Problem of the Week 1095

Betting on the Next Card

Bob shuffles a standard deck of 52 cards thoroughly and then plays cards face up one at a time from the top of the deck. At any time, Alice can interrupt Bob and bet $1 that the next card will be red. Alice bets once and only once. If she never interrupts then she automatically bets on the last card.

Can Alice do better than even money? What is her best strategy?

Source: Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A.K. Peters, 2004.

© Copyright 2008 Andrew Beveridge and Stan Wagon. Reproduced with permission.