Russian Roulette — Spin or Not?

The problem
6-shooter · 2 consecutive bullets · spin, fire → click123456opponent's turn done · safeyour turn:spin again, orjust pull the trigger?

A six-shot revolver has two bullets loaded in adjacent chambers. The other four are empty.

Your opponent:

  1. Spins the cylinder.
  2. Pulls the trigger at himself. Click. Empty.
  3. Hands you the gun and offers a choice: spin again before your turn, or just pull the trigger.

What should you do?

Tempting (but wrong)
"same odds either way — just spin"123456spin: 2/6 die123456no spin: 2/6 die?

Two common wrong intuitions:

  • "Spin — reset the randomness." Feels like spinning is "safer." It actually throws away a piece of information.
  • "Same either way — two of six chambers are loaded." Treats the gun as memoryless. But the bullets are placed consecutively, so the empty click is informative about which chamber comes next.