MathDB

You play a game with a biased coin, which has probability

\tfrac{3}{4}

of landing heads. Each time you toss heads, you score

1

point, while tossing tails earns no points. After any turn, you can stop playing the game and keep the points you currently have. However, if you are still playing when you toss tails for the second time, you lose all of your points. If you play to maximize your expected score, what is your expected score from playing this game?

Problem Statement