Secret Santa draw

No. The draw shuffles the whole list and throws the attempt away if anybody got themselves or landed on a forbidden pair, then shuffles again from scratch.

That sounds expensive and is not: the share of shuffles where nobody draws themselves settles near 36.79 percent, so the average is under three attempts, and it does not grow with the size of the group.

Write the two names on one line of the second box, separated by a comma. The rule counts in both directions, so neither of them can get the other.

Every pair you add makes valid draws rarer. Two couples in a group of six take about six attempts instead of three, which is still instant; but a rule that leaves no valid draw at all, like two people who cannot draw each other in a group of two, gets a warning rather than an answer.

Because that always produces a single closed chain, which is a small slice of all the valid draws. The problem it causes is not statistical, it is about the secret: in one chain, two people who compare what they got learn a stretch of the line, and a few comparisons unravel the whole thing.

Drawing by rejection can produce two separate chains, and then comparing tells you nothing outside your own.

No. The whole draw happens in the browser: nothing is sent to a server, nothing is saved, and closing the page loses the result.

That also means there is no link to send and no e-mail going out. The screen is the delivery: each person opens their own line and closes it again.