UAH > Math > Math Club > 3/28/2008
In the game of red and black, a player bets, at even stakes, on a sequence of Bernoulli trials with success probability p, until she either reaches a fixed goal or is ruined. The player's probability of reaching the target is the fundamental quantity of interest, and the player's only strategy consists of decisions on how much to bet on each trial. Is there an optimal strategy? If so, is it unique? How does the optimal strategy depend on p? We will explore these questions and others, and along the way discover some beautiful and surprising mathematics.