Russian Roulette And Certainty

An American Classic
An American Classic
Suppose one fine day you pick up your Smith & Wesson 586 ($809 MSRP), a .357 Magnum revolver—which means that thingee in the middle spins around, advancing one round at the time. It has an old-fashioned, manly wooden grip and six inch barrel (not wooden).

You savor it for a moment, considering it is not, or at least not yet, on a list the White House can peruse. Then, as you take out your cleaning rag, a knock comes at the door! The rag and oil can are pushed aside. As you load it, you shout, “Just a minute!”

The hallway seems longer than usual. But as you near the door—the gun comfortably nestled inside your pocket—you begin to relax as you recognize the outline of the man standing at the entrance. It’s your neighbor Fred, a professor down at the college who frequently drops by to try his latest theories out on you.

Fred had been reading Peter Kreeft’s Summa Philosophica and came across this passage:

[S]ometimes we need certainty, e.g. in matters of life or death. If a gun had 100 chambers, then 100 of them must be checked, yielding certain safety, and not just 99, unless you want to play “Russian roulette.”

Fred notices the bulge in your pocket and says, “What a coincidence! Would you, for one million tax free dollars, play Russian roulette with your .357? One chamber with a round, the others a empty, and so forth?”

Since you are not an idiot, you say no. This is because you deduce there is a 1 in 6 chance you’d fail to take the dog for his evening walk, this night or any other.

It is not certain you’d live, nor is it certain you’d die. If it were certain you’d live, every chamber would have to be empty; and for it to be certain you’d die, every chamber would have to be loaded. So much is elementary.

But Fred makes the game more interesting. “Suppose I were to build a machine which is like your gun but could hold N chambers. Only one would be loaded, the rest empty. Same game. How large would N have to be for you to play?”

And that, dear reader, is the question to you. Is an N of 1,000 large enough? That gives you a probability of 999/1,000 of not ceasing upon the morrow. But it’s still a 1 in a 1,000 shot of the wrong kind of haircut. Maybe 10,000?

Besides telling us your N, would you agree with me that no matter how large N gets it is never certain you will survive? And that the phrase practically certain has the same logical relation to certain as practically a virgin has to a virgin?

Do you think you would say N = NA, or N = NaN. I.e., no number? That you would refuse to play? Then I wonder why you strap yourself into your car and drive yourself to your paycheck-issuing location each weekday. There is, after all, a non-zero chance that you will become the subject of a high school drivers training film.

Real examples abound. Flying, skiing, walking along a road, eating donuts, listening to NPR, etc. All which prove you are willing to endanger your life in return for moola or thrills.

Is there a difference between purposely risking your life, as in Russian roulette, and routinely risking it, as in driving to work? If so, what is it?


26 Comments

  1. Small point: you can’t be 100% certain that the next trigger pull will result in a discharge even in a fully loaded gun with the safety off. Sometimes there are duds.

    Is there a difference between purposely risking your life, as in Russian roulette, and routinely risking it, as in driving to work? If so, what is it?

    None, particularly if there is no cost/benefit consideration.

    Most people (I assume) consider the benefit vastly outweighs the risk in driving to work. Plus there’s that, I’m in control, feeling that tends to minimize perceived risk.

    Russian roulette seems to convey no benefit so the price for doing it would be very high. For some, perhaps the thrill would be enough.

  2. I don’t need the money. So I wouldn’t play as this is a completely avoidable risk.

    Change the circumstances and the reward and it might be a different. Perhaps my child has a dread disease that disfigures/debilitates but isn’t fatal and the reward is the cure.

    Probably N < 50. Thinking about it is making my head hurt.

    It's a fascinating conundrum.

  3. “s there a difference between purposely risking your life, as in Russian roulette, and routinely risking it, as in driving to work? If so, what is it?”

    Yes, there is a difference. The majority of accidental deaths occur inside the home. This means that driving to work is arguably the less risky alternative.

    Safety is an illusion. There are no alternative options that entail zero risk of premature death.

    Assuming as stated in the article, a 1/N chance of death vs a $1 million tax free payout for surviving it becomes financially stupid not to pay once N gets large enough that 1/N falls below the background risk that you will die in the next second or so without playing.

    While the exact point at which N becomes large enough is difficult to determine we can put an upper bound on it. Average US life expectancy is 78.49 years which comes to 2,476,956,024 seconds. So the point at which N becomes large enough that it’s stupid not to play is less than or equal to 2,476,956,024

  4. “And that the phrase practically certain has the same logical relation to certain as practically a virgin has to a virgin?”

