12.13.2018

01.19.2008

Melchior’s Mixup Madness 2007 — 15:12

In years past, I’ve been a part of a Secret Santa party with a bunch of Pasadena folk. To ennerdify the proceedings a bit, I volunteered to make a web site that would automate the task of drawing the Secret Santa names out of a hat. This, apparently, put me in charge of the whole party… in saecula saeculorum. This year, I decided to abuse that power and completely change the rules. Instead of Secret Santa, we’d be celebrating the holidays just like the magi did: showing up late with questionable presents. Melchior‘s Mixup Madness was born, and it was born in the holy form of a White Elephant party: everyone brings a gift and the presents are doled out over the course of a game involving lots of backstabbing and treachery. Here’s a basic flowchart showing two things: the traditional rules of a White Elephant party and that I am a giant nerd. White Elephant Party Flowchart The first person to go opens a gift, the second person can open a new gift or steal the first person’s gift, and so on until all the presents are opened. Note that I’m using := as the assignment operator, that M is an index ranging from one to total number of people playing the game, that M indexes both the people playing the game and what “round” of the game is currently being played, and that (though no start and end are explicitly shown) we start at M:=1 and end when all the presents under the tree are opened. Greg, Paul.za, Michelle and I identified a few problems with this setup, though, while we were planning the party.
  1. The person who goes first doesn’t get to play the game much unless he or she happens to open a popular present.
  2. The last person to go has the most information about the presents and so can make the best choices.
  3. Even with no stealbacks, there is the possibility of entering an infinite loop (for certain definitions of “stealbacks”). Artificial rules must be introduced to break that possibility (imposing finite limits on the number of times a particular present can be stolen, on the number of times a particular person can steal, or so forth).
Even by randomizing the play order, the first two points are still kind of lame, and the third point is tricky to solve in a “natural” feeling way. We brainstormed. Our goals were to increase participation, to make stealing risky, to make each person’s outcome and level of participation less dependent on the initial ordering of players, and to stop infinite loops in a “natural” way. Time limits, different rules (or randomly chosen ones) for each round, dynamic creation of rules, stealing limits, the ability to block steals, voting… we thought of a bunch of ideas. In the end, I decided to try the following. At the beginning of their turn, each player is presented with a choice: open a present from the tree, or roll a die. If you roll the die, there are three possible outcomes: open a present from under the tree, steal an already opened present from someone, or be forced to take the present from a randomly chosen “chump” (and to switch turns with that chump). Melchior’s Mixup Madness Flowchart The “tree” outcome of the die probabilistically (though not deterministically) breaks infinite loops, stealing is risky (you might end up with a random present instead of the one you want), the ordering of players is changed throughout the game, and there’s more yelling. I think all our goals were met. The party was last night, and it was totally fun. Dylan, Roger, Jeff and others had some really nice ideas for version 2.0. Next time we do this, I may eliminate the freedom of choice (you’ll just plain have to roll the die), and have the outcome probabilities change as the game progresses (lots of trees in the beginning, more stealing at the end, more randomization everywhere). And yes, I drew the flowchart for the party. Melchior’s Mixup Madness Flowchart (whiteboard) And no, I didn’t know how to spell the singular form of “dice” until today.

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