Russian Roulette: what is the probability of survival?

Credits: Wikimedia Commons

Russian roulette is a well known but extremely dangerous game -if indeed it should even be called a game. In fact, according to the rules of the game, you can only lose -either you die or you abandon it. A study was carried out in order to calculate the probability of surviving each pull of the trigger, depending on the number of bullets and their position in the cylinder of the revolver. 

It is a game of risk and the stakes are extremely high -it is potentially fatal. This game of chance consists of putting a cartridge into the cylinder of a revolver, turning the cylinder randomly and fairly quickly so that you can’t follow where the loaded chamber lands, and then pointing the revolver at your head before pulling the trigger. People die every year while playing this game. Russian roulette can be played alone or with others, possibly not even pointing the weapon at yourself, but sometimes at another participant. Playing alone is like gambling, and represents either extreme thrill seeking or suicidal behaviour.

When the gun is loaded with only one bullet, the chances of survival are 83.3%. If the cylinder contains two cartridges placed side by side before the first shot is taken, the player has a 66.7% chance of survival. So is it then better to turn the cylinder or to pull the trigger a second time? The player has a higher chance of survival if they take the two shots one after another, without turning the cylinder. In fact, if you turn the cylinder, the percentage of survival is the exact same as it was for the first shot, at 66.7%. If the cylinder is not turned, the percentage likelihood of survival goes up to 75%. In this case, there are normally 6 chambers in a cylinder, two of which are loaded side by side. There are thus 4 empty chambers, which are also side by side, although only 1 of these 4 empty chambers are next to a loaded chamber, which leads to ‘only’ a 25% chance of death.

The probability of surviving the second shot, with two bullets placed randomly in the cylinder, offers 15 possible combinations. The probability of surviving a second shot is therefore 60%. For 3 bullets, the probability of surviving the second shot is 40%. Additionally, in order to increase your chances, it is best to spin the cylinder between the two shots, with a 50% chance of survival in such a case. The chances of survival are 20% when there are 4 bullets loaded. If the game is not lost during the first round when the cylinder contains 5 bullets, there is no point in trying a second time. And if the gun is fully loaded from the start, the game is re-christed “Belgian Roulette”, and there is certainly no point in playing.

If the revolver is held horizontally, the cylinder will tend to stop turning when the bullet is at the base, because of the weight of the bullet, which increases the player’s chances of survival. What’s more, the chances of each chamber of the cylinder ending up in the firing position are not equal. To limit the impact of the weight of the bullet, you can shoot the gun with the barrel pointing upwards. In this way, the cylinder turns on a vertical rather than a horizontal axis. Additionally, the rotation of the cylinder is not entirely random, because an experienced player can manage to take into account the initial position of the bullet, and spin it so as to maximise their chances of shooting from an empty chamber. It is only by giving the gun to a third party that the shot can be truly considered to be taken blindly.

Accidents often happen with this game -if they can even be considered accidents. Certain people who don’t fully know how to play the game do not take into account the basic recommendations, which lead all too often to tragedy. For example, by using a pistol and not a revolver, you are guaranteed to lose. In fact, with a pistol, the bullet is automatically placed in the correct chamber as long as the chamber is loaded and the gun is cocked.

Sources : slate ; Wikipedia