Bayesian Coin Selection and Sequential Betting

Probability · Medium · Free problem

You have two coins. Coin 1 has $P(H) = 2/3$ and Coin 2 has $P(H) = 1/3$. One coin is chosen uniformly at random and flipped 3 times, producing 3 heads. (a) What is the probability that the next flip (with the same coin) is heads? (b) Counterparty A offers you a bet: if the next flip is heads, you win $\

$; if tails, you lose $\ $. Should you take it? If offered repeatedly (always using the same coin), should you keep taking it? (c) Counterparty B offers a different bet: if heads, you lose $\ $; if tails, you win $\$3$. Should you take it? (d) If you can take bet B at most once and bet A up to 100 times, what is your optimal strategy?

Open the full interactive solver, hints, and worked solution →