Two bullets side by side, spin or not?

Question

A revolver has six chambers. Two bullets are loaded into adjacent chambers, the other four are empty. The cylinder is spun, the gun is pointed at you, the trigger is pulled, and it clicks on an empty chamber. Now it is your turn. You may either spin the cylinder again before pulling the trigger, or pull the trigger straight away on the next chamber. Which choice gives you the better chance of survival, and by how much? How does the answer change if only one bullet were loaded?

Accepted Answer

Do not spin. Pulling straight away gives a 1 in 4 chance of a bullet; spinning gives 1 in 3. Spinning. A fresh spin lands on a random chamber: 2 bullets out of 6, so the chance of firing is 1/3. Not spinning. The click told you the cylinder is on one of the four empty chambers, each equally likely. The chambers run in a circle: bullet, bullet, empty, empty, empty, empty. Only one of the four empty chambers is immediately followed by a bullet (the last empty one before the pair). So the chance the next chamber holds a bullet is 1/4. Since 1/4 is less than 1/3, you should not spin. One bullet i…

Two bullets side by side, spin or not?

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