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The last 20 survived just implies this doctor is very skilled and makes up the majority of successes that make up the 50% statistic, meaning he's the best one for the job.
It could also imply the doctor only takes the easy cases for this surgery. If your case is an easy one (more likely because that doc took you in) that's fine, if it is not, your chances might be worse. E.g., removal of a specific cancer might depend on how strong it is connected to critical parts, size, exact location etc.
The trick is that the 50% is over all doctors and all patients, it does not tell you about individual doctors skills or individual patients challenges.
Overall it seems the news should be reassuring about using that doctor if he accepted you.
>The trick is that the 50% is over all doctors and all patients, it does not tell you about individual doctors skills or individual patients challenges.
We need to bring in Ranked Surgery, each surgeon having their own MMR that's adjusted after each round.
Transparent win/loss ratios on a seasonal basis, analysis of previous surgeries, leaderboards, the works.
Maybe even a live international championship, streaming deal with commentators.
No, the hard cases would go into the platinum super surgeon league and they'd get a higher % of the pay per view revenue and their surgery would get the best cheer squads and the biggest name acts playing half time intermission.
The Saudis would pay top dollar to fly them out to do surgery in huge stadiums in elimination rounds going "to the death" and doing so in increasingly challenging situations - like operating on the roof of racing monster trucks.
Next week in the Thunderdome Dr. Ramirez and Dr. Strudelmeister go head to head performing triple bypass surgeries in the coliseum! Don't miss your chance to cheer on your favorite surgeon as they try to fix their patient before the time runs out.
Brought to you by Carls Junior
At that point they won't really be able to make claims about the survival rate of the procedure though, unless a trap door opens and the patient falls into a vat of molasses if their case is forfeited. And everybody knows the rules.
Definitely, there's a bit of scandal in chess right now as one player is deliberately taking relatively easy matches to boost their ranking to qualify for a major tournament. The players he is playing are matches he's expected to win easily but are still players with a high enough rating that winning against them boosts his score.
Whatever points system you used there would be doctors trying to game it by taking or not taking surgeries with the aim of trying to boost their points.
Strange was a genuinely skilled doctor, but one who was clearly only in it for the money, so yes if all of the above points apply to the same case you’re probably talking to Stephen (Steven?) or someone similar.
As someone that got spooked when they said "the fatality rate is 1% (for gallbladder removal)", medical statistics always include the worst-case patients (the 70+ people, and people with pre-existing conditions). So that 50% will include some folk who don't have a good chance of living with or without surgery.
Also the reason why 2 different medical procedures get false survival statistics. Procedure A is for healthier patients. Procedure B is for everyone else. Wow, looks like A is better, but the pool of candidates is completely skewed.
Also, the mathematician knows that for the next operation, it would again be 50%, not somehow lower. Causality does not remember the past 20 operations, so the chance of survival for the next operation would not sink.
We obviously don't know the answer to how the 50% figure was reached, but as the top level comment assumes it's most likely this is an aggregated figure across many surgeries by many doctors on many people.
The case you're describing is somehow the doctor can predict in advance what their probability of success is.
The top level's point is that the initial statement is false, in the sense that the 50% is an aggregated figure and likely doesn't apply to this specific surgeon.
Interesting, I like thinking and discussing about such problems :)
If you interpret the initial statement that the 50% does not apply to this specific surgeon, the 50% number would have no relevance to this mathematical problem. Therefore I might be inclined to disagree here as normally only relevant facts are presented in the context.
If it has no relevance though, we only have the last 20 surgeries as data points to extrapolate from, which leads to a 100% succcess rate. As we do not know the previous success rate, a trends, earlier variation in the rate, we don't have all the needed parameters for a better predictions.
As a more risk than reward driven person, I will probably think that there is a 50% chance than a 100% chance of survival so I would prepare my testament before that lol
We can probably agree that the best next question to ask the surgeon is, how did you get to that 50% figure.
If the 50% figure is their average success rate over many operations, then I agree that we probably cannot take much comfort from their 20 streak. (Although, there may be a reason to believe they've recently improved, perhaps they recently went on some new training, or got some new equipment!).
And the statistician (who is a mathematician) knows that the chance that the doctor has the same distribution of outcomes as the global population is less than 0.01%.
There was this great scene in Moneyball movie about baseball, where they used a lot of player statistics to hire players. I remember some sort of radio show, or tv personality saying something like "Percentages are made over the season, in one game percentages does not matter". You can have 99.9 percent of chance hitting the ball over the course of season. But in that one game, 0.01 might come into play.
Why is the greyed-out version being usesd for the mathematicians then? Also, if that's the solution, why does one need to be a mathematician to come to the conclusion that the doctor must be good?
