This means we’ll all have to take the same strategy, trusting in the fact that all the other logicians will choose the same one.
The four prisoners can’t communicate and they’re in symmetrical situations. Simulating four prisonersīefore we jump into our simulation, we can start with a bit of logic. I’ve also posted a 30-minute screencast of how I first approached the simulation and visualization.
#Coin flip sim how to#
In an appendix, I’ll show how to get a closed form solution for \(N=4\). I’ll solve this with tidy simulation in R, in particular using one of my favorite functions, tidyr’s crossing(). The only tools you and your fellow prisoners have to aid you are random number generators, which will give each prisoner a random number, uniformly and independently chosen between zero and one. If all flipped coins come up heads, you will all be set free! But if any of the flipped coins comes up tails, or if no one chooses to flip a coin, you will all be doomed to spend the rest of your lives in the castle’s dungeon. But it just so happens that all of you are logicians (of course)….Įach prisoner will be given a fair coin, which can either be fairly flipped one time or returned to the guards without being flipped. You are locked in the dungeon of a faraway castle with three fellow prisoners (i.e., there are four prisoners in total), each in a separate cell with no means of communication. I love 538’s Riddler column, and I’ve enjoyed solving the May 1st puzzle.
What is a coin toss simulation?Ĭoin toss simulation is a game where two people flip a coin back and forth until one of them has at least one side with either all heads or all tails. If you did 10 flips with two people per coin then that would only be 100 coins total between them both. So my friend was actually totally wrong about doing more than 100 flips of the coin. But before you read on further, try figuring out what is wrong with the game! When she said that, I just started thinking about how this made sense and how it wouldn't work with the same two people.Īfter thinking about it for a few minutes, I realized what this guy meant. So then this guy that was really quiet before (he was also in class today, which is why I know his name) said that he had heard you could bet up to 1337 coins, but our teacher said no because that would be too many. But anyhow, we were playing this game and I was telling them about how you can bet more than 50 coins with two people. So if you got a hundred-year-old coin and it landed heads, it'd be worth 100 points. Or if the coins are different values, they could be worth more points if it lands on your side, and the coins would equal the face value of your coin when it lands on heads. And then we played the coin toss game that you play when you are bored at school or work or something, where you have to guess heads or tails for fifty coins. So I was teaching a class and we were talking about probability.
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