# Logic puzzle: Russian Roulette

Here is another logic puzzle, see what you think:

You are tied to your chair and can't get up. Here's a gun. Here's the barrel of the gun, six chambers, all empty. Now watch me as I put two bullets in the gun. See how I put them in two adjacent chambers? I close the barrel and spin it. I put the gun to your head and pull the trigger. Click. You're still alive. Lucky you! I'm going to pull the trigger one more time. Which would you prefer, that I spin the barrel first, or that I just pull the trigger?

1. spin it.(but ,actually it wont make a difference because there are only two chances hit or miss)

2. Michael says:

Spin it again (33% is better than 40%)

My gut reaction was "spin again, there’s a 1/3 chance of getting shot each time it’s revolved, but you’ve used some of that chance up if you don’t respin", inspired by the goat and 3 doors puzzle. However, that’s wrong.

There’s a 1/3 chance you’ll get shot on the first trigger following a spin. As the bullets are in consecutive chambers, let’s number the chambers 1 to 6 and have bullets in chambers 1 and 2. If you live after the first trigger, there’s a 1/4 chance the gun was on chamber 6 and would kill you on the next shot, in other words a 3/4 chance you’ll survive if you don’t respin vs a 1/3 chance if you do. So please don’t spin.

4. Garry says:

Spin, That leaves me a one in six chance of the barrel being full, otherwise I am left with a 1 in five chance

5. Wax Eagle says:

spin again. For 2 reasons. 1 there is a 4 in 6 chance a spun chamber is empty. There is only a 3 in 6 Change that the next chamber is empty. Also if you spin the bullets are heavier and this should cause them to settle in the bottom two or three chambers when the gun is spun.

6. James says:

I’d prefer it if you just pulled the trigger

7. Whatever says:

The donut was was interesting – now this is a little creepy….

8. Dave says:

Always spin the barrel before you shoot, the fact that the first was an empty slot means you have reduced odds for the next shot. At best you are 3/5 to live, a fresh spin is 2/3 to live.

My math may be fuzzy, however

9. Hanan says:

After spinning there is a 1/3 chance of the chamber being filled.

After firing the first time and it being blank I can now eliminate the which chamber is next by two. It can’t be the blank chamber that was just fired and it can’t be the second of the two loaded chambers. It’s possible that the blank that was just fired is the one after the loaded chambers leaving me with a ratio of loaded/onloaded chambers of 1/4.

Just pull the trigger again.

10. Cole says:

Just pull the trigger. By spinning again there is a 33% chance of landing on a bullet. However, by using the old position there is a 25% chance that the space it’s on is right next to a bullet and when cocked will move to that bullet spot. That is, assuming the gun is cocked…..

11. Michael says:

I’m not much of a stats guy but I’d say just pull it again. Please post the analysis behind your question!

12. Michael Fayez says:

I think just pull the trigger (this has probability of 1/4)

while spinning the barrel will have probability 2/6)

13. HeartattacK says:

Simple…I’d say "Just shoot!!".

If I’m alive after the first shot, it means that in order for me to die on the next shot, the first shot would have to be fired from the slot before the one before the one that contains the first bullet. That’s a 1/6 chance. If the barrel is spun again, it’d leave me with a 2/6 shot of dying as two slots have bullets in them. 1/6 is half of 2/6 and as such, I’d have a greater chance of living if the trigger were pulled without spinning the barrel.

14. Brandt Beal says:

I would rather you spin the barrel first.  There is a 40% chance of biting the bullet after the first spin since the first chamber was empty.  By spinning again the chance of dying reduced to 33%.

15. Chris Hardy says:

I’d spin the barrel again as the first time you spin it you have a 1/3 chance of getting shot but the second time there’s 1/6 chance that you’ll get a bullet.

The other option is that you have a 1/2 chance that the next chamber contains a bullet since one of the free chambers has been revealed.

Personally I wouldn’t like you pointing a gun at me.

16. Brandt Beal says:

My bad, i didnt’ read the two ajacent chambers.  The original chance stays the same 33%.  However, the result changes.  After the first spin there is only a 20% chance that the next click will be the bullet (1 in 5).  So I would rather you pull the trigger with out spinning.

