Bang! Precisely one of us is dead.

Imagine, if you will, a table.  This table is nothing out of the ordinary itself but rather has three extraordinary people sitting around it.  The reason the these people are extraordinary is that they are planning on pointing a revolver with one bullet in it at their own heads and seeing who dies.  The question becomes how do we design this revolver / maniac game so that it is intuitive, fair and quick?  The entertainment value of Russian Roulette is pretty much guaranteed to be there or not depending on the observer so my job is entirely to make sure that the game is the best one possible.

Usually the way the game is described a single bullet is put into the gun, the chambers are spun to randomize the location of the bullet and people put the gun to their heads and pull the trigger one at a time.  The trouble as I see it is that you sometimes end up with somebody knowing that the only remaining chamber has a bullet and it is their turn to point and fire!  While it is quite a bit nutty to be involved in a game of Russian Roulette in the first place it requires even more moxie to complete the game when you know you are the one to die.  Clearly cheating in a game of RR is going to have some pretty serious consequences so even if you have a 50/50 shot it seems very reasonable to try your luck - it isn't likely a bunch of people willing to be in this game are going to let you get away with chickening out or shooting somebody else.  However, once you know that you have a 100% chance to die I expect that the prospects of a bunch of homicidal, vengeful RR players looks not too bad after all.

You could avoid that certainty by simply rerandomizing the gun after every pull.  Each time somebody pulls the trigger the chambers are spun again before the next lunatic takes his turn.  This avoids any certainty of death for sure but has the issue that the first person to go is at a substantial disadvantage.  You can keep it random by simply having the players draw cards to see who has to go first but that seems like an inelegant solution because it introduces another random element into the game from outside - functional, but ugly.  I think the best solution is to rerandomize after each round rather than after each pull.  Have each player pull once and if the bullet is in the unused chambers you spin them again and start from the beginning.  This way there is no disadvantage for going first but nobody ever ends up certain that they are killing themselves either.  It has a decent likelihood of taking awhile if the bullet ends up unused a number of times but I figure since the game isn't going to be played a lot of times we can probably afford the extra time spent.

So there you go, if you want to play RR you just make sure you have less than 6 players and have everyone take a turn before you spin the chambers again.  Now you know!

I wrote up a little simulator to figure out your approximate likelihood of dying based on your position from 1-3 when the gun is randomized after each shot...  the lesson is don't go first.

1:  39.4 %
2:  33.0 %
3:  27.6 %