Being a senior engineer is knowing the difference between doing what your told and figuring out what needs to be done to achieve project success. In this case, getting to the next round.
Next question?
Of course, many game theory calculations assume all players know the payoff matrix and equilibrium strategies of the others; making sure the bullet isn't in the next chamber is the rational universal strategy if the game has a fixed number of rounds.
Presumably the actual question has a bunch of provisos making sure you can't intentionally miss, or accidentally miss, or dodge, or shoot early, or fail to pull the trigger, or shoot the gang.....