17. Koolraagaa says:

At the start the probability of getting shot was 2/6 i.e. 33%

Now once a Blank is fired, the probability of getting a bullet next to it is 3:1 blanks so it is better not to spin before trying the next trigger.

18. Gregory Suvalian says:

If you click next then your chances to get empty slot is 3 out of 6 while if you spin it’s 4 out of 6, so spinning always wins.

Variance in number of chambers shall have no effect on logic so if you had only 3 chambers then spinning will be the only chance to stay alive.

19. G-Man says:

I would prefer you spin. If you spin I have a 4/6 chance that it’ll be a blank chamber. If you pull I have a 3/5 chance which is slightly less that if you spin. Am I right?

20. Bengan says:

Assume the chambers are numbered from 1 through 6 and that the two chambers containing bullets are assigned numbers 5 and 6.

After pulling the trigger once (and surviving) we can be sure that the next chamber will not be chamber 1 or 6 (since that would mean that the last chamber contained a bullet).

The remaining 4 chambers, of which 1 contains a bullet, have an equal probability of coming up next, giving us a 3 out of 4 (75%) chance of survival.

Spinning the barrel would mean that all chambers have an equal chance of coming up next, giving us a 4 out of 6 (66.667%) chance of survival.

Survival chance breakdown:

4/6 or 66% for first pull after a spin

3/4 or 75% for the second (provided the gun hasn’t fired yet)

2/3 or 66% for the third

1/2 or 50% fourth

0/1 or 0% fifth (duh)

21. Ian says:

Spin again !! (33.3% chance you get the bullet)

Click again (50/50 chance you’ll be history)

22. Garry Trinder says:

There are 6 chambers and 2 with bullets — Hence your odds of being shots if you spin are 1 in 3.  (33%)

There are 4 empty chambers: 3 of them are followed by another empty chamber, and 1 is followed by a bullet.  Hence your odds of being shot if you don’t spin 1 in 4.  (25%)

All tolled, you have an 8% better chance of being killed if you spin again.

23. Steve says:

Spin it again so my odds are increased of another empty chamber being fired since you will be putting the previously fired round back into play.

24. Jeff says:

25. Nick Miller says:

If you spin the barrel, you start over with a regular probability of 4 empty chambers out of 6 total, which is a probability of 2/3 that you will survive.  You can figure out the probability without spinning it by realizing that there are 6 possible combinations of two adjacent chambers.  3 of those combinations do not contain a bullet, 3 of them do.  That gives you a probability of 1/2 that you will live.  That means you should spin the barrel because 2/3 > 1/2.

26. James says:

The probability of the next chamber being full is 2/5.  If you spin, the probability is 2/6.  That’s a 7% greater chance of living if you spin it.

27. Jason says:

Spin it so you have a chance at getting the empty chamber you’ve just used.

28. Chris Eargle says:

If I’m in this situation, I tell you to just pull the trigger. I like my odds of survival better.

29. Dustin says:

Please don’t spin. You have a 1/3 chance of having one at the spin. 1/5 if you don’t. (I think that’s right anyway)

30. Dave says:

That seems pretty straightforward, if a little counter-intuitive.  I would want you to pull the trigger without respinning the barrel.  If you were to spin it again, I’d have a 2 in 6 (33%) chance of contracting high-velocity lead poisoning, but I’d only have a 1 in 4 (25%) chance if you didn’t respin the barrel.  That’s because, while you’ve used one of the empty chambers, you’ve ruled out one of the loaded chambers.

Good one; I’ll have to ask my friends the same question, right after I ask them if they should pick another curtain after Monty Hall shows them what’s behind one of the ones they didn’t pick.

31. Jason Lee says:

The first time the gun is spun and fired you have 2/6 or 33.3% chance of getting a bullet in the noggin.  Upon getting the click (no bullet) You have a 50% chance of getting a bullet on the next pull of the trigger.  I’ll stick with the percentages and have him spin the chamber again.

32. Lee Culver (Microsoft) says:

Pull the trigger again.  If you spin the barrel I have a 1 in 3 chance of being shot.  If you pull the trigger a second time, I have only a 1 in 4 chance of being shot since you put the bullets next to each other.

