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.

Author Bio

Daniel Crane contributed to this paper during the summer of 2015. He is now a Ph.D. candidate at Michigan Tech University studying applied mathematics.

Tanner Dye graduated from Taylor University in 2017. He is currently studying math as a graduate student at Ohio University.