284
$\begingroup$

Assume that we are playing a game of Russian roulette (6 chambers). Assume that there is no shuffling after the shot is fired.

I was wondering if you have an advantage in going first?

If so, how big of an advantage?

I was just debating this with friends, and I wouldn't know what probability to use to prove it. I'm thinking binomial distribution or something like that.

If $n=2$, then there's no advantage. Just $50/50$ if the person survives or dies.

If $n=3$, then maybe the other guy has an advantage. The person who goes second should have an advantage.

Or maybe I'm wrong.

  • 3
    @lhf impossible to get a real gun in the UK. Was just having an argument about how fear makes you do illogical things. Surely it's illogical to go second, yet people would fear going first.2012-01-04
  • 0
    Is n the number of participants?2012-01-04
  • 8
    I think it would be appropriate to specify the rules of whatever variant of Russian Roulette you have in mind and what *n* represents (I assume you mean number of players, but it could also be number of bullets).2012-01-04
  • 13
    I would think there would be a *lot* of shuffling after the shot went off: shuffling of brain matter into the air, shuffling of feet as people got out of there before the cops show up, etc.2012-01-04
  • 49
    There's an implicit assumption here that it's an advantage to survive. [Apparently](http://www.brightreview.co.uk/ARTICLE-The-Man-Who-Invented-Russian-Roulette.html) what's now called "Russian roulette" originated in circumstances where the players were sometimes weary of life and didn't mind "losing".2012-01-04
  • 17
    If after the first guy fires a blank, the host offers you to swap turns, should you?2012-01-04
  • 11
    Not a mathematician but if I may put a non-math spin on this one... In real life, the added mass of the bullet will bias the spin and probably keep the bullet in one of the lower chambers.2012-01-05
  • 1
    That depends. Are you using an automatic or revolver?2012-01-05
  • 0
    @Everyone that's an excellent question for the physics SE2012-01-06
  • 0
    I think is better not go.2012-01-06
  • 0
    @JackN: The magazine in an automatic wouldn't leave much room for probability/chance. The person who loaded the magazine would be aware of the initial state.2012-01-06
  • 2
    I think it's just best not to go last.2012-01-06
  • 0
    http://www.smbc-comics.com/?db=comics&id=7#comic Does Zach Weiner read math.SE?2012-01-07
  • 0
    I remember reading in the literature, quite some years ago, the remark (actually a complaint by a Russian) that this pastime is actually misnamed, as it actually originated in the American Civil War. Can anyone verify or refute this claim?2012-01-09
  • 0
    I am pretty sure that there is a Russian Roulette scene (although it's not called that) in Lermontov's "A Hero of Our Time", which was written in 1839.2012-01-26
  • 0
    For those interested in probability theory, note that this problem is equivalent to sampling without replacement from the set of 6 chambers. It is a general property of sampling w/o replacement that the probability for a certain sequence of draws is only dependent on how many draws there were of each "type", and not on their order ("exchangeability")2017-07-21

5 Answers 5