Here is a trick I found that solved an old problem: How can coin flipping ever be fair if only one person chooses head or tail ?
I remember Chrissy complaining about that to Jack in an episode of “Three’s Company”. Above the humour, I remember thinking about fair coin flipping back then, many years before I learned anything about cryptography.
The other day, I was asked the very same question by my daughter. Children are great entropy generators (you can tell by the mess they make of their toys). I found a way to solve the problem by having both of them part of the coin flipping. Well I don’t flip a coin. I hide it in one of my hands, behind my back. Here is how it goes:
I lay out the outcome first. Something like “If you get the coin, you’re the one who take her bath first”
I start shuffling the coin from one hand to the other, behind my back.
One of them says “stop”.
I leave the coin in the hand it was when I was told to stop.
I show both hands (fists, actually) to my other kid, who gets to choose a hand.
(The entropy gathering is at step 3). If she gets the coin, she knows the outcome. No more “it’s not fair” complaints ;)