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Comment by WA | Hacker News Reader

I once read that the chance of Russian Roulette is NOT 1:6 but more like 1:600, since you play with one bullet and the weight of the bullet makes it relatively unlikely that the bullet stops next to the top position in the barrel when you spin it.

Don't know if this is true but in the end, it doesn't matter for this stupid game.

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Someone reportedly did an informal experiment. One gun, 200 spins. Results:

  Position    Times
  1 (barrel)   20 (0.100)
  2            25 (0.125)
  3            35 (0.175)
  4 (bottom)   38 (0.190)
  5            41 (0.205)
  6 (death)    41 (0.205)

Source: http://boards.straightdope.com/sdmb/showpost.php?p=11585888&...

I love how people have so much trouble understanding the Monty Hall 'paradox', but when you give them basically the exact same problem in the form of Russian roulette then suddenly it becomes trivially intuitive that you REALLY want to spin in between turns.

It's hard to understand even after reading about it :) .

http://en.wikipedia.org/wiki/Monty_Hall_problem

And I did take probability classes (and passed :) ).

I had the same reaction to the link.

But, since I've been checking out the Go language, I decided to whip up a little simulation[1] to prove the claimed probability. And indeed, it is true: choosing the moderator's offer wins 2/3 of the time.

[1] http://play.golang.org/p/7ua2ZCSuVD

The trick is to imagine the same scenario but with a billion doors. You choose a door, and then the moderator closes every single door except for yours and one other door. Then it's much easier to see why it's better to go with the other door.

How do you map Monty Hall to Russian Roulette? I choose a slot, you choose an _empty_ slot - should I spin or not?

Or I choose a slot, you choose the bullet... no that doesn't make sense either.

You spin, fire, no bullet.

I now have 1/5 of a chance that there is a bullet in the next chamber, if I spin I have 1/6th. The odds gets more and more favourable towards spinning, the more people fire the gun.

Depends on if you're re-spinning between turns. Otherwise the first guy might get a 1/600 chance, but everyone afterward has better (or worse?) than 1/6 odds.

Well, if it's the case that there's a 1/6000 chance that the first guy gets hit, it's 5999/6000 chance that the third guy gets it. (Not true, but it's gesturally correct).

So I imagine the odds are much less skewed or NOBODY forgets the spin between rounds. Also, if you don't spin between rounds and you're the 6th person to try it... this isn't really a game of risk anymore.

Why is the parent down voted? He was responding to the hypothetical case that the odds are initially 1/600 due to bullet weight and no one else spins.

Granted, he wrote 1/6000 instead of 1/600, but his basic point is correct: if no one else spins, the odds for each of the other 5 players would not remain ~1/6.

Thanks for the nudge! I did misread the hypothetical distribution the parent claimed. I definitely wrote that response in a hurry as a thought experiment to flesh out what the least bizarre rules for R.R. might be, but I was surprised by the vehement negative response.

Heh, you really have no idea of what you're talking about, do you? (Or are just plain stupid)

One, the other, or both might by true. However, in polite company there is rarely a need to ask the former and definitely not the latter.

Putting other people down, even or especially when they are wrong says more about you than them. Please don't.

I think he understands better than you, quite frankly.

Your odds never change, this is not how maths work. It's always 1/6, just like the odds of getting heads/tails in a coin flip is ALWAYS 1/2 no matter how many times you flipped already. Odds of receiving a certain outcome X number of times in a row can change,but the odds of a single event never,never,never do. Even if you flip a coin 10000 and got tails 10000 times, your 10001 flip also has a 50/50 chance of being heads or tails.

That's not how maths work. You're describing something that works for non-dependent events. Flipping a coin 50 times previously has no bearing on how it will flip the 51st time. The events are said to be independent.

In a six round revolver loaded with a single bullet and then randomized, pulling the trigger advances the next round. The first pull has a 1/6 (or 1/600, whatever) chance of firing. You will fire (assuming no mechanical malfunction and no randomization of the round after each pull) in those first 6 shots with a probability of 1.

Sorry, I honestly thought that you would spin before every try, in which case, every test would have the same 1/6 probability of firing.

Which just means you didn't read the comment to which you were replying...

I did, but because I didn't know that in Russian Roulette you are not supposed to spin before each try, I assumed that the guy I was replying to was wrong.

Simple misunderstanding that I made as well until I read your comment chain.

Im not sure you understand how a revolver works.

This is hacker news, chances are 1/6 he knows what a revolver is.

