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Comment by Dalewyn | Hacker News Reader

I once heard a wise doctor say that even if the chance of survival for a medical operation is either 10% or 90%, the practical chance the patient is battling is always 50% because he either lives or dies from that operation.

Likewise, the chance of someone being in an aviation accident is close to nil (you're more likely to be in a car accident), but you are either going to be in an aviation accident or not (a 50% chance) and you're going to be either dead or alive from it (a 50% chance).

So you might as well at least not have your epitaph be "Killed by some bozo in the aisle TikToking" if you do end up dying.

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> even if the chance of survival for a medical operation is either 10% or 90%, the practical chance the patient is battling is always 50% because he either lives or dies from that operation

I think this is rarely a productive way to think about it. For example, the chance that I might die in the next year is somewhere between 0% and 100%, and actuarial tables put it somewhere around 0.3%. [1] Should I refrain from having a kid because I'd have a "50% chance" of leaving them without a dad before they turned 1?

[1] https://www.ssa.gov/oact/STATS/table4c6.html

Well, using this logic, every day you have a 50% chance of dying, since you either die or you don't. Or perhaps every second you have a 50% chance of dying.

...obviously this "math" doesn't quite work out.

I mean, it clearly doesn't work if taken to be literal probabilities. But I think it also doesn't work as a more metaphorical guide to life?

It clearly does not work in any circumstances. We over-emphasise the likelihood of rare events already, saying that something has even odds just because it is conceivable that it could happen is completely useless.

Which is not to say that you should not plan for extremely rare events, but you certainly should not make decisions assuming they are likely to happen.

I think you're maybe missing the point. My understanding would be something like:

My chances of being killed by a shark is basically 0%. But, if I'm in a shark cage surrounded by sharks the idea that some global probability is 0% isn't relevant. Something like that?

If I'm in a shark cage then the probability that matters is conditional on being in a shark cage, sure. And it should certainly be higher than the global probability. But I don't see how this connects to saying that anything that can go two ways is 50-50? ("always 50% because he either lives or dies from that operation")

I think the 50% part should be ignored and the message is "when dealing with an individual sample, the general probability distribution isn't that useful?" I don't actually agree with that, just trying to steel man the point a bit. I do kind of see what he means

There's also a 50/50 chance a world ending meteor hits in the next minute. But don't worry, there's a 50/50 chance you'll win the lottery tonight.

There's a 50% chance that this doctor failed probability

I recall the original context was that telling a patient to not worry because the chance of success is high isn't actually helpful, because the objective argument doesn't take into account the patient's personal perspective.

I've since extrapolated that to meaning that objective measures cannot always tell or respect the whole story, because personal perspectives can bowdlerize everything down to life or death or a 50% chance.

To put it another way: Telling someone they have a negligible chance of being in an aviation accident is worthless comfort if they end up in one.

> Telling someone they have a negligible chance of being in an aviation accident is worthless comfort if they end up in one.

It's significant comfort in all those flights where no crashes occur, and for most of the time up to and during those that do end in crashes.

Anyone who really believes they are about to embark on an activity having a 0.5 probability of killing them should put their affairs in order, but then, by the same reasoning, there's a 0.5 probability of dying while doing that!

I believe the fallacy here is using an uninformative uniform prior when a much better, empirically-verified one is available.

> To put it another way: Telling someone they have a negligible chance of being in an aviation accident is worthless comfort if they end up in one.

Sure. It’s also callous and insensitive, which is why we don’t tend to do that. But saying to the vast majority who are never going to experience a plane crash (a number larger than the number of victims by a few orders of magnitude) that it’s a coin toss is at least not very smart.

>because the objective argument doesn't take into account the patient's personal perspective.

Suppose a friend is afraid of crossing the street. Would it be more helpful from a personal perspective POV to tell your friend the odds of being hit by a car, or to make up the fact that you are just as likely to die today crossing that street as not dying? Because the latter strikes me as unhelpful from either an objective perspective or a personal perspective.

The purpose of probability is not to give you good feelings

I had a dentist explain to me that my lip could go numb with a 50% chance after my wisdom teeth removal with that exact explanation just two minutes before the surgery. I was infuriated, turns out I was on the lucky side of her coin.

I could be wrong, but I really don’t think permanent loss of sensitivity is anywhere that high. Though it sounds low for temporary loss, but then it goes away after a couple of hours or so.

Yep, that was for permanent loss.

It can really depend on how badly impacted the wisdom teeth are. There's apparently a lot of nerve bundles around the back of the jaw bone. If they really need to dig in there to get it out there's a risk. I've had multiple dentists talk to me about my wisdom teeth and all have talked about there being some significant risks with mine.

Cue 50-50 scene from the movie The Naked Gun:

* https://www.youtube.com/watch?v=aLLbuyWBCzQ

Also relevant (hilarious movie btw): https://www.youtube.com/watch?v=DrezGdru6TQ&t=20s

And an analysis of the scene: https://puzzlewocky.com/fallacies/the-50-50-fallacy/

(I don't think that's what most mean when they say 'chance', but I get what you mean ;) It's similar to realizing how seating choice radically alters your (very small) chance of death by train crash.

I was going to say 'chance of death on that day' but apparently rail transport is remarkably safe and in micromorts, you're as likely to die in one day at 20 years of age as in 10000 km by rail, or (only!) 1600 km by air.

Now, it appears that 1600 km is also nearly the distance of the average passenger flight (a disappointly difficult datum to discover on the internet in 2024). Is this a counterpart to the reassuring quips comparing the chances of death by lightning: that boarding a plane doubles your chances of dying that day?

https://en.wikipedia.org/wiki/Micromort#Travel

This is very silly. There are much better ways to express the idea that a binomial distribution is different than a multinomial or continuous one than to make up fake statistics.

By that logic, there's a 50/50 chance the sun will come up tomorrow.

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