You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will proceed:
- You may fill any of the chambers with a bullet. You must place at least 1 bullet into the revolver, but you have enough bullets to fill the entire revolver
- After you have chosen the configuration, your opponent may do 1 of 2 things:
- Choose whether to go first or second
- Move a single bullet, and flip a coin to decide whether they go first or second
- After the opponent action is complete, the cylinder is spun exactly once
- You both continue to fire the revolver until one player can no longer continue
Going "first" means that person is the first target of the revolver. Find a) the strategy/strategies that maximize(s) the odds of survival for yourself, and b) the corresponding strategy/strategies that maximize(s) the odds of survival for your opponent. Additionally, show that your opponent can bound your maximum probability of survival to 50%, and that you can bound your opponent's maximum probability of survival to 50%.