EasyProbability
3 min read
Expected Flips
Problem Statement
A biased coin with P(H) = p is flipped until the first head appears. What is the expected number of flips?
A biased coin with P(H) = p is flipped until the first head appears. What is the expected number of flips?
How can you simulate a fair coin using an unfair coin?
You have $100 and a fair coin. You can play up to 100 rounds of tossing the coin. During each round, you can bet an amount up to your current holding, and if you win, you gain double your bet + your original bet back. Otherwise, you lose your bet. What is the optimal strategy to maximize expected value?
Kelly rolls a fair standard 6-sided die. She observes the value on the face. Afterwards, she is given the option to either receive the upface (in dollars) as a payout or to roll again. If she rolls again, she receives the upface of the second roll (in dollars) as payout, regardless of what she rolled on the first turn. If Kelly plays optimally, what is her expected payout?