# Trains, Rock Paper Scissors, & Hannah Fry: What do these three have in common?

How can Rock Paper Scissors (RPS) have a winning strategy? It’s all just luck, isn’ it?

Well, no, actually.

It’s true that if your opponent plays strictly randomly, then you have no winning strategy. It’s really all just luck. But a human opponent (as opposed to a computer program) cannot play strictly randomly, so you do have a winning strategy. Math conquers all, of course.

So…I’ve recently been learning about the distinguished British mathematician Hannah Fry, and I would like to recommend a look at her contributions to two small topics in applied math: a winning strategy for RPS, and the astonishing use of math in the earliest creation of train timetables. These are just two of her many Numberphile videos, all aimed at a general audience. Brief remarks on these two:

• Just to nudge you off the obvious but flawed assumption that RPS is purely random, let me just ask you a couple of questions: if you choose, say, Paper as your initial play, are you more likely or less likely to choose Paper next time? The answer might help dictate your opponent’s strategy. And then, once you predict your opponent’s next play, what should you do? After you’ve thought about these two questions, go watch Fry’s first video (link in the previous paragraph).
• Almost everyone does better with visual representations than with tables of numbers. And yet almost all of us are far more familiar with train timetables in the form of tables of numbers (times of day) than with geometric tables (which we probably can’t even imagine). After you’ve thought about this fact, go watch Fry’s second video (link in the previous paragraph).

Categories: Math, Model Railroading, Teaching & Learning