Spoiler for The way I read it
if neither spun the cylinder the bullets would both fire on the sixth shot.
Now, to me, spinning the cylinder a turn means a full turn to me putting it back in the same spot. So we have the same situation as the initial condition meaning that both die on the sixth shot.
Now lets assume that spinning the cylinder a turn means the next chamber is now on top. If they are both given the exact same revolver the cylinder would come out on the same side for both guys meaning that they could only spin it one way, pushing from the top down.
If the cylinder comes out on the right side of the gun then they spin it clockwise making the chamber one clockwise from the bullet on top meaning that both guns will fire on the first shot since the next cylinder is the 'active' one.
If the cylinder comes out on the left side of the gun then they spin it counterclockwise making the champer on counterclockwise from the bullet on top meaning that both guns will fire on the fifth shot.
So in all cases it is a lose/lose situation.
Not if it's one of these: http://www.trackofth...t/aal-344_2.jpg