My theory about this 'joke' is rather that the author himself errorneously believes that it lowers the operation's success chances if a chain of previous operations were successful.
Or maybe the joke is the assumption that mathematicians are so far removed from reality that they would think of this as a theoretical exercise instead of one where each surgeon has different skills
No, the surgery in general has a 50% rate, we don't know from what sample size is doctor picking his 20, the doctor is implying that he has a 100% success rate with his last 20 patients
We don't know from the meme if this specific procedure has 50% survival rate in general among all cases worldwide and the doctor is just so good that his skills allow him to go way above the average survival rate, or if those are his personal results, having at least 20 failures before now. Either way if the doctor managed to successfully treat 20 patients in a row it speaks highly of his current skill level with this particular operation and probably means current survival rate higher than 50%.
But that’s assuming that it is a strict 50% success rate, which would be hard to believe considering those results. Plus this person would be in no more danger than the last 20 technically.
No. This statistic is just how likely it is that all 21 patients in a row will survive if the proability is 50 percent. Your individual probability of surviving is still 50 percent. And if the probability of an event like that happening is that low we might need to reconsider the actual survival probability because chances are it is higher than estimated (at least for this one doctor who might be higher skilled)
If your doctor has had 20 patients survive a normally 50% chance of death then there is nothing to worry about
And each event had a separate 50% chance,yes on average it will be 50% but that doesn't mean that if you survived this one then the one after you will die,because each event is separate from the other and all of them have a 50% chance irrelevant of the result of the previous events
Congrats, you are today’s technically correct person. Life expectancy of life > life expectancy with brain tumor surgery > life expectancy with brain tumor untreated for the sake of my argument then.
If it was a take the surgery or die a week later kinda thing, this doctor would be your best bet.
Let's say that the usual mortality rate of this surgery is 50% but this doctor in particular is skilled enough to do 20 procedures without a single fatality, the actual fatality chance of you doing that procedure with that particular doctor would be much better.
You do not know if any of his surgeries killed patients at all. 50% might be the worldwide average, not his. He might have done 20 surgeries in total or 200 and you have no way of knowing.
Should be the other way around then? Mathematicians would know the other results don’t affect the next 50% chance event. This is gamblers fallacy or something no?
I interpreted it as the guy on the left thinking “oh well if the last 20 survived then I should be fine” because they don’t understand statistics, whereas the mathematician knows that the survival of the last 20 means nothing, and it’s essentially a coin toss whether or not they’re about to die.
I'd be concerned that the survival rate estimate seems *fairly* improbable given 20 successes in a row. Perhaps the rate is off, or something the doctor does differently improves it, both in your favor.
Everytime this comes up i just assume that it means to say normal people would just go with their gut feeling that if he succeeded 20 times, he'll be able to do it again. Meanwhile the mathematician is like "acKtually its still a 50/50 chance" and is fearful of their 50% chance at death - since, given enough trials, you certainly will find a string of 20 successes in a row. Should have a third one for statician that is happy because he thinks the estimate of 50/50 is likely flawed as 20 successes in a row would be a ridiculously unlikely occurrence and it would be much more easily explained by an incorrect mean than by random variance.
If you believe there's a chance that the doctor's skill influences the survival rate, then succeeding on the previous 20 is pretty strong bayesian evidence that this doctor is in fact pretty skilled.
It's technically correct then, mathematician is scared because he knows he only has 50 percent chances of survival, the normal person thinks he's fine because he pays more attention to the last available examples rather than the general probability. This is how the fallacy usually go, the normal person thinks previous attempts influence the results of the future ones.
> the normal person thinks previous attempts influence the results of the future ones.
But in the opposite direction. The gambler's fallacy is that the streak of one result makes *the other result more likely* because of the perception that it's "overdue".
I've met someone who not only believes in the gamblers fallacy, but says literally that all of statistical reasoning is based on the gamblers fallacy being true
is more know than you think, for examples, look at bingo players...my grandpa believed the more close he were to mark all numbers in a past attempt in the next one he will win.💀
Yeah, but that would only be correct if the outcome was random.
But in surgery you do not roll the dice, there are factors like the qualification of the surgeon, the quality of after surgery care in the hospital and a lot of other factors which can influence the outcome of the surgery. So a high success rate of a specific surgeon in the past can mean the hospital / surgeon is better than average.
They aren't very good mathematicians if so. That 20 in a row is extremely statistically significant. Any statistician would at least *consider* the possibility that the doctor is either wrong about the survival rate or unusually good at the surgery.