    Actually, this I’d disagree with.

    Assume that Certainty and Virginity both = 100. Assume that the Practical Certainty Quotient (PCQ) and Practical Virginity Quotient (PVQ) both = the maximum possible fraction of 100 that does not equal 100. The question then becomes: What’s the minimum physical increment by which PCQ and PVQ can fall short of a perfect 100, and does that reduce PCQ or PVQ to values which cannot be practically treated as equivalent to 100?

    The PCQ of the Russian Roulette example, above, can reach 99.9 to any arbitrary number of places depending on the defined size of N. If you define the difference between virginity and non-virginity as the flat either-or “has engaged in heterosexual intercourse,” on the other hand, then PVQ can only be 0 or 100. So while PCQ may never be able to reach 100 it can certainly reach a number high enough to be equal for all intents and purposes, while PVQ may not be able to; both PCQ and PVQ meet the definition of “not 100%,” but this is not the same as saying they are identically valueless in assessment.

  5. Most people die in bed, so you don’t want to play Russian roulette in bed or you’re a goner for sure.

  6. MattS,

    Average US life expectancy is 78.49 years which comes to 2,476,956,024 seconds. So the point at which N becomes large enough that it’s stupid not to play is less than or equal to 2,476,956,024

    Or N of any value once you’ve passed your 79th birthday?

  7. Interesting that I was thinking N = 1000 or so until you mentioned the risks I take every day! I would seriously consider N = 100.

  8. DAV,

    I was only describing the calculation of an upper bound to the point at which not taking the risk becomes the less rational decision.

    If you want to get to a specific number for a specific individual it gets far more complicated. To address your specific example of someone who is already 79 you would have to dig into actuarial tables, but I would think that for example your odds of reaching 100 years increases significantly if you have already passed average life expectancy with no major health issues.

    It would never make sense to play at N=1, or even N=2.

    For just $1,000,000 I personally wouldn’t consider playing at any N < 1000 unless I was told I had less than a year to live.

  9. Insurance companies estimate that most people value their lives as being worth between 3 and 10 million dollars. They come to this conculsion by looking at what a person is willing to pay for something that might improve their safety and the likelihood it saves their lives. For example, if you have paid $35 divide that number by the chance that your house catches fire while you are asleep (say 1/100,000 over the life of the smoke alarm) for the sake of this exercise) we can say that you value your life at at least $3.5 million.

    Of course, there are some behavioral confusion to this…. a person unwilling to pay more than $100 to prevent a (1/100,000) risk may not accept payment of $100 to take on a 1/100,000 risk, although most economic models say a rational person should. And, if that person was willing to accept $100 to take on a 1/100,000 risk doesn’t mean that he would be willing to accept 10,000 to take on a 1/1000 risk.

    Why does it seem so much harder to think about sitting down and taking a risk deliberately than it does to go about one’s life and take many risks without much concern? Maybe it is because I believe I am a safer than average driver and I won’t be killed. Or maybe it is the illusion of control.

    Nonetheless, there exists an N for which I would play Russian Roulette, because a million dollars for a 1 in a million chance, I think I would take that. I don’t want to think too hard on what the smallest N might be such that I would play that lottery.

    As Terry Pratchett said, the million to one chance turns out 9 times out of 10.

  10. I lose nothing if I don’t play the life-or-death roulette game. I can’t lose anything that I don’t have to begin with.

    However, I might lose my job if I don’t take the risk of driving to and from work. Just another way of weighing our decisions.

  11. I agree with JH. I drive because I have to go to buy groceries, see doctors, etc. Yes, sometimes I do go for “pleasure” drives, but again, it is something I value.

    It is probably true that when N hits the number of people who die in car accidents in the area in which I drive, the gun and the car are equally dangerous. Perhaps it has more to do with the “thrill” value in the roulette–it’s immediate and a real adrenal rush (assuming you don’t get the chamber with the live round). Same for race car driving, sky diving, extreme sports, etc. Some people are willing to take huge risks for the adrenaline rush. While this is about risk, it’s also about risk/reward. If you don’t need the money and you don’t like the rush, you probably will pass on the offer.

  12. MattS,

    I guess subtlety doesn’t work. Your calc is upside down. If you only have 1 year left to live (vs. 78.5) then you are effectively devaluing the remaining minutes. N=31,536,000 (for 1 year) against N= 2,476,956,024 for 78+). I would think the value of 1 second would rise instead of falling. Old people seem less reckless than young people. Could it be they value their remaining time more?

    It would never make sense to play at N=1, or even N=2.

