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In many schools throughout the United States, it is customary to hold ayearly "Secret Santa" event. With the approach of Christmas, all the studentsplace their names in a hat; each student, in turn, draws a name out of the hat,thus becoming Secret Santa to the student whose name is drawn. On the daybefore Christmas break, each student places a gift in front of the locker ofthe student to whom she or he is Secret Santa.  Unfortunately, children being children, some students might forget to bringgifts on this day. Students who do not find gifts next to their lockers,feeling cheated, angrily take their gifts back from their recipients, who inturn reclaim their gifts from their recipients, and so forth.  We analyze the distribution of the number $L$ of students whose Christmas isruined, as a function of the number of students who do not bring gifts. We givea simple, explicit formula for the probability of every possible value for $L$(backed by three proofs of distinct flavors), as well as closed-form formulaefor its expectation and variance. Notably, we show that if $m$ kids forget tobring gifts, then the expected fraction of kids whose Christmas is not ruinedis less than $\frac{1}{m+1}$ (regardless of the total number of students), withlow probability for a large deviation from this fraction.  The underlying theoretical results are applicable to the study ofmanipulation in matching markets within game theory.

"Secret Santa" and the Combined Length of Spanned Cycles in a Random Permutation