Comments on: “Assuming a fair coin toss”

By: Liz

Liz — Wed, 02 Sep 2009 03:15:08 +0000

Radiolab had an interesting podcast titled Stochasticity (randomness) and it has an interesting bit about coin tosses. What it really gets at is the predictability of humans, but your blog made me think about it and I think you will find it interesting too. http://feeds.wnyc.org/radiolab

By: phil

phil — Tue, 25 Aug 2009 16:04:33 +0000

I should clarify. The “API” there was based on my notion of how a fair coin toss should be structured, given that the flipper can influence the outcome. I removed that because I hear that students sometimes use the Internet, and I didn’t want to spoil the pedagogy for you. If the context isn’t obvious (and you care), I can email it to you.

By: phil

phil — Tue, 25 Aug 2009 16:02:25 +0000

Do you do game theory? If the fairness of a coin toss can be manipulated by the tosser, how can you structure the coin toss to restore fairness? Is there a dominant strategy? Is there a Nash equilibrium?

This could also be the start of a programming problem. Write an API for refereeing coin flips. (i.e., submit_coin(side), flip(num_flips), get_result()) and pit people against each other. To make things more interesting, make each contest a series of n thousand trials, each of which trial consists of n thousand flips of a single coin. Introduce random variations in coin weight, and let the flipper adjust parameters to indirectly control spin, inferring the effects from the results of previous flips. (Binomial theorem and other statistics.) The person who best figures out when they’re flipping an unfair coin will have a huge advantage.