We explore the Secret Santa gift exchange problem. A group of n people draws names at random, giving a gift to the person drawn. First, we examine the probabilities of gift exchanges under various scenarios when everyone draws names at once, similar to Montmort's matching problem. We then consider the probabilities of certain gift exchanges when people take turns drawing names and develop a strategy to maximize the likelihood of receiving a gift from the most generous participant.
Crane, Daniel and Dye, Tanner
"The Secret Santa Problem Continues,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 18.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/18