He didn't have a 1/6 chance
He had a 50/50 chance of the chamber containing the last bullet.
With two bullets in a six chamber revolver the chances are 1/3 of being killed on any given chance. After Garfield is killed, the next chamber will either be empty or contain the last bullet. The only way he could change his chances were if he were to spin the revolver before he pulled the trigger after Garfield had just done so, but he did not.