Choosing Rarity: An Exercise in Stopping Times
Ewa Kubicka, Grzegorz Kubicki · Mathematics Magazine · 2011
SummaryYou enter an online game, hoping to win a prize. You know that thirteen envelopes of two colors will appear one by one on your screen, and you know that there will be five of one color and eight of the other. Each of the five envelopes, those with the “rare” color, contains $100, while the others are empty. However, you do not know which color is which, and you can only select one envelope; once you click, the game is over. How should you play to maximize the probability of winning? We provide an optimal strategy for this game and a generalization.