    Surely you mean for yourself. Some might argue that no amount of money is worth the risk while another might settle for $100K. Some people take seemingly inordinate risks for the sheer fun of it. It really depends on how one views the costs & benefit analysis.

  13. DAV,

    “Old people seem less reckless than young people. Could it be they value their remaining time more?”

    I would consider this observation questionable at best. I would say from my own observations that recklessness/risk aversion has little if anything to do with age.

  14. DAV,

    “Playing Russian Roulette with a non-revolver doesn’t leave much to chance.”

    Not necessarily true, it just takes more preparation. Create a bunch of duds by removing the bullet, dumping the gunpowder and replacing the bullet. Mix one live round into the duds and load the magazine on the semi-auto.

    Blanks won’t work because they are visually distinct and at point blank range even a blank round can kill.

  15. Crazy. I was right there with Sheri’s 1st sentence. I was going to spout some babble about driving to work to buy food to stay alive. Reality is I drive like a drunk Frenchman except I do it on my morning commute. But I would not put your 1000 round revolver to my head willingly. Then again. Put the same gun to my wife’s head and I will demand you point it at me and pull the trigger.

  16. I see a difference: It is the case that if I pull the trigger enough times, the negative result will occur (adopting an arguendo position, with all the normal conditionals assumed) . It is not the case that, if I drive a large number of miles, I will be in an accident, of any kind.

  17. Bill – Interesting comment about someone putting the gun to your wife’s head and you would demand you take her place. People do seem more willing to risk death themselves than watch a loved one do so. Hadn’t thought of that factor.
    Maybe we should ask if one’s choice of taking the risk for the million dollars in a Russian roulette game would be different if their spouse/child/parent were in the room at the time of game?

  18. The movie “13 Tzameti” (being remade as “13”) takes the Russian Roulette to its extreme. There is a tremendous amount of money available to the one who survives.

    Would we play RR if the stakes were high enough? If we knew that our insurance would pay our families if we lost? If we knew (with high certainty, of course) that we were dying soon? And, how “soon” is “soon”?

  19. Funny nobody is answering this question considering what happens *after* you lose the game. It’s one thing to go to your Judgment having died in a car crash or choked on a bite of steak. It would be entirely different to go to Judgment having just shot yourself for a chance at some unnecessary money. This would be the overarching concern for me and why I wouldn’t play the game.

  20. To the layman, this is an example of likelihood of the event happening vs the importance of it happening if it did. On a 10 scale, likelihood X importance.

    Low likelihood: 1 High importance, death:10.
    Even 1 X 10 = 10, too high a risk.

  21. I might point out one other philosophical issue here: when the probability of an extreme consequence is believed to be extremely low, it is dwarfed by the possibility that the belief about that probability (i.e. the model) is itself wrong. I once read a paper that dealt with “low-likelihood events” in this way, e.g.:

    [Probability that turning on the LHC will create a black hole and swallow up the earth: 0.0000000001] times [the cost if that disaster occurred, let’s say: 100000000000] = “expected” loss

    vs.

    [Probability that the PROBABILITY is actually much higher because our theory is wrong: 0.01? 0.001? who knows?] times [Probability of earth-consuming black hole disaster given alternate theory] times [cost of disaster] = significantly higher expected loss

    In the case of Professor Fred’s proposition, if he were to say that N is 1 billion (there’s a 1/1000000000 probability of dying), we would also have to consider also the small (but higher than 1/1000000000) probability that, for example, the game is rigged somehow. At a certain point N can keep increasing but our aversion to the game will not decrease because we’re thinking of these other risks.

  22. Well i think you’re asking the wrong question, Briggs. You should ask what the ratio is. How much $$$ would it take for 1/N roulette.

    For a trillion dollars many would probably go with a normal revolver. For $1, you’d probably need a 1 in trillion machine.

    Now then for me:

    1) As a thought experiment: I would probably play RR at a 1/5 chance at a guaranteed $1 mil. (in other words, I’d wager my life on a 1 mil payout on a 1 in 5 odds)

    2) In real life (and the problem with thought experiments and a lot of statistics), there are too many factors that play out in our minds. If the benefactor is going to pay out some insane sum, then I can increasingly assume he might be willing to cheat. I could likewise cheat by picking a gun I know frequently misfires and/or loading it with the wrong bullet type, etc.

    Which is why “ordinary” people are so “bad” at statistics (at least many statisticians seem to think so). Statisticians seem to take everything at face value. Most people realize that everybody cheats. 😉 (see for example: Monty Hall riddle)

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