Secret Santa matcher
Draw names with exclusions — and nobody has to see the whole list.
6 participants
1 exclusion — applied in both directions
How it works
A Secret Santa draw is a derangement: a permutation in which no element stays in its original position — nobody draws themselves. Exclusions add further forbidden pairings.
The hat method is flawed
Drawing names from a hat has a real failure mode: the last person can end up with their own name, forcing a restart that leaks information about everyone else's draw. Computing the assignment all at once avoids that entirely.
How the derangement is found
By rejection sampling: shuffle, check every constraint, and retry if any is violated. This is uniform across all valid arrangements, which a “fix it up afterwards” approach is not. About 37% of random shuffles are already derangements — the proportion converges to 1/e — so a valid one is usually found in the first few attempts.
Keeping it secret from the organiser
The reveal cards let each person see only their own assignment. If even the organiser should not know, have someone outside the group run the draw, or pass the device around without looking. Everything is computed locally, so nothing is stored or transmitted either way.
Common exclusions
Couples and housemates are the usual ones — the point of the exchange is generally that people buy for someone they would not otherwise have bought for.