Russian roulette

Remember the Monty Hall problem? This is somehow a similar one. You guys should give it a try:

You are in a game of Russian roulette, but this time the gun (a 6 shooter revolver) has three bullets _in_a_row_ in three of the chambers. The barrel is spun only once. Each player then points the gun at his (her) head and pulls the trigger. If he (she) is still alive, the gun is passed to the other player who then points it at his (her) own head and pulls the trigger. The game stops when one player dies. Now to the point: would you rather be first or second to shoot?

Lenko Donchev
Thursday, September 11, 2003

2nd shooter by far

Possible gun positions...

111000
011100
001110
000111
100011
110001

1st = 3/6 = 50% survival
2nd = 3/6(1st guy dead) + 2/3 = 5/6  = 83% surival

Since the game stops if the first guy dies, 2nd place will always have better odds

B
Thursday, September 11, 2003

Unlike the Monty Hall problem -- the game starts at the first pull, not the first 'choice'.

Therefore, I agree with the answer given.

T.J.
Sunday, September 28, 2003

B:  Does it bother you that the percentages total > 100%?  Why or why not?

Brian
Tuesday, September 30, 2003

Why shouldn't the percentages total more than 100? Each percentage represents the chances of that person alone. If the game were played with 6 people, the last two would both fairly obviously have a 100% chance each of surviving.

Paul Viney
Tuesday, September 30, 2003

Since it's obviously OK for the percentages in the 6 person game to total > 100%, it follows that it's ok in the 2 person game.
Have I summerized accurately?

Brian
Thursday, October 02, 2003

The reason that the percentages can total more than 100 is that you can have more than one person surviving. Seeing as the game stops when one person dies, the percentage chance of dying cannot add up to more than 100%, and will add up to exactly 100% when at least 4 people are playing.

Paul Viney
Friday, October 03, 2003

Incidently, as I understand Russian Roulette, the whole point is that the bullets are heavier and should end up at the bottom. If this is indeed the case, then it skews the probabilities considerably and going first might be the best option after all!

Paul Viney
Friday, October 03, 2003

Paul:
Russian roulette is usually a 2 player game.  That's not explicitly stated to be the case here, but the language suggests that it's what the OP intended.

Brian
Tuesday, October 07, 2003

Thanks Brian, that's what I get for not reading the question properly :-). To disown all my previous posts - with 2 players the chances of survival can't add up to anything except 100%. Assuming all start positions are equally possible, player one loses in 4 of them, implying that going second would be a very good choice.

Paul Viney
Wednesday, October 08, 2003

Paul,

what if you go second and survive, and then is the other person's turn and again he also survives and then is your turn again -> you are almost sure to be dead. Maybe it is better to be first this way?

what if
Friday, October 10, 2003

Yes, in this case you're dead. Carrying your argument through, it's always better to choose to go first in the case when the second person will die. Unfortunately you don't know when that will be.
Taking a 1 to be a bullet, the possibilities are
111000
110001
100011
001110
(player one dies on these possibilities)
and
011100
000111
(player dies on these 2 possibilities).
If you are player 2 and the pistol has said 'click' three times, this is probably a good time to contemplate the vagarities of maths,probability,life, etc. :-)

p.s. You wouldn't catch me playing

Paul Viney
Friday, October 10, 2003

I think that you should not work out the possibilitys because if you are stupid enough to play the game then you should take the consequences without trying to be a smartass. SO THERE!

fluffy
Tuesday, November 25, 2003

The probabilities of survival are as follows:

1st player: 50%
2nd player (assuming 1st survived): 66.7%
3rd player (assuming 1st and 2nd survived): 50%
1st player (on second round, assuming all players survived 1st round): 0.0%

Have I just done someone’s homework assignment from statistics class? :-)

IG
Wednesday, December 10, 2003

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