A Microsoft Interview Question (aka basic Bayes' Theorem)

[AEKDBet]

[ QUOTE ]
If you spin you have 4 chambers without a round and
2 with a round. You have 4/6 to survive when you pull the trigger.

When you just have pushed the trigger:
There are 4 empty chambers. Lets name them 1-4.
If he clicked chambers 1-3 you will get an empty chamber.
If he clicked chamber 4 you are in trouble. [img]/images/graemlins/smile.gif[/img]
That means you will survive 3/4 times.

The conclusion is: just pull the trigger (75% > 66%)

[/ QUOTE ]

This is the exact reasoning I came up with. I am googling bayes theorm now to see if my math is wrong, but I think that the reasoning here is correct.

[karr2242]

Ok I believe I have solved it, however I did think I solved it quickly, and read a post and saw `conditional probability.` That led to some further thought and then I solved it ( I think ).
Take the six-chambered gun. Take spots 1,2,3,& 4 and leave them blank, thus leaving bullets in spots 5 and 6.
When your friend first shoots and misses, this tells you he is in Spot 1 through 4. This rules out the possibility of your next shot being in spot 6 (if it is Spot 6 next, then your friend bleeding on the floor is probably not still alive [img]/images/graemlins/grin.gif[/img] ). Since the first shot was in one of the spots 1-4, and not in spots 5 and 6, the next shot Cannot be in spots 6 and 1.
The next shot is in spot 2, 3, 4, or 5 (shot). There is equal probability that it is Now in any of those 4 spots.
Thus it is 3 spots safe, and 1 spot dead.
Leaving 3/4 , or 75% survival rate.
If you instead spin the revolver, you deal with BOTH bullets as your shot could land in EITHER spots 5 or 6. So 4 spots save you, and 2 spots kill you.
That means 4/6, and a 66.67% Survival rate.

Your best bet to Survive is to Shoot again after your friend does.
This explanation may be a little long winded, but thats just best how I can explain the answer I came too.
I would appreciate a reply back from Ed if I got this (atleast for the most part) right.
Thanks for reading and good Poker to you.
MasterTrav

[EliteNinja]

There are 4 configurations in which the chambers can be in after your friend clicks off an empty chamber.

O - denotes an empty chamber
B - denotes a bullet
X - denotes the empty your friend has clicked off.
() - marks the chamber you will fire (after your friend)

The 4 situations are as follows:

1. X (O) O O B B

2. O X (O) O B B

3. O O X (O) B B

4. O O O X (B) B (in this case you die)


These 4 situations all have the same chance of occurring. And since there is one case where you will shoot a bullet through your head, your chance of staying alive is 75%.

Had you spun, your chance of staying alive is only 66%

On top of having 1.136 times better chance of surviving, you can also appear as being MANLIER to the not so statistically inclined.

Any friend who can convince me to play Russian Roulette with him is not my friend. He can play with himself if he so chooses.

[soko]

I think I solved it. I dont think it matters if you spin it agian or not. Because before the spin there is a 1/3 chance that gun will fire, after a blank you now know the round can not be in the very first position before the round or else the previous round would have been a bullet, and you also know it can't be in the position of the bullet adjacent from there or else the round would have also gone off. so you still have a 1/3 chance that that next round will be lethal.

This is right? [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/cool.gif[/img]

[TomCollins]

[ QUOTE ]
I think I solved it. I dont think it matters if you spin it agian or not. Because before the spin there is a 1/3 chance that gun will fire, after a blank you now know the round can not be in the very first position before the round or else the previous round would have been a bullet, and you also know it can't be in the position of the bullet adjacent from there or else the round would have also gone off. so you still have a 1/3 chance that that next round will be lethal.

This is right? [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/cool.gif[/img]

[/ QUOTE ] No.

[Dan Mezick]

Guys, at the time the first player pulls the trigger, there are SIX possible states for 2 bullets in the 6-gun:

2 Bullets adjacent in 6 possible chambers:

1&2
2&3
3&4
4&5
5&6
6&1 (whoops)

OK, six.

Let's assume chamber #1 was the chamber that clicked for player #1.... with no bullet inside.

That eliminates the first possible state (1&2) and the last possible state (6&1) from consideration, leaving 4 possible states (of initially 6 possible) remaining for the 2nd player to deal with.

Only one of them can kill you now (2&3) so you are looking at 1 chance out of 4 that you are going to die if you do not spin.

If you choose to instead spin the 2 bullets in the 6 chambers, there is a 2/6 = 1 out of 3 chance you will get a headache.

Don't spin and you have a 1 in 4 chance of a bullet.

Spin and you have a 1 in 3 chance of a bullet.

Don't spin.

[JoshuaD]

Why is everyone ignoring the rounds subsequent to that one round? Your analysis ends up coming to the right answer, but there are times where not re-spinning is immediately +EV, but ends up being in the longterm (after a round or two more) -EV.

[na4bart]

I know nothing of Baye's Theorem, read the name somewhere, but that is it, so...

If I spin it the odds are 2:1 I survive.
If I don't spin it would appear either I die or live. Even money.

I opt to spin as I like 2:1 better than even money.

Did I get it?

Edit: [censored], I had it ass backwards. Glad I play poker and am not appling at MS

[CardSharpCook]

PULL THE TRIGGER!!!!!

Your friend has a one in three chance of redecorating the living room. If you were to spin the chamber, the same would be true for you. However, because you know that the loaded chambers are adjacent, if you pull the trigger NOW, your odds of living are 1 in 4.

Of the four empty chambers, only one of them is next to a loaded chamber (as the gun turns). So, your friend shot one of the empty chambers, there is a one in four chance it was the empty chamber next to a loaded one.

FIRE AWAY!

CSC

[Eclypse]

Well, I didn't read any of the replies, so forgive me if this has already been answered this way.

You should pull the trigger again without spinning. The reason is that the revolver always turns in the same direction which means there is a 3-to-1 chance the next pull will be an empty chamber whereas if you spin you're only getting 2-to-1.

The key is that the bullets are in "adjacent" chambers.