Puzzle of the week: Nobody gets their own
Six people put their hats in a box and each draws one at random. What is the probability that nobody gets their own hat?
Last week: Fair ruin
You start with $3 and bet $1 on fair coin flips until you have $0 or $10. What is the probability that you reach $10?
Answer and write-up
0.3
Your wealth is a martingale and the game ends surely, so its expected final value is 3. With p the chance of reaching 10, 10p = 3 and p = 0.3.