#139 — Alan Hájek on puzzles and paradoxes in probability and expected value

A casino offers you a game. A coin will be tossed. If it comes up heads on the first flip you win $2. If it comes up on the second flip you win $4. If it comes up on the third you win $8, the fourth you win $16, and so on. How much should you be willing to pay to play?

The standard way of analysing gambling problems, ‘expected value’ — in which you multiply probabilities by the value of each outcome and then sum them up — says your expected earnings are infinite. You have a 50% chance of winning $2, for '0.5 * $2 = $1' in expected...