The arguments at a white elephant party are almost never about the gifts. They are about the rules nobody said out loud: whether a gift can be stolen straight back, how many times the good one can change hands, whether player 1 gets a swap at the end. The game goes by several names, Dirty Santa and Yankee Swap among them, and nobody publishes an official rulebook for any of them. Whatever the group agrees before the first gift is opened is the rulebook.
Two of those rules do most of the work, and both are about fairness. A freeze limit stops the one gift everybody wants from travelling round the room all night: after its last allowed steal, whoever holds it keeps it. The last swap exists because of the turn order. In a group of twenty, the last player chooses from nineteen opened gifts and player 1 chose from none, so giving player 1 the final move is the only way the first number is not the worst one.
The table on this page keeps score so nobody has to. Tap a wrapped gift to open it or an opened one to steal it, and it counts each gift's steals, freezes the gift on the steal your rules say, refuses a steal straight back, and moves the turn on to whoever was stolen from. Undo takes back a mis-tap. The rules you set are written out in full under the table and print on one card, so they can sit on the table where everyone can read them.
White elephant is not the only way to swap presents. If your group would rather buy for one person each than fight over a pile, that is a Secret Santa, and our Secret Santa generator draws the names, keeps couples apart and gives each person their own link. The exchange is usually one line in a busy month: the printable Christmas planner puts the gifts, the dinner and a six-week countdown on three sheets, and when the party is a bring-a-dish one, the potluck sign-up sheet stops the table filling up with four bowls of the same salad.
The honest limit of the screen is the limit of any scorekeeper: it only knows what is tapped on it. Give one person the job, put the phone or laptop where the room can see it, and let the printed card settle anything the screen cannot.