33. Brian says:

I’ll take the spin and the 4:6 odds over the 1:2 odds of the next chamber being full.

Assuming the spin is random you have 4 emtpy holes to hope for. The next shot must either be an empty or a bullet.

34. CodePosta says:

Just pull the trigger again.  The chances of the next chamber being empty is 3:1.

35. You’ll laugh, but I found it easier to solve by brute-forcing a solution in C# than to think about it logically π

In a million iterations, without spinning you get 75% of survival (3/4) and with spinning you get 67% of survival (2/3).  So it’s best if you don’t spin the barrel.

36. Chris says:

Umm, just pull the trigger?  Odds are 1/4 that youll get shot, vs 1/3 if you spin first?

Is that right? There are only 4 possibilites left now that the first has missed.  bullet, empty, empty, empty.

No?

37. Cary says:

I’ll take another spin.. By spinning each time you have a 1/3 (33.3%) shot at eating a bullet.. Now that you’ve had one of the possible empty chambers fired your chance of having an actual bullet in place is higher with a 2/5 (40%) chance.

38. GPirate says:

spin the barrel and hope the gravity is on my side π

39. A Developer says:

I would spin the barrel because that increases my chance of survival by 6.67%. So if you were not spinning the barrel my surival chance was 60% (3*100/5). But the moment I asked you to spin the barrel, I increased my chance of survival to 66.67%(4*100/6). Make sense?

40. Meg says:

spin.   that would be a 1 in 6 probability.   If I picked just pull trigger again, it would be a 1 in 5 since I have no knowledge of where the 2 bullets together would be.  The only benefit for knowing the 2 bullets were adjacent would be if I were already dead π

41. Max says:

The wise choice would be to ask you to spin the barrel first because I would have a chance of 4/6 not to be shot again. If you do not spin again there would be a smaller chance of 3/6 because the bullets were put in 2 adjacent chambers.

42. I would prefer if its my turn now…

You have an equal chance on landing on any of the 4 empty chambers. Only only will be lethal on the next shot… So my chance of survival would be 75%, vs 2/3 on a spin

I think dont spin it…

43. Nick Miller says:

I’ve posted once before, but after further thinking am changing my answer.  The probability of living if you spin the barrel stays the same as my last post, 2/3.  If you don’t spin the barrel then you can count that there are 6 possible combinations of 2 adjacent chambers, 4 of which begin with an empty chamber and only one of those 4 combinations have a bullet in the second chamber.  So, the probability of living if you don’t spin it is 3/4.  So you don’t want to spin the chamber since 3/4 is bigger than 2/3.

44. Mark says:

Do what you want – it’s Russian Roulette, and as I’ve had my turn – it’s yours next – so go ahead, you decide!!!

45. Alfred says:

It is Russian roulette! – So you spin it and put it against your own head, – It is your turn now.

However, I suggest you to spin, – If you spin the barrel, you now have a 2/6 chance of death equaling 33.3%, and have 1/4 of being shot, if not to spin.

We both know that this is much easier than Georgian aggression on Ossetia.

Regards, Alfred.

46. Jason says:

I’d prefer you just pull the trigger.

after the first empty shot, there are only 4 potential positions the chamber could be in, with 3 being safe, or 75% chance of living. Spinning it would result in 4/6 being safe, or 66%.

It’s only a 9% gain, but every bit helps π

47. achh1 says:

Spin it again… It anyway a game of chance.. Not spinning again decrease the chance while spinning it again may increase the chance…

48. ZagNut says:

Pull the trigger.  There’s only a 1-in-5 chance I’ll be shot.  If you spin again, it’s 1-in-3…

49. Jeff says:

Just pull the trigger again.

There’s only one of the four chambers that was empty which is followed by a round. Given that we know the first chamber was empty, there’s a 25% probability that it was the one chamber followed by a round. (Or if we didn’t know it was empty, it’s a 16% probability that you hit the one before the live round)

If you spin it again, there’s a 33% probability you’ll hit a live one.

50. Jon says:

Don’t spin – because the two bullets are contiguous there’s actually a 1/4 chance it’s in the next chamber (bullet 1 has an equal chance of being in chamber 2,3,4 and 5).  If you spin it, there’s a 1/3 chance you hit a bullet.

