Russian Roulette — Two Random Bullets

A 6-chamber revolver has its chambers arranged in a circle. Two bullets are randomly placed in 2 of the 6 chambers (not necessarily consecutive). The barrel is randomly spun once. Two players take turns pulling the trigger without further spinning — after each pull, the barrel advances to the next chamber.

Your opponent went first and survived. You are given the option to spin the barrel before your turn. Should you spin?

What is your probability of losing with the optimal strategy?