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Russian Roulette
| January 14th, 2019 at 1:46:22 PM permalink | |
| Nared Member since: Jan 13, 2019 Threads: 2 Posts: 8 | Russian roulette is a game played by sadistic prison guards with prisoners in czarist Russia. It can be played with from two to six players. We shall consider the following variation with two players. A bullet is placed in one of the six chambers of a revolver and the cylinder is spun. The first player places the gun to his head and pulls the trigger. If he survives, he gives the gun to the second player, who does likewise. Back and forth until one of them is killed. The guards have chosen prisoners Ivan and Boris to play this game. They cannot refuse. They will give Ivan the choice of who takes the first shot and Boris of whether or not the cylinder is spun between tries, in that order. What is the best strategy for each and who has the greatest chance of survival? Case 1, the cylinder is not spun: The bullet is equally likely to be in any of six positions. The first player survives if the bullet is in position 2, 4, or 6. The second player survives if the bullet is in position 1, 3, or 5. 3/6 chances for player 1 and 3/6 chances for player 2, so p = 1/2. Same chance for either. Case 2, cylinder is spun: Player A wins if the gun does not fire on the first pull and does fire on the second pull. P1 = (5/6)(1/6) = 5/36. He loses if the gun fires on the first pull P2 = 1/6. It is possible for the gun not to fire on either the first or second pull but we don't count that since it doesn't decide the game and we just start over. His overall probability of winning is P1/P1+P2 = 5/11 = 0.4545... Ivan should choose that Boris should take the first shot. The Boris should choose no spin since that will give him an even chance instead of just 45%. The Wizard has two other solutions as Problem 33, but I think this one is the simplest and easiest to understand. |
| January 14th, 2019 at 5:11:11 PM permalink | |
| odiousgambit Member since: Oct 28, 2012 Threads: 154 Posts: 5098 | Ivan should have the first shot be with himself at risk, to preserve the original 1/6 chance, otherwise Boris can create a state where the probability is 1/5, should the gun not fire, by not spinning the cylinder. Boris should spin or not spin depending on if he is next or not, creating 1/6 for himself and 1/5 for Ivan. This is so basic that each would instinctively make these choices even if they slept through math class in school. After reading your solution, I think you did not fully explain Boris's choices? But the best choice for both is to do it like it was done to the Viet Cong in the movie "the Deer Hunter" and that is to see if your captors are stupid enough to actually hand you the gun unrestricted, leaving you the opportunity to shoot *them* instead of yourself. Of course almost anything is possible *except that*, as you could hunt the globe every day for centuries on end and never, absolutely never, find anyone stupid enough to do that. I'm Still Standing, Yeah, Yeah, Yeah [it's an old guy chant for me] |
| January 15th, 2019 at 11:35:44 AM permalink | |
| Face Member since: Oct 24, 2012 Threads: 61 Posts: 3941 |
You must not watch much cctv footage of robberies on YouTube lol. I assure you, there's someone that stupid in every corner of the world =) Be bold and risk defeat, or be cautious and encourage it. |
| January 15th, 2019 at 12:07:27 PM permalink | |
| AZDuffman Member since: Oct 24, 2012 Threads: 135 Posts: 18204 |
My corner can spare some if you are short. The President is a fink. |