Pull again or add a bullet and spin

A six-chamber revolver holds two bullets in chambers separated by exactly one empty chamber. The first player spins once, fires at himself and survives. The second player may either (1) fire the next chamber as it is, or (2) load a third bullet, spin the cylinder at random, and then fire. Which option gives the second player the better survival chance? Answer $1$, $2$, or $3$ if they are equally good.

$3$ (equally good). With option 2, three of six chambers are loaded, so survival is $\tfrac12$. With option 1, the first shot was one of the $4$ empty chambers, and exactly $2$ of those are followed by another empty chamber, so survival is also $\tfrac24=\tfrac12$.