Puzzle: Russian Roulette

[primelord]

I saw this on another board and thought I would post it here. The concept should seem familiar to most of you. The standard disclaimer applies. This is not my puzzle, yada yada yada. This may be very easy for some of you, but here goes.


You and a friend are playing Russian Roulette with a standard 6 chamber revolver. You place two rounds in adjacent chambers and give the wheel a spin. You give the gun to your friend and he pulls the trigger.

Click. He hands the gun to you. You have a choice. You can spin it again, or you can simply shoot the next chamber. Does it matter which one you choose? If it does, why?

[albionmoonlight]

I would pull the trigger without spinning. I'll leave my reasoning, however, so as not to spoil it for others (on the chance that I am right).

[Raiders Army]

I agree. The possibility that your buddy pulled the empty chamber next to a loaded one is less than the possibility he pulled an empty chamber next to an empty chamber. Not sure how the numbers work out, but that's my reasoning.

Also, I wouldn't play this game.

[st.cronin]

I break it down like this:

The first shot had 2/6 chances to be fatal. Without spinning, the second shot now has 2/5 chances to be fatal. Spinning it again leaves you with 2/6 chances.

Although the bullets are adjacent... how does that change the probabilities?

1. ----bb
2. ---bb-
3. --bb--
4. -bb---
5. bb----
6. b----b

So the first 'empty' shot had to be either 1-4.
1. ---bb-
2. --bb-
3. -bb--
4. bb---

So actually, there is a 1/4 chance that shot 2 will be fatal...

I conclude you are better off NOT spinning.

[Raiders Army]

Hey also, why would my buddy let me spin for him? If it were me, I'd definitely be spinning it myself.

[Blackadar]

Agreed. Pull the trigger without spinning.

If you don't spin, the 2nd bullet is immaterial. For all intents and purposes, it doesn't exist because it cannot fire withou the first bullet firing. Once the friend pulled the trigger, there's 3 empty spaces left and 2 bullets. But remember the 2nd bullet cannot fire without the first - therefore, it doesn't exist. Without getting too deep into statistics, for me that's a chance of 3 empty spaces and 1 bullet = 25% of a bullet.

Spinning the barrel and starting over means there's 4 empty spaces and 2 bullets = 33% change of a bullet.

I may not be correct, but that's my reasoning.

Of course, I'd turn the gun on my friend and unload the other 5 chambers on his ass for asking me to play such a stupid game.

[st.cronin]

Originally Posted by Blackadar

Of course, I'd turn the gun on my friend and unload the other 5 chambers on his ass for asking me to play such a stupid game.

I actually think this is the correct answer. Aim for the chest, unless he's wearing body armor.

[primelord]

I figured this might be fairly easy for you guys. You are correct pulling the trigger without spinning is the correct answer. And the math shown here is correct. You have a 25% chance of the next chamber being a bullet where as with a spin you have a 33% chance of running into a bullet.

[SackAttack]

Originally Posted by Blackadar

Spinning the barrel and starting over means there's 4 empty spaces and 2 bullets = 33% change of a bullet.

But if the second bullet doesn't exist until the first one's fired, doesn't that actually make it a 20% chance?

(I'm joking, of course)

[BrianD]

On a board like this with all of the poker talk going on, I would imagine any probability question would be answered pretty quickly.

[QuikSand]

Originally Posted by BrianD

On a board like this with all of the poker talk going on, I would imagine any probability question would be answered pretty quickly.

Actually, the history of probability puzzles here substantiallty predates the poker outbreak.

Some of my favorite probability puzzles from this forum:
(at least the ones still standing, not lost to the cyber-ether)

Monty Hall, revisited – probably its third or fourth offering here, but a nice discussion

Monty Hall in Parade magazine – any chance to beat up on Marilyn works for me

The infamous flush puzzle – can’t be revived, but quite a discussion about probability (and in the end, semantics)

[BrianD]

Some very interesting reading in there.

With all of the poker talk that has popped up, do you think a discussion like those you posted is still possible?

I suppose in a different context, the formulation of the actual probability problem could still be open for discussion.

[albionmoonlight]

Originally Posted by BrianD

With all of the poker talk that has popped up, do you think a discussion like those you posted is still possible?

Yes. If someone came to this board and started posting difficult, but not impossible, puzzles, I think that there would be a group ready, willing, and able to engage in that kind of discussion.

The problem, of course, is coming up with the puzzles.

[Franklinnoble]

It's simple, really. I spent the last few years building up a resistance to iocane powder.

[st.cronin]

Originally Posted by Franklinnoble

It's simple, really. I spent the last few years building up a resistance to iocane powder.

You only think I guessed wrong - that's what's so funny. I switched glasses when your back was turned. Ha-ha, you fool. You fell victim to one of the classic blunders, the most famous of which is "Never get involved in a land war in Asia", but only slightly less well known is this: "Never go in against a Sicilian, when *death* is on the line.". Hahahahahah.

[QuikSand]

The enigma puzzles, it seems, have largely turned into cryptpgraphy and crossword-style clues... I guess that style of puzzle just fits the genre better. But we have had our fair share of puzzles in these parts. Quite a few involving probability, too... always a rich subject.

[BrianD]

Originally Posted by albionmoonlight

Yes. If someone came to this board and started posting difficult, but not impossible, puzzles, I think that there would be a group ready, willing, and able to engage in that kind of discussion.

The problem, of course, is coming up with the puzzles.

Yes, thinking about it more, the puzzle isn't in the probability calculations, but in the setup of the problem. Forget I said anything.

[Maple Leafs]

Originally Posted by albionmoonlight

Yes. If someone came to this board and started posting difficult, but not impossible, puzzles, I think that there would be a group ready, willing, and able to engage in that kind of discussion.

Actually, history has shown that any attempt to post an original puzzle on this board immediately results in:
- Dead silence
- The poster making several sad bumps of his own post
- Several people pointing out that there won't be any response because the puzzle is too difficult
- Some half-hearted attempts to solve the puzzle
- Someone getting answer, and posting the entire thing immediately to prove how smart they are
- Several people pointing out that the puzzle was too easy
- Dead silence
- Complaints that nobody ever posts any puzzles

[QuikSand]

I'm willing to take that risk. Maybe we can revive an old favorite...

[BigJohn&TheLions]

Real men play RR with 5 bullets, and only one empty chamber.

[BrianD]

Originally Posted by BigJohn&TheLions

Real men play RR with 5 bullets, and only one empty chamber.

Sure, real dead men.