Revolver with one bullet and no re-spin

Two players share a six-chamber revolver holding a single bullet. The cylinder is spun once at the start and never again. They alternate pulling the trigger, your friend going first, and whoever fires the bullet loses. What is your probability of winning?

$1/2$. After the single spin the bullet is equally likely to be in any of the six chambers. Your friend fires chambers $1,3,5$ and you fire $2,4,6$, so you survive exactly when the bullet sits in an odd-numbered chamber: probability $\tfrac12$.