russian roulette

[poker1O1]

ok, so this should be an easy one for you guys. say you and one other person play russian roulette, switching after each trigger pull. the revolver can hold 6 bullets, but only contains one bullet. it is not spun inbetween trigger pulls. my question is, can you show me the odds of getting shot if you go first? second? (I assume both are 50%) For whatever reason I cannot reach an answer

[Kips Bay Kid]

probably wrong but...

if you treat each pull of the trigger as an independent event then the probability of each pull is:

A: 1: 0.166666667
B: 2: 0.2
A: 3: 0.25
B: 4: 0.333333333
A: 5: 0.5
B: 6: 1

Then if you do 100 trials at each slot you get:
A: 1: 16.6666667
B: 2: 20.
A: 3: 25.
B: 4: 33.3333333
A: 5: 50.
B: 6: 100

Adding the total up yields 245 "kills"
A dies: 91.66666667 (37.4% of the time)
B dies: 153.3333333 (62.6% of the time)

It does not seem right though, I would think it would be closer to 50/50 if not exactly.

[Kips Bay Kid]

actually it is wrong, once you subract the previous total you get this:

A: 1: 16.6666667 = 1/6 * 100
B: 2: 16.6666667 = 1/5 * (100 - 16.6)
A: 3: 16.6666667 = 1/4 * (100 - 16.6 - 16.6)
B: 4: 16.6666667 = :
A: 5: 16.6666667 = :
B: 6: 16.6666667 = :

or exactly 50/50

[PairTheBoard]

Going First:

(1/6) + (5/6)(4/5)(1/4) + (5/6)(4/5)(3/4)(2/3)(1/2) =

= .5

Notice the denominators other than 6 cancel out all the numerators.

With that answer there must be a way of looking at it where the answer pops out as obvious. Don't know what it would be though.

PairTheBoard

[BruceZ]

[ QUOTE ]
ok, so this should be an easy one for you guys. say you and one other person play russian roulette, switching after each trigger pull. the revolver can hold 6 bullets, but only contains one bullet. it is not spun inbetween trigger pulls. my question is, can you show me the odds of getting shot if you go first? second? (I assume both are 50%) For whatever reason I cannot reach an answer

[/ QUOTE ]

Come on guys. If you go first, you get shot if the bullet is in chamber 1,3, or 5. If you go second, you get shot if the bullet is in 2,4, or 6. Either way the probability is 3/6 = 50%.

[kyro]

[ QUOTE ]
[ QUOTE ]
ok, so this should be an easy one for you guys. say you and one other person play russian roulette, switching after each trigger pull. the revolver can hold 6 bullets, but only contains one bullet. it is not spun inbetween trigger pulls. my question is, can you show me the odds of getting shot if you go first? second? (I assume both are 50%) For whatever reason I cannot reach an answer

[/ QUOTE ]

Come on guys. If you go first, you get shot if the bullet is in chamber 1,3, or 5. If you go second, you get shot if the bullet is in 2,4, or 6. Either way the probability is 3/6 = 50%.

[/ QUOTE ]

Hey, at least it wasn't the Monty Hall problem.

[Marlowe]

Dunno if this is nit-picking, but I don't think there is a 1/6 chance of the bullet finishing in the top chamber (ie the weight of the bullet is a factor in where is ends up).

[TheHammer24]

[ QUOTE ]
[ QUOTE ]
ok, so this should be an easy one for you guys. say you and one other person play russian roulette, switching after each trigger pull. the revolver can hold 6 bullets, but only contains one bullet. it is not spun inbetween trigger pulls. my question is, can you show me the odds of getting shot if you go first? second? (I assume both are 50%) For whatever reason I cannot reach an answer

[/ QUOTE ]

Come on guys. If you go first, you get shot if the bullet is in chamber 1,3, or 5. If you go second, you get shot if the bullet is in 2,4, or 6. Either way the probability is 3/6 = 50%.

[/ QUOTE ]

lol I stumbled in here, and thought i was missing something since every one was trying so much math.

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
ok, so this should be an easy one for you guys. say you and one other person play russian roulette, switching after each trigger pull. the revolver can hold 6 bullets, but only contains one bullet. it is not spun inbetween trigger pulls. my question is, can you show me the odds of getting shot if you go first? second? (I assume both are 50%) For whatever reason I cannot reach an answer

[/ QUOTE ]

Come on guys. If you go first, you get shot if the bullet is in chamber 1,3, or 5. If you go second, you get shot if the bullet is in 2,4, or 6. Either way the probability is 3/6 = 50%.

[/ QUOTE ]


I blame it on years of breathing L.A. smog back when all the cars used leaded gasoline.

PairTheBoard