Stayin’ Alive

How to win at Russian Roulette

Demircan Celebi


A little bit about me first: I like math, statistics, programming, behavioral economics and I like to think I behave rational most of the time.

So; anytime I encounter a problem, I think the ways to solve it, pros and cons of the each possible solution, trade-offs, and so on. Then I try to solve the problem. This could mean implementing an algorithm, making an important decision about life, answering a statistics question or in this case, all of them.

I saw this question on a brain-teaser book (sadly I do not remember the book’s name) and had some thoughts on it.

The Question

Imagine you are in a Russian roulette game with a revolver having not one but two bullets. The capsules with the bullets are next to each other and the game is on. Your opponent takes the gun, spins the cylinder, puts it to his head, and pulls the trigger. Luckily (for him), he is still alive. It is your turn now. You take the gun and you now have two options.

You can either pull the trigger immediately or you can spin the cylinder and then pull the trigger. What should you do to increase the chance of you staying alive after this turn?

The Answer

Maybe you would like to think about it first, so I stop here. If you do want to read the answer though, here it is:

Since your opponent is still alive, it means he was on one of the free 4 capsules when he pulled the trigger — A revolver takes 6 bullets and 2 of them were full as we know— . For 3 of these capsules, the next capsule was also bullet-free, only one of them was next to a capsule which had a bullet in it. So if we choose to pull the trigger immediately, we will be alive with a chance of 3/4 (%75). If we choose to spin the cylinder though, we will not know the final order and since 4 out of 6 capsules are bullet-free, we will be alive with a chance of 4/6 (%66.67)

So we should not spin the cylinder and pull the trigger immediately.

Well, this was an easy question. I wondered how should we play this game if the number of bullets were different. What if there were not 6 but 20 capsules? What if the order of bullets were very different?

To answer these questions, I hacked things up a little bit and developed a tool which you can play with:

A screenshot from the tool I developed in order to answer those questions

Codes of this tool can be found on Github.

You can play with it here.

P.S. I originally wrote this in Turkish on Nov. 28 2012, on my personal blog.