Russian roulette

Russian roulette (Russian: Русская рулетка, romanized: Russkaya ruletka) is a potentially lethal game of chance in which a player places a single round in a revolver, spins the cylinder, places the muzzle against the head or body (of the opponent or himself), and pulls the trigger. If the loaded chamber aligns with the barrel, the weapon fires.
The term Russian roulette was possibly first used in a 1937 short story of the same name by Georges Surdez, published in the January 30, 1937, edition of Collier's magazine:
References to the term in the context of the Collier's story appeared in some newspapers during 1937. The first independent appearances of the term in newspapers began in 1938 with the reports of young men being killed while playing it. The earliest instance appears to have been the death of a 21-year-old former journalism student in Austin, Texas, appearing in The Austin Statesman and some other Texas newspapers on January 8, 1938. At least four other deaths were attributed to Russian roulette during the year: a 34-year-old policeman in Peoria, Illinois, a 20-year-old in Houston, an 18-year-old in Saratoga Springs, New York, and a 16-year-old in Los Angeles.
The term has become a metaphor for taking foolhardy risks, and its usage steadily increased in reportage of diplomacy, politics, economics, medicine and sports.
An early example of Russian roulette can be found in the short story "The Fatalist" within the 1840 novel A Hero of Our Time written by Russian poet and writer Mikhail Lermontov. In the story, which is set in a Cossack village, the protagonist, Grigory Alexandrovich Pechorin, claims that there is no predestination and proposes a bet in order to prove it, laying about fifty gold pieces onto a table. A lieutenant of the dragoons of the Tsar, Vulič, a man of Serbian origins with a passion for gambling, accepts the challenge and randomly takes one of a number of pistols of various calibres from its nail, cocks it and pours gunpowder onto the pan. Nobody knows if the pistol is loaded or not. "Gentlemen! Who will pay 20 gold pieces for me?", Vulič asks, putting the muzzle of the pistol to his forehead. He then asks Grigory to throw a playing card in the air, and when the card lands, he pulls the trigger. The weapon fails to fire, but when Vulič cocks the pistol again and aims it at a service cap hanging over the window, a shot rings out and smoke fills the room.
Calculations in this section are based on the use of a six-shot revolver with a single chamber loaded. Abnormal factors, such as the possibility of a dud round, are not included.
With this variant, turn order is essential, because the probability of losing decreases the later one's turn is.
Given a six-shot revolver, for any given single trial (pull), the probability of losing is 1 6 ≈ 16.7 % {\displaystyle {\tfrac {1}{6}}\approx 16.7\%} . However, since all players only come into the game if and when each of the players before them has caught an empty chamber, the all-game loss probability for player k {\displaystyle k} (starting from 0) is reduced to ( 5 6 ) k ⋅ 1 6 {\displaystyle ({\tfrac {5}{6}})^{k}\cdot {\tfrac {1}{6}}} . The all-game loss probabilities for each of the six players are hence, in order, 16.7 % {\displaystyle 16.7\%} , 13.9 % {\displaystyle 13.9\%} , 11.6 % {\displaystyle 11.6\%} , 9.6 % {\displaystyle 9.6\%} , 8.0 % {\displaystyle 8.0\%} , and 6.7 % {\displaystyle 6.7\%} to one decimal place. More generally, for a revolver with n {\displaystyle n} chambers, player k {\displaystyle k} 's all-game loss probability is ( n − 1 n ) k ⋅ 1 n {\displaystyle ({\tfrac {n-1}{n}})^{k}\cdot {\tfrac {1}{n}}} .
The probability of the revolver having fired after six pulls is 1 − ( 5 6 ) 6 {\displaystyle 1-({\tfrac {5}{6}})^{6}} , or about 66.5 % {\displaystyle 66.5\%} . More generally, for a revolver with n {\displaystyle n} chambers, the probability of the revolver having fired after k {\displaystyle k} pulls is 1 − ( n − 1 n ) k {\displaystyle 1-({\tfrac {n-1}{n}})^{k}} , as this would be an instance of a geometric distribution where the success probability is 1 n {\displaystyle {\tfrac {1}{n}}} .
