The probability the shot is fired is more and more important after each try for n>=2 (with n=1, the first try is the good one). So now, the question is: is it

The probability the shot is fired is more and more important after each try for n>=2 (with n=1, the first try is the good one). So now, the question is: is it best to go first? In terms of probability, yes you have to go first. But. This is like going all-in in a tournament of poker: the winner is the last man, so you have to avoid at maximum each situation which can make you out even if the probability are in your favor: once you are out, you've loose. The simple fact of going all-in makes you far in danger: you are just playing your life. If you aren't all in, for the moment, you are not playing your life and if you are not playing your life, you can't loose it. Knowing that you can't repeat the game infinitely, don't play first because the theory of probabilities become nul and void in this case: the bullet is in one chamber, the latest you press the trigger, the latest you die.