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Ethan Hunt is tied to a chair and can't get up.
The super-villain Matt Fillimore stands in front of him.
There's a gun.
There's the barrel of the gun, six chambers, all empty.
Fillimore is putting two bullets in the gun, in two adjacent chambers.
He closes the barrel and spins it.

He puts the gun to Ethan's head and pulls the trigger.
Click.
Ethan Hunt is still alive.
Lucky him!
Now Fillimore is going to pull the trigger one more time.
He lets Ethan choose: whether he should spin the barrel first or whether he should just pull the trigger.

What should Ethan choose?

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He should just pull again.

Since all empty spots are adjacent, there's only a 1/4 chance that the spot that last 'clicked' was just before a bullet, so a 3/4 chance of survival. When spinning the barrel, assuming it happens randomly, there's a 2/3 chance of survival, which is less.

If the bullets were not adjacent, he should spin again - 1/2 chance vs 2/3.

If the bullets were placed randomly (adjacent or not), spin again. The next spot will be a bullet two times out of five, so survival is 3/5, while if we spin, we might hit the same empty chamber again, for (again) 2/3 chance of survival.

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