Every rule you add to a Secret Santa draw removes some of the possible draws. A few rules are free, and a few quietly leave almost nothing. This page counts the draws for a small group so you can see where the cliff is. The numbers below are recomputed from the generator's own engine by its test suite.
Ann and Ben are a couple, and so are Cara and Dev. Nobody may draw themselves or their partner. That leaves Ann and Ben giving to Cara or Dev, and Cara and Dev giving to Ann or Ben.
| Rule | Valid draws |
|---|---|
| Swaps allowed | 4 |
| No swaps | 2 |
| One big loop | 2 |
With swaps allowed, Ann may give to Cara while Cara gives to Ann. Forbidding that leaves only the two draws where the gifts go around in a circle: Ann to Cara to Ben to Dev to Ann, and Ann to Dev to Ben to Cara to Ann. Here "no swaps" and "one big loop" happen to mean the same thing.
Three people with one couple, Ann, Ben and Cara with Ann and Ben together, have no valid draw at all: Ann and Ben can each only give to Cara, and Cara can only receive one gift. The generator tells you exactly that, naming Ann and Ben, instead of failing with a vague error.
Excluding last year's draw adds one more forbidden pair per person. Where swaps are allowed, a group of five goes from 44 valid draws to 13, and a group of eight from 14,833 to 4,738. It never makes a draw impossible on its own, but in a small group it leaves little surprise. Paste last year's group link into the next-year box and the generator applies it for you, and tells you if the combination has become impossible.
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With three people and one couple, both halves of the couple can only give to the one remaining person, and a gift can only go to one giver. No draw exists, and the generator names the two people who are stuck so you can add a player or drop the rule.
Four is the minimum, and with exactly two couples there are only two valid draws, so the surprise is small. Six or more people, or a mix of couples and singles, gives a much larger set of draws.
Both are fair if the shuffle is. The computer draw has the advantage that it can respect rules for couples and last year's pairs, and that the organizer never has to see the result.