Secret Santa Generator with Exclusions

A Secret Santa generator with exclusions lets you rule out matches before the draw instead of fixing them afterwards. An exclusion is a pair of people who must not be matched. In the generator you tap two names in the rules step, and that pair is blocked in both directions: if Maya and Leo are a couple, Maya won't draw Leo and Leo won't draw Maya. That covers the usual reasons to keep people apart: partners who would buy their gifts together anyway, housemates who would see the parcel arrive, or a parent and a young child who shop together.

The second kind of rule is one-way. Under last year's pairs you paste lines like Alex -> Sam, one per line, and Alex simply won't get Sam again. Sam can still draw Alex. That's usually what you want: the goal is that nobody repeats the person they bought for last time, not that two people can never be linked. If last year Alex and Sam had each other, add both lines.

1. Type or paste everyone's names, one per line. If two people share a name, the second gets a suffix such as "Sam (2)" so you can tell them apart.
2. In the rules step, tap two names for each pair that should be kept apart. A household of three people is three pairs, and each pair takes two taps.
3. Paste last year's pairs, if you have them. The organizer page never shows who has whom, so collect last year's list from the participants, or jot it down at this year's exchange when the gifts are opened.
4. Decide whether you're in. Switch on "I'm taking part too" and you're drawn like everyone else; you still won't see anyone else's match.
5. Optionally switch on "One big circle", which links everyone in a single chain (A gives to B, B to C, and so on back to A). It's made for in-person reveals where people open gifts in order.
6. Press Draw names. If the rules can be met, you get your organizer link and one private link per person. If they can't, the generator tells you which person or rule is blocking the draw.

The table above counts every possible draw exactly, for groups made up of couples. With 6 couples (12 people) there are 479,001,600 ways to shuffle the names. Of those, 176,214,841 have nobody drawing themselves, and 59,245,120 also keep every couple apart. That's 12.4% of all shuffles, roughly one in eight, and the share hardly changes as the group grows. The generator draws by shuffling and throwing away any shuffle that breaks a rule, so with 12 people it needs about 8.1 tries on average, which takes a computer no time at all.

Small groups are a different story. With 2 couples there are only 4 valid draws, and with one big circle switched on, only 2. Everyone can work out that their Secret Santa is one of the two people in the other couple. Add last year's pairs on top and exactly 1 valid draw is left: everybody can deduce who has whom. In a group that small, either drop a rule or accept that the secret is thin.

A draw exists only if every group of givers still has at least as many allowed recipients as there are people in that group. Mathematicians call this Hall's condition. In practice it fails in a few recognizable ways:

• Three people, one of them a couple. Both partners can only give to the third person, and one person can't receive two gifts, so there are 0 valid draws.
• A household bigger than half the group. In a group of five where three people live together, those three need three different recipients outside the house, and only two exist. Half is the limit: 6 out of 12 people can be one household, 7 can't.
• One person excluded from nearly everyone. Each exclusion takes options away. Someone blocked from all but one person must give to that person, and if that person is also someone else's only option, the draw breaks.
• Last year's pairs in a small group. With two couples, adding last year's pairs leaves exactly one possible draw, and a single extra exclusion can leave none.
• One big circle with many rules. A single loop is stricter than an ordinary draw, so a rule set that works normally can fail with the circle on.

When that happens the generator says which person or rule causes the conflict. The fixes, in order of preference: remove the least important rule (usually a last-year pair), switch off one big circle, add a participant, or split the group into two separate draws.

Adding rules shouldn't make a draw less random. In a Secret Santa generator with exclusions, fair means every valid assignment has the same chance of being picked. The generator gets there by being strict: it shuffles the whole list on the server, using a cryptographically random seed, checks the result against every rule, and starts over from scratch if anything breaks. Because rejected shuffles are thrown away whole, no valid draw is favored over another. That's not true of the common shortcut of drawing first and then swapping whoever got a bad match, which makes some pairings more likely than others. Only when the rules are so tight that random shuffles almost never pass does the generator switch to a slower search to find a valid draw.

• People who live together even if they aren't a couple: they'll see the shopping bag or the delivery.
• A parent and a young child who shops with them. Otherwise the parent ends up choosing both gifts.
• Last year's pairs. A repeat is the most common complaint in a group that does this every year.
• Two people already exchanging gifts privately, who'd rather spread the surprise around.
• At work, managers and their direct reports, if your team prefers to keep gifts out of reporting lines.

Keep the list as short as you can. Every exclusion removes options for everyone else, and in small groups each extra rule makes the remaining matches easier to guess.

Yes. Tap as many pairs as you need. Each pair counts both ways, so a household of four people is six pairs: tap two names for each.

No. A line such as Alex -> Sam only stops Alex from drawing Sam. If last year they had each other and you want to rule out both directions, add Sam -> Alex as well.

Nothing is drawn. The generator tells you which person or rule causes the conflict, so you can remove a rule, add a participant or switch off one big circle, then draw again.

In small groups, yes. With 2 couples, each person's Secret Santa has to be one of the two people in the other couple. In groups of 10 or more the effect is small.

Between 3 and 200. Exclusions and last year's pairs work at any size; the rules step of the Secret Santa generator with exclusions above is the same for 4 people or 200.