To respin or not with two randomly loaded chambers

Two bullets are loaded into two randomly chosen chambers of a six-shot revolver, the cylinder is spun, and your opponent pulls the trigger and survives. It is now your turn. Would you rather pull the trigger straight away (moving to the next chamber) or spin the cylinder first?

Spin. A fresh spin fires with probability $\tfrac26=\tfrac13$. Without spinning, you know the current chamber is empty, so the next chamber is one of the other five, two of which are loaded: probability $\tfrac25>\tfrac13$. (If the two bullets were in adjacent chambers instead, not spinning would be safer at $\tfrac14$.)