51. psycotech says:

Shoot me twice. If the first one hasn’t killed me,i still have hope the second one will. but its only a 1 in 4 chance.

52. kudlur says:

Pull the trigger. Only 25% chance of dying.

Spin the barrel 33% chance of dying.

So I am ready to "bite the bullet". Go ahead and pull the trigger..

53. zafi says:

Definitely I would prefer you to pull the trigger without spinning. It is because there is a chance of 1/5 of getting the bullet (since the bullets are in adjacent chambers) whereas if you spin there is a chance of 1/3(two out of six) which is much more dangerous.

btw nice dream you are having about firing π

54. Ajay Deewan says:

I’d say you spin the barrel first because that increases the chances of aligning the empty chamber with the trigger. In this case I have better chances as this means getting 4 out 6 chambers to survive (4/6 = 2/3 = 66%)

The second option of just pulling the trigger has lesser chances of me surviving as one empty chamber has already been consumed and now I have just 3 out of 5 chambers to survive (3/5 = 60%).

55. gus says:

I like this kind of problem; variable change?

Round 1: Odds are 2/6.

Round 2 without spinning: Odds would be 2/5 if I didn’t know what position the bullets are in. However, without spinning the barrel, I know that it is impossible for the next position to be the 2nd bullet (or I’d be dead) or the next position to be the 1st space after the 2nd bullet (again I’d be dead already…) which means that odds are really 1/4 without spinning. I think that’s right anyway…?!

Round 2 with spinning: Odds revert to 2/6

So I would prefer you NOT to spin the barrel please as 1/4 is lower than 1/3 (or even 2/5) π

If that’s right do I win a prize? π

gus

56. Christian says:

That’s simple: spinning the barrel again giving me a second 3-1 chance of survival as opposed to a 2:1 chance of survival without the second spin.

57. Alex says:

The pin is now in an empty chamber, one of a row of four. The chance that the next chamber is empty, is 3 out of 4 (75%). Spinning the barrel gives a chance of an empty chamber of 4 out of 6 (66.6%), so the best bet is to pull the trigger again.

My preference would be to meet you in another situation π

58. Richard says:

Well mathematically speaking the probability of being shot is 1/3. After the first miss, it becomes 2/5 – hmmm, slightly higher. Maths isn’t everything but hey, I’ll take a spin.

59. JosephTyrrell says:

You should spin the barrel. That way you get a 4 in 6 chance of survival. If you do not spin the barrel you have a maximum of 3 in 6 chance. This is because only the first 3 empty chambers after the bullets will have an empty chamber following them.

60. Mark says:

Spin barrel first because I atleast have a chance at the same empty chamber.

61. Venshi says:

I’d say you’re better off just pulling the trigger.

You have a 1 in 3 chance of being shot if it’s spun.

You have a 1 in 4 chance if the trigger is pulled.

Only 4 and not 5 because you know the second bullet follows the first only leaving 4 unknown values.

62. Ken Pespisa says:

Pull the trigger.  You have a one in four chance that the next chamber has a bullet, since there’s only one scenario of a blank followed by a bullet and there are only four empty chambers.  There’s a two in six (one in three) chance that with a spin you’ll land on a bullet.   It’s not much, but you’re better with the 75% chance of being safe than the 66% chance.

63. joshsusen says:

You have 1/3 chance with a spin (2 bullets, 6 chambers, 2/6=1/3) of finding a bullet.

After the click, the problem is the remaining chambers have a total of .66 chance of having a bullet.  Your odds just went down in avoiding those bullets.

64. James says:

Easier to think about the chance of getting shot.

On fresh spin chance of getting shot is 1/3.  Or 2/3 chance of not getting shot.

If you know the last shot was blank and the chambers are consecutive the chance of getting shot is 1/4.  There are four blank chambers and only one precedes the bullets.  Or a 3/4 chance of not getting shot.

So it is better to NOT to spin, unless you want to get shot, then you should find someone with more bullets.

65. Andrew Ward says:

Take the next shot (75% chance that you survive as it is impossible that one of the loaded chamber can be used)