Russian Roulette - Interviewer suggests to play imaginary Russian Roulette with you

[Yarik]

Hi everyone,

This one is not very difficult, but I really like it (perhaps, because I'm Russian? )

Anyway, this is one of the (in)famous Microsoft's interview brain teasers that I think is actually quite good for an interview (assuming that the interviewee is expected to know the basics of logic and probability theory):

Interviewer suggest to play imaginary Russian Roulette with you.

Interviewer takes an imaginary revolver gun with 6 empty chambers, and loads 2 adjacent chambers with bullets.

Interviewer has the first turn: rolls the cylinder, puts it to his head, and pulls the trigger... no shot.

The lucky interviewer passes the gun to you and gives you two options before you put the gun to your head and pull the trigger:

(a) to roll the cylinder again

or

(b) not to roll the cylinder

Which option would you choose?

Bonus questions:

Which option would you choose if 2 bullets were placed into non-adjacent chambers?

Which option would you choose if it was a classic Russian Roulette - that is, if only one chamber was loaded?

Good luck,
Yarik.

[ScottK]

Neither - I would flee from the interview the minute I saw a gun.

[Craig H.]

OK, we know where one empty chamber is, and there are 3 remaining. The other two have a little surprise in them, but they are together, so only 1 counts. That means that there is a 1 in four (25%) chance that things will end badly if we do not spin.

On the other hand, if we re spin the cylinder, there is a 2 in 6, or 33.3%, chance that the thing will go boom. So, do not re spin.

If the bullets are separated, there will be a bullet next to 2 of the empty chambers. We already know where one of the empties is. If we do not spin, then the chance of a bad outcome on the next try is 2 out of 5, or 40%. If we do spin, the chances are 2 out of 6, or 33.3%.

Similarly, with 1 bullet, the interviewer "used up" one empty chamber, so spinning improves the odds from 1:5 to 1:6.

Right?

[Yarik]

In Reply to Parent Post by Craig H.

OK, we know where one empty chamber is, and there are 3 remaining. The other two have a little surprise in them, but they are together, so only 1 counts. That means that there is a 1 in four (25%) chance that things will end badly if we do not spin.

On the other hand, if we re spin the cylinder, there is a 2 in 6, or 33.3%, chance that the thing will go boom. So, do not re spin.

If the bullets are separated, there will be a bullet next to 2 of the empty chambers. We already know where one of the empties is. If we do not spin, then the chance of a bad outcome on the next try is 2 out of 5, or 40%. If we do spin, the chances are 2 out of 6, or 33.3%.

Similarly, with 1 bullet, the interviewer "used up" one empty chamber, so spinning improves the odds from 1:5 to 1:6.

Right?

Well, not exactly...

Would you like to try to reword (or revise) your reasoning? For example, the statement "we already know where an empty chamber is" is not correct. All you know is that "a chamber that is currently facing the barrel is next to an empty one".

[Craig H.]

In Reply to Parent Post by Yarik

Well, not exactly...

Would you like to try to reword (or revise) your reasoning? For example, the statement "we already know where an empty chamber is" is not correct. All you know is that "a chamber that is currently facing the barrel is next to an empty one".

In a revolver, we would know that the chamber under the hammer after the trigger is pulled is empty. As the trigger is pulled (for a double action revolver anyway) the cylinder advances to the next chamber. Of course for many revolvers you could just look at the back of the cylinder and see if there is daylight or not...

[Yarik]

In Reply to Parent Post by Craig H.

In a revolver, we would know that the chamber under the hammer after the trigger is pulled is empty. As the trigger is pulled (for a double action revolver anyway) the cylinder advances to the next chamber.

My bad. Did not hold a revolver for quite some time.

All right, you do know where the empty chamber is. And my suggested correction wasn't a good one, anyway. Moreover, all the final choices that you came up with are correct. But... the probability of dying without spinning in the second scenario (the scenario with two bullets in non-adjacent chambers) was calculated incorrectly, which makes the correctness of your logic in all scenarios questionable. That's why I said that your answers are "not exactly correct"...

In Reply to Parent Post by Craig H.

Of course for many revolvers you could just look at the back of the cylinder and see if there is daylight or not...

Yeah, that's true. That's one of the reasons why our imaginary revolver is so much better for Russian Roulette: (1) you can't cheat by looking at it; (2) it can't kill anybody.

[Neil V.]

you should spin in the second scenario. if the two bullets are not adjacent you only have a 50% chance of the next cylinder being empty. spinning with two of 6 loaded would be the 66% chance of being empty.



if you really were asked this question or one close to it in an interview would it be bad to ask for scratch paper?

[Yarik]

In Reply to Parent Post by Neil V.

you should spin in the second scenario. if the two bullets are not adjacent you only have a 50% chance of the next cylinder being empty. spinning with two of 6 loaded would be the 66% chance of being empty.

Yep, exactly.

In Reply to Parent Post by Neil V.

if you really were asked this question or one close to it in an interview would it be bad to ask for scratch paper?

First, it depends on the interviewer, of course. If I were the interviewer, I wouldn't mind at all. Maybe it's just me, but during interviews I am much more interested to see how people approach the problem and think than to get correct "end results" from them.

Also it may depend on how you (as an interviewee) estimate your chances to solve the problem (or at least explain your thinking) without scratch paper. If such chances are low you might want to take the risk and ask for scratch paper. The additional bonus would be that you'd get a chance to learn something extra about your current interviewer...