Two bullet roulette: Difference between revisions

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The following is supposedly a question given to mathematics graduates seeking jobs on Wall Street:

A revolver handgun has a revolving cylinder with six chambers for bullets.

It is loaded with the following procedure:

1. Check the first chamber to the right of the trigger for a bullet. If a bullet

is seen, the cylinder is rotated one chamber clockwise and the next chamber

checked until an empty chamber is found.

2. A cartridge containing a bullet is placed in the empty chamber.

3. The cylinder is then rotated one chamber clockwise.

To randomize the cylinder's position, the cylinder is spun, which causes the cylinder

To randomize the cylinder's position, the cylinder is spun, which causes the cylinder to take

~~to take~~ a random position from 1 to 6 chamber rotations clockwise from its starting position.

a random position from 1 to 6 chamber rotations clockwise from its starting position.

When the trigger is pulled the gun will fire if there is a bullet in position 0, which is just

counterclockwise from the loading position.

The gun is unloaded by removing all cartridges from the cylinder.

According to the legend, a suicidal Russian imperial military officer plays a game of

According to the legend, a suicidal Russian imperial military officer plays a game of Russian

~~Russian~~ roulette by putting two bullets in a six-chamber cylinder and pulls the trigger

roulette by putting two bullets in a six-chamber cylinder and pulls the trigger twice.

~~twice.~~ If the gun fires with a trigger pull, this is considered a successful suicide.

If the gun fires with a trigger pull, this is considered a successful suicide.

The cylinder is always spun before the first shot, but it may or may not be spun

The cylinder is always spun before the first shot, but it may or may not be spun after putting

~~after putting~~ in the first bullet and may or may not be spun after taking the first shot.

in the first bullet and may or may not be spun after taking the first shot.

Which of the following situations produces the highest probability of suicide?

A. Spinning the cylinder after loading the first bullet, and spinning again

A. Spinning the cylinder after loading the first bullet, and spinning again after the first shot.

after the first shot.

B. Spinning the cylinder after loading the first bullet only.

C. Spinning the cylinder after firing the first shot only.

D. Not spinning the cylinder either after loading the first bullet or after

D. Not spinning the cylinder either after loading the first bullet or after the first shot.

the first shot.

E. The probability is the same for all cases.

;Task:

# Run a repeated simulation of each of the above scenario, calculating the percentage of suicide with a randomization of the four spinning, loading and firing order scenarios.

# Show the results as a percentage of deaths for each type of scenario.

# The hand calculated probabilities are 5/9, 7/12, 5/9, and 1/2. A correct program should produce results close enough to those to allow a correct response to the interview question.

;Reference:

Youtube video on the Russian 1895 Nagant revolver [[https://www.youtube.com/watch?v=Dh1mojMaEtM]]

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