YouTube/Numberphile/MSRI
Caralynn Lippo
November 26, 2016 3:04 pm

Thanksgiving is officially behind us, so we can dive full-speed ahead into winter holidays traditions – like the inevitable awkwardness of Secret Santa gift exchanges. If you’ve ever felt that there’s a fundamental design flaw in the covert gift-giving tradition that needed addressing, you’re in luck. This woman explaining the math behind Secret Santa is oddly soothing.

Much like the mathematically-perfect way to cut pizza, IRL useful math is always ~much~ appreciated. In this particular video, Dr. Hannah Fry explains the issues with the way names are typically drawn, something that should be familiar to anyone who watched Secret Santa mishaps as portrayed by The Office. The standard route most groups take is putting a bunch of names into a hat and going around a table pulling names one by one.

But as Dr. Fry explains, that’s mathematically imperfect. There’s the chance of pulling your own name and, as you go around the table and names are chosen, the odds of picking various gift-recipients change. According to Dr. Fry, total anonymity and the equal probability of your name being selected by anyone else are the two key components of Secret Santa – both of which fail in the standard name-picking method.

I’ll just let Dr. Fry explain, because again, her much more eloquent explanation will lull you into a state of precious pre-holiday calm (before the holiday gift-buying stress begins).

Per the video (and Dr. Fry’s mathematical reasoning), the optimal way to choose gift recipients for Secret Santa is to pick both a number designation for yourself as well as which number you’re getting a gift for. That would keep the anonymity aspect on lockdown, while also insuring that you don’t accidentally pick yourself and mess up the whole game.

The video is part of the Numberphile series YouTube Channel from Brady Haran, an Australian filmmaker and video journalist known for his educational BBC News and YouTube videos, and supported by the Mathematical Sciences Research Institute.

Dr. Fry, one of several regular contributors to Numberphile, is a mathematician and a lecturer in the Mathematics of Cities at the Centre for Advanced Spatial Analysis at UCL. She studies mathematics as it relates to human behavior (specifically in urban settings) and “her research applies to a wide range of social problems and questions, from shopping and transport to urban crime, riots and terrorism.”

Basically, she’s one of far too few brilliant women in STEM fields showing that math can be interesting and relatable, and that’s awesome. Yay math! Yay holiday gift-giving!

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