Russian Roulette Riddle

In the morbid game of Russian Roulette, a partially loaded revolver with a six-chamber cylinder is randomly spun, pointed at one of the players, and fired. If the revolver landed on an empty chamber, the lucky player is safe, and the process is repeated with the next player. The obvious objective of the game is to not get shot.

You find yourself stuck in a game of Russian Roulette. A freshly loaded revolver is aimed at the first player, and it turns out to be an empty chamber. Your turn is next, and you are given the choice to either:

• Spin the cylinder before pulling the trigger (i.e., you get a random new chamber)
• Or just pull the trigger (i.e., let the revolver fire whatever is in the next chamber)

Which choice should you pick if the revolver was originally:

2. Loaded with bullets in two random chambers?
3. Loaded with bullets in two consecutive chambers?

Assume the revolver cannot misfire, and that spinning the cylinder lands on all chambers with equal probability.

Some variation of this Russian Roulette riddle was once asked in interviews at Jane Street, Susquehanna International Group (SIG), Facebook (now Meta), UBS, Capital One, and more.

Solution

You should spin the cylinder.

Spin: equal chance of landing on any chamber, so 1/6 chance you get shot.

Don’t spin: equal chance the next chamber is any 1 of the 5 remaining chambers, and 1 of them is loaded, so 1/5 chance you get shot.

2. Loaded with bullets in two random chambers

Again, you should spin the cylinder.

Spin: equal chance of landing on any chamber, so 2/6 chance you get shot.

Don’t spin: equal chance the next chamber is any 1 of the 5 remaining chambers, and 2 of them are loaded, so 2/5 chance you get shot.

3. Loaded with bullets in two consecutive chambers

The bullets being in consecutive chambers changes everything – in this scenario, you should not spin the cylinder.

Spin: equal chance of landing on any chamber, so 2/6 chance you get shot.

Don’t spin: you know the first trigger pull landed on 1 of the 4 empty chambers. But because the 2 loaded chambers are consecutive, you know that these 4 empty chambers must also be consecutive. That means for 3 out of the 4 empty chambers, the “next” chamber must also be empty. So there is a 1/4 chance you get shot.