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

Christmas only comes once a year – as do Christmas party games. It’s hard to get good at any of them with so little practice.

let me help I’m going to share with you some expert tips tested through mathematical modeling to win one of the most popular games: Bad Santa – aka Dirty Santa, White Elephant, Grab Bag, Yankee Swap, Thieving Secret Santa, or simply “the gift stealer”. -Game”.

That’s not advice to be a bad sport. It’s about being a good bad Santa – that’s the name of the game. You might even get away with a good gift and boastful rights.

How evil Santa Claus works

Bad Santa is a twist on the classic Kris Kringle (or Secret Santa) game, in which each guest receives an anonymous gift purchased by another guest. Part of the fun (for others) is unwrapping silly and useless presents, which is done one at a time.

Bad Santa spices things up. All gifts are pooled. Guests take turns choosing one to unwrap. Or they may choose to “steal” a gift that has already been opened by someone else. The person who loses their gift then has the same choice: open a wrapped gift or steal someone else’s.

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

Player order is usually determined by drawing numbers from a hat. This is important because you’ve probably already noticed the downside of going first and the upside of coming last. The right rules can mitigate this. There are at least a dozen different versions of this game released online and some are a lot less fair than others.

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How I Tested Bad Santa

The best way to test Bad Santa rule variations and gameplay strategies would be to watch games in real life – for example, by attending 1,000 Christmas parties (funding agencies please call me).

I did the next best thing, using the same type of computer modeling (known as agent-based modelling) that has been used to understand everything from how bids are placed in the electricity markets to how the human immune system works.

In my model there are 16 virtual guests and 16 gifts. Everyone has different gift preferences and will rate opened gifts on a scale of 1 to 10. They will steal a gift that they rate better than 5. To make it interesting, three gifts are highly valued by everyone and there are three that no one really wants – probably a novelty mug or something.

Bright sweater with Christmas Pudding motif.
Or so.

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

Choosing the fairest rules

The graphic below shows the results for four different game variants.

The higher the line, the greater the overall satisfaction. The flatter the lines, the fairer the result. (If gifts were randomly selected without stealing, each player’s average happiness score would be 5.)

Made with Flourish

The most unfair result comes from the “dark blue rules” which dictate that each gift can only be stolen once per round. This means if you’re the last person, you have the most choice and can keep what you steal. If you go first, you are bound to lose.

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Fairest and Best Bad Santa Rules

The fairest results come from the “red rules”:

  • A gift can be stolen multiple times per round. This keeps gifts moving between guests, adding to the fun.

  • Once a person holds the same gift three times, it becomes “locked” and can no longer be stolen. It balances the game a lot. Later players will still see more gifts, but earlier players have more chances to lock the gift they want. It also ensures games don’t go on for hours.

  • After the last player’s turn, there is another round of stealing, starting with the very first player. This also gives them a chance to steal at least once – and a slight advantage. But overall, these rules provide the most consistent results.

As with most games, the rules are not perfect. But the math shows they are better than the alternatives. If you want to test other scenarios with my model, you can download my source code here.

On your turn you can either steal an open gift or open a new one.  If you are robbed, you can steal from someone else or open a gift.  If you hold a gift three times, it's locked.  The first person gets a final steal.
Optimal game rules for Bad Santa.
Joel Gilmore / Background by Monika from Pixabay

Three tips on game strategy

The right rules help level the playing field. They don’t eliminate the need for strategic thinking to maximize your chance of receiving a desired gift.

As in real life, seemingly fair rules can be manipulated.

One thing you could do is team up with other players to rig the three-holds-and-locked rule. To do this, you need at least two co-conspirators.

Say your friends Donner and Blitzen have their favorite gifts, and now it’s your turn. You steal Blitzen’s gift. Lightning, in turn, steals thunders, which steals yours, and so on. At the end, Donner and Blitzen hold their chosen gifts a second time, then a third time. You have helped them and then you can choose another gift.

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Okay, let's go over the plan again.  I steal this gift, then you steal this gift, and then you steal my gift.
Okay, let’s go over the plan again. I steal this gift, then you steal this gift, and then you steal my gift.

In competitive markets, this type of collaboration is usually referred to as collusion – and it’s illegal. In sports, that would simply be called cheating. So I’m not saying you should do that; I’m just explaining how the strategy works. If you do this and end up on the naughty list, don’t blame me.

I have not yet tested rule variations in my model to see how best to eliminate or minimize these collusion. Maybe until next Christmas. (Or maybe not — to me, cheating with math is half the fun of the game.)

So let me leave you with two perfectly legitimate strategies.

First, and most obviously, you need to steal presents!

My modeling quantifies how necessary this is. I simulated a game where four guests will never steal a present. These guests are 75% less satisfied with their recent gifts than players who steal. They’re also a lot less fun at parties.

Made with Flourish

Second, steal even if you don’t want to.

Steal the gift you think someone else might want. If a later player steals your gift, you will get another chance to choose again if more gifts have been opened.

And if someone gets Grinchy using these techniques to wrap the best present, just tell them you read about it in The Conversation.

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