Secret Santa

What it's for

To organize Secret Santa at Christmas or a party without slips in a hat. Everyone taps their own name and sees only who they must give a gift to.

How it works

The draw makes sure no one gets themselves. Pass the device around: each person checks their match and then hides it.

The constraint that looks obvious and is not

«Nobody draws themselves» looks like a trivial condition, and instead it is why drawing slips from a hat fails so often: it is enough for the last person left to draw their own name and everything has to start again. With ten people that happens in roughly one case out of three.

The mathematically correct way is generating a permutation with no fixed points, that is a pairing in which nobody stays on themselves. The count of such pairings is called the derangement number, and their proportion of the total tends to a curious value: about 37%, that is one divided by Euler's number. It holds for three people as for a thousand.

Why the hat reveals more than it seems

In the classic method whoever draws last has far fewer alternatives, and whoever has already drawn can deduce a great deal by looking at who is left. In a small group two people talking to each other are enough to reconstruct nearly every pairing, and the game loses its only ingredient.

A draw made all at once and shown to each person separately avoids this: nobody sees the order, nobody knows who is left. One rule remains that no software can enforce, though: do not tell anyone who you got, not even afterwards, not even as a joke.

The rules that make it work between people

A spending cap decided in advance and the same for everyone, because the difference between someone spending ten and someone spending fifty is the fastest way to make everybody uncomfortable. A clear date too. And a short list of preferences or of things not wanted, because a gift that misses is nearly always down to nobody knowing anything.

It is also worth deciding beforehand whether couples can draw each other: in a group of friends including two people who live together, pairing them removes the point of the game, and it is better to exclude it before drawing than to redo everything afterwards.

When the draw has to be redone, and when not

It has to be redone if someone joins or drops out: adding a person at the last minute without redoing everything creates a broken chain, in which somebody gets two gifts and somebody else none. It is the commonest failure, and it is discovered on the evening itself.

It does not have to be redone because someone dislikes who they got: the rule applies to everyone, and the first time an exception is granted the game becomes a negotiation. If a pairing really is impossible — two people who are not on speaking terms — the thing to do is say so beforehand to the organiser, not after the draw.

Nearby tools

To form groups there is Random team maker, for a draw with more options Wheel of fortune and for numbers Random number generator. To organise shared spending Group expenses.