How to win the gift-stealing game Bad Santa, according to a mathematician

Christmas comes but once a year – as do Christmas party games.

With such little practice, it’s hard to get good at any of them.

Let me help.

I’m going to share with you some expert tips, tested through mathematical modelling, on how to win one of the most popular games: Bad Santa – also known as Dirty Santa, White Elephant, Grab Bag, Yankee Swap, Thieving Secret Santa, or simply “that present-stealing game”.

This isn’t advice on being a bad sport.

It’s about being a good Bad Santa – which is the name of the game.

You might even come away with a good gift and bragging rights.

How Bad Santa works

Bad Santa is a variation of the classic Kris Kringle (or Secret Santa) game, in which each guest receives an anonymous gift bought by another guest.

Part of the fun (for others) is the unwrapping of silly and useless gifts, which is done one by one.

Bad Santa spices things up.

All the gifts are pooled.

Guests take turns choosing one to unwrap.

Or they can choose to “steal” a gift already opened by someone else.

The person losing their gift then gets the same choice: open a wrapped present or steal someone else’s.

It’s a good alternative to buying a gift for everyone, and a great way to ruin friendships.

The order of players is usually determined by drawing numbers from a hat.

This is important because you’ve probably already noted the disadvantage of going first and the benefit of going last.

The right rules can mitigate this. There are at least a dozen different versions of this game published online, and some are much less fair than others.

How I tested Bad Santa

The best way to test Bad Santa rule variations and playing strategies would be to observe games in real life – say, by attending 1,000 Christmas parties (funding bodies please call me).

I did the next best thing, deploying the same type of computer modelling (known as agent-based modelling) used to understand everything from bidding in electricity markets to how the human immune system works.

In my model, there are 16 virtual guests and 16 gifts.

Pexels Rodnae Productions 6519235

Each has different present preferences, rating opened gifts on a scale of 1 to 10.

They will steal a gift they rate better than a 5.

To make it interesting, three gifts are rated highly by everyone and there are three no one really wants – probably a novelty mug or something.

After simulating 50,000 games with different rules, I’ve found a set of rules that seems the fairest, no matter what number you draw from the hat.

Choosing the fairest rules

The following graph shows the results for four different game variations.

The higher the line, the greater the overall satisfaction.

The flatter the lines, the fairer the result. (If gifts were chosen randomly with no stealing, every player’s average satisfaction score would be 5.)

Bad Santa Which Rules Are Most Fair

The most unfair result comes from the “dark blue rules”, which stipulate that any gift can only be stolen once in any round.

This means if you’re the last person, you’ve got the biggest choice and get to keep what you steal.

If you go first, you’re bound to lose out.

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