Russian Roulette with 2 Adjacent Bullets (Spin or Pull?)

Scenario

A standard 6-chamber revolver has 2 live bullets placed in two adjacent chambers, leaving 4 consecutive chambers empty. The cylinder is spun once, randomly aligning the chambers. Player 1 points the gun at their head and pulls the trigger. Click! The chamber was empty; Player 1 survives. Now it is Player 2's turn. Player 2 is offered a choice:

• Option A: Pull the trigger immediately without spinning the cylinder.
• Option B: Spin the cylinder again before pulling the trigger.

Your Task

1. Calculate the conditional probability of firing a bullet under Option A (no spin).
2. Calculate the probability of firing a bullet under Option B (re-spin).
3. Conclude which option maximizes Player 2's survival probability.

Constraints

• Clockwise cylinder advance.
• Bullets placed in adjacent chambers $(1, 2)$.

Examples Re-spinning resets the bullet probability to $2/6 = 33.33\%$. Not spinning conditions on the preceding empty chamber.