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Game Theory of Dirty Santa December 4, 2010

Posted by eric22222 in General, Math.
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I really like when I break into some unexplored territory on the net. I haven’t found anything on this subject online. I’ll start by saying I don’t have any calculations done here, but I’d like to make the points that were brought up available.

Dirty Santa, or White Elephant, or whatever you want to call it, is a gift exchange game. Participants each bring one gift. Order is randomly assigned. Each person may either open a gift or steal a gift that a previous player has opened. If your gift is stolen, you get another turn to either open or steal a gift. Pretty simple. In one variant, gifts are locked in place (no longer stealable) after they have been stolen so many times.

As the game was about to begin at our annual CSC Christmas party, a few of us nerds begin to discuss some of the finer points of the game. Is there an optimal turn one would want? How would we go about figuring that out?

Here’s some of the ideas that were brought up to consider:

  • You wouldn’t steal a valuable gift early, for fear of it being locked with someone else.
  • One could steal a gift with the intention of it being stolen later, granting them a turn later in the game.
  • Value may not be objective, but each player should have some idea about the average value a gift may hold.

So the question becomes “given a certain steal limit per gift and a certain number of gifts, what turn would allow a player to achieve the highest value present?”

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