Revolver is a 1 in 6, but I say much higher he knows what a Desert Eagle or AWP is =). #CSDoesntStandForComputerScience

AWP lol.

Actually, it's 1/2 chance since it's either "yes" or "no".

Ahh, the freshman probability theorem. AKA the Lotto player's defense.

It's not just freshmen and lotto players. Sometimes it derails useful work:

http://www.thedailyshow.com/watch/thu-april-30-2009/large-ha...

Plus I'm feeling pretty lucky today, so how could I lose?

So the chance that I'm God is 1/2? Cool.

Ouch, looks like you are taking a lot of slack for this --- don't worry, I didn't realize the protocol for Russian Roulette was not to spin again after the first attempt, either. You're right if they spun it again afterwards, they are right if you just continue through the 6 bullet slots in the revolver.

Yeah, that's exactly what I thought, was really surprised by the number of down votes initially.

It's because you're underestimating the average intelligence of an HN reader. Basically everyone here knows how probability works for independent events.

He's saying that when it is first spun, the odds are low because of the weighting explained earlier. After that it is not re-spun and is instead advanced to the next bullet, which does change it, because you now are limiting the number of total possible places for the bullet.

I believe he meant that he first person has 1/6 (at least or most...idk) but assuming the next person goes there is one less chamber each time. 1/5, 1/4, etc. until you get to 1/1 at least. There would have to be some change between rounds to change that part.

Actually the chance of the 6th person getting the bullet is initially no greater than the chance that the nth person gets the bullet, since you have to take into account that the gun fires before the first person gets the gun, which happens to be 5/6.

> until you get to 1/1 at least

Possibly even more!

That is true with coin flips because the probability of a next coin toss coming up heads or tails is independent[0] of any previous coin tosses. Assuming you aren't spinning between turns, the probabilities are not independent anymore.

0: http://en.wikipedia.org/wiki/Independence_(probability_theor...

If you're not re-spinning between turns you're not doing independent trials like flipping a coin repeatedly.

Sorry, I honestly thought that you would spin before every try, in which case, every test would have the same 1/6 probability of firing.

People often (well in films at least) spin the barrel out of the gun and then snap it shut at a random time while it is still spinning. That would take your chances back up to 1/6.

I can safely say that is not true. The weight of a bullet is pretty small compared to the weight of a cylinder. Try it (not the shooting part). It's not a big effect.

Spinning the cylinder is also bad for the revolver's timing and cylinder stop/cylinder flutes. So, the odds of pissing off the gun's owner are near 100%, even if you don't end up dead.

I lubs mah guns.

The way I though you spin it is with the gun facing up. The would negate the gravity effect. And yes, people "play" it, stupid drunk people.

With the gun facing up is probably the most reasonable way to play. The round would have a good chance of falling out.

It's terrible but the phrase "life is cheap in Russia" comes to mind, which I think I heard when these videos of Russian kids showing off on tall structures started emerging. Of course kids in most all countries enjoy such thrills.

I thought it was a theoretical game that no one actually plays.

Definitely not just theoretical. List of 'notable incidents' including deaths on Wikipedia[1].

[1] http://en.wikipedia.org/wiki/Russian_roulette#Notable_incide...

Last year alone four people died in the US while playing the game. http://www.huffingtonpost.com/2012/09/05/dion-von-mays-dies-...

Combining this with the 1 in 600 statistic of the grandparent comment, it seems like ~2000-3000 people played Russian Roulette last year. To me, that's even more astounding than the number of deaths -- although the number of deaths is certainly more tragic.

That's a pretty big leap of faith assumption though. Does anyone have a source or a revolver?

I have spun a revolver with one round in the cylinder. First, you wont wait for it to settle, so it doesn't matter. Second, a cylinder is pretty heavy, so even if you did, it's not that big an effect. Third, there is significant friction between the cylinder and the pin it rotates on, which will prevent it from settling in that manner. The 1:600 number isn't true.

Even if the 1/600 estimate(which I'm skeptical of) is correct, it wouldn't translate to that many people having played, but that many trigger pulls.

I think it's more likely that someone who plays once will play multiple times than it is for someone who has never played to start.

That's assuming that everyone who dies from playing it only played it once. It could be that only 4 people played it at all, and they all played it ~600 times.

Incredible.

If you create something, no matter how completely ridiculous and stupid and dangerous and outright retarded it is, and then release it onto the population, someone somewhere will do it. In all likelihood, many people will.

No. You snap the cylinder shut while it is spinning.

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