The average number of pulls for the gun to fire is n {\displaystyle n} in this variant (six pulls, for a six-shot revolver).
With this variant, turn order has no effect on the all-game loss probability, which remains the same for all players, but influences the single-pull probability, which increases with each pull.
Given a six-shot revolver, at pull k {\displaystyle k} (starting from 0), the fact that all k {\displaystyle k} previously tested chambers were empty reduces the total number of possible locations of the bullet to 6 − k {\displaystyle {6-k}} , and the loss probability is therefore 1 6 − k {\displaystyle {\tfrac {1}{6-k}}} . The single-pull loss probabilities for each of the six players are hence, in order, 16.7 % {\displaystyle 16.7\%} , 20 % {\displaystyle 20\%} , 25 % {\displaystyle 25\%} , 33.3 % {\displaystyle 33.3\%} , 50 % {\displaystyle 50\%} , and 100 % {\displaystyle 100\%} to 1 decimal place. More generally, for a revolver with n {\displaystyle n} chambers, the loss probability at pull k {\displaystyle k} (starting from 0) is 1 n − k {\displaystyle {\tfrac {1}{n-k}}} .
However, since, like in the re-spinning variant, all players only come into the game if and when each of the players before them has caught an empty chamber, the all-game loss probability for player k {\displaystyle k} is
1 n − k ⋅ ∏ i = 0 k − 1 n − i − 1 n − i = n − 1 n ⋅ n − 2 n − 1 ⋅ . . . ⋅ n − k n − k − 1 ⋅ 1 n − k = 1 6 ≈ 16.7 % {\displaystyle {\tfrac {1}{n-k}}\cdot \prod _{i=0}^{k-1}{\frac {n-i-1}{n-i}}={\frac {\cancel {n-1}}{n}}\cdot {\frac {n-2}{\cancel {n-1}}}\cdot ...\cdot {\frac {\cancel {n-k}}{\cancel {n-k-1}}}\cdot {\frac {1}{\cancel {n-k}}}={\frac {1}{6}}\approx 16.7\%}
for k > 0 {\displaystyle k>0} and 1 n − k = 1 6 ≈ 16.7 % {\displaystyle {\frac {1}{n-k}}={\frac {1}{6}}\approx 16.7\%} for k = 0 {\displaystyle k=0} . Hence, the all-game loss probability for all players is 16.7 % {\displaystyle 16.7\%} to 1 decimal place.
The probability of the revolver having fired after six pulls is 6 6 {\displaystyle {\tfrac {6}{6}}} or 100 % {\displaystyle 100\%} in this variant (meaning the revolver will fire within six trigger pulls). And, more generally, after k {\displaystyle k} pulls, it is k n {\displaystyle {\tfrac {k}{n}}} .
The average number of pulls for the gun to fire is n + 1 2 {\displaystyle {\tfrac {n+1}{2}}} in this variant (3.5 pulls, for a six-shot revolver).
The Deer Hunter is a 1978 war drama film about three of Slavic-American steelworkers in the Vietnam War that imprisoned by the Viet Cong are forced to participate in Russian roulette while the jailers bet.
13 Tzameti is a 2005 dark psychological thriller by Georgian Babluani. Thirteen men undergo series of Russian roulette, arranging into a circle and pointing at the man in front of them (American remake in 2010). 'Tzameti' is the Georgian word for thirteen.
Live! is a 2007 mockumentary-thriller where a TV network executive tries to produce a reality show where contestants play Russian Roulette.
In Death Is a Problem for the Living (Finland, 2023) two men, one a gambling addict and the other with 15% brains left, start a hearse business, but end up in a criminal organization that runs an illegal Russian roulette game show.