the game. The game is defined by the following rules: - you pay 1 dollar to play the game - you roll a die 100 times - if you roll a number 1-3 you lose all of your money bet - if you roll a number 4-6 you get your bet back plus double your bet - you may choose to end the game at any moment. The optimal strategy is the entire amount won so far after each roll of the die without ending the game early. What is the expected value of your total winnings after 100 rolls, assuming you follow the optimal strategy?