Well done OP! This is the kind of analysis I love to encounter on HN, as this is a question I've definitely thought about before. > Each player has a different

Well done OP! This is the kind of analysis I love to encounter on HN, as this is a question I've definitely thought about before. > Each player has a different random set of preferences for those gifts, ranging from 0 to 100 (inclusive). This is my biggest point of criticism with the methods, as it's completely implausible and the excellent results of White Elephant relative to the best distribution are probably at least partially the result of this assumption. The first problem is what another commenter called "shit gifts", gifts that are relatively interchangeable and aren't at the top of anyone's preferences. For example, two people in my gift exchange this year stopped at the gas station on the way to the party and bought ~$25 worth of scratch-offs. The only way you'd want that is if you disliked almost every other gift. There are also usually one or two novelty items that almost no one wants. There's also (on the other end) "gold gifts", gifts that are really thoughtful or purchased by someone who ignored the price limit. These gifts will be at the top of most people's preferences, but usually not everyone's. The middle category of gifts is the one where there is a true mix of preferences, but they are still going to be significantly non-random. Some gifts will be more towards the top of everyone's preferences, but with significant dissenters who don't want them at all. Others will be agreed by nearly everyone to be "middling" gifts. And so on. I think you need to capture something about this complexity in your model of preferences. One consequence of all this is that stealing lacks some of the obvious benefits it has in the random model. For example, someone who opens a gift and is then stolen from tends to benefit in the random model, because the random preferences of the person who stole it reflect nothing about how the recipient valued the gift. On the contrary (which I have observed in real life), people who are stolen from are frequently disappointed. That's because the preferences of the thief do reflect something about the true value of the gift as measured by the overall preferences of the group. Only the good gifts get stolen, and anyone with a bad gift never gets to steal. Along with improvements to the preferences model, I'd be interested in seeing more alternative rules explored. I bet there are a bunch of alternative rulesets that generate better results, and also do better by the metric of satisfaction with the game itself, which is harder to measure. For example, I suspect the following ruleset does very well: 1. Choose a random ordering of the participants. 2. Everyone (in order) opens an unopened gift they choose from the pile. 3. Everyone (in order) may swap their gift with another participant's. Anyone swapped with may swap with someone else (and so on) before the order continues. Anyone who has already swapped on that turn may not be swapped with.