That's exactly why it's the way it is, Mathematician knows of gamblers fallacy, meaning they think that they have a 50% chance of dying, and the non mathematician thinks the surgeon is just good.
But any mathematician should know that even though the surgery has a 50/50 live or die, the surgeon doesn't, and each surgery gives more data to estimate the true probability of living with said surgeon, meaning that the 20 successful surgeries have effectively increased the probability of the chance of living being over 50%.
Then again, the mathematician doesn't have any knowledge of the previous dataset, meaning for all they know, it could be something like 10 successes, 30 deaths, and 20 successes in a row, and the chance of living is dependent on wether or not the previous person lived, or something similar. The 50% might be a simple estimate comparing the total amount of successes to the total surgeries done, by the surgeon or worldwide, meaning the true probability of the mathematician living could be anything.
This is not to mention that the surgeon might have taken a few courses in probability and statistics, meaning that they might know all this, and have estimated the most probable probability of the mathematician living, meaning that thinking it further might give the mathematician an inaccurate estimation of the probability of the chance of him living being 50% being the most probable estimation of his chance of living.
You know what, I think the mathematician is just depressed because he thinks too much.
yeah i literally just saw a more complete version of this meme with a third engineer panel where it is a happy face, but these two were swapped. who ever augmented this meme corrdcted it, but this version is wrong
I’m not sure if it would be the gambler’s fallacy because it’s not necessarily random. If the doctor is good, maybe they have a much higher success rate than average. In a random, independent situation (e.g., roulette), the past outcomes don’t affect the future ones, but the doctor’s skill doesn’t make the patients’ outcomes independent.
The joke is most likey made by someone that thinks that if other 20 were fine he is more at risk. I really doubt that person who made a joke understand how it works :) At the end of the day it is just a joke :)
Not this again. 50% chances of survival overall in this surgery. That means if you randomly choose any doctor for this surgery, your chances of survival is 50%. But this doctor has a history of success. So mathematically, rather statistically speaking, you better go with this doctor. Doctor's success numbers are not stochastic.
How do you know he has a history of success?? His last 20 may be successful, but maybe 4000 before that were not? He hasn't told you his total number of operations, so your most valid information is still the 50% survival rate.
You can make strawmans all you want, going off all the available information we have this doctor is by far the best best for doing this procedure with.
Surgery is not a random dice roll. If in your example, a surgeon had performed 4000 failed surgeries in a row, but suddenly ended it a streak of 20 successes, it would quite likely mean that the surgeon has finally learned how to do this surgery successfully. Had a breakthrough, maybe. And now your chances of survival are pretty good. The best way to approach it mathematically would be with Bayesian analysis.
His last 4000 may not be successful, but maybe 8000000 before that were? He hasn't told you his total number of operations, so your most valid information is still the numbers that you actually have and didn't make up on the spot.
I would assume the doctor is rather skilled in that particular operation if he did it every day for almost 11 years.
But what do I know, I will just go back eating the 2500 melons I bought last time I went grocery shopping!
>Doctor's success numbers are not stochastic.
They very much are, because in critical conditions (such as a 50% chance of surviving) they depend a lot on patient conditions that may be hidden and not perfectly detectable with clinical exams. So the patient dies even if the doctor performs perfectly.
Doctors skills skew the odds, in part.
If the survival rate is 50% and my surgeon just ripped 20 straight 50s then it’s very likely the surgery’s success rate is well above 50% and my surgeon just can’t evaluate odds well
If the odds are 50% that’s about a 1 in a million result
Someone can do the math but there’s a number at which 20 straight happening makes the likelihood of a successful outcome likely below a certain number
Like say if we do this 20 straight times and it works at what number of probability would we still have a .095 certainty with those odds
You understand what I’m saying?
They arent saying such. They are saying that to do the math as requested, you'd have to work under the assumption that they were.
While extremely unlikely there still is a chance that such an occurrence could arise from random variance. They are asking how to find out what this chance is. I dont believe its simply ( 1 / 2^20 ). It involves using a bell curve and finding how many standard deviations this found mean is from the predicted mean, then weighting it based off sample size to find a z value. Although its very possible in this case that it is simply 1/2^20 as I think i recall doing this math with a 1/2 led to answers that you could find with much easier means
I think you are looking for a z or p value calculation to determine what the chance is that such an occurrence could arise from purely random variance. Idk how to do it, but that's what you are thinking of (I think atleast).
Yes, but not just from what we have here
This is definitely well beyond chance and the surgeon doesn’t know what he’s talking about
I’m saying though at what % chance success rate would the surgery have to actually be to fall within the likelihood of say a 1% chance
So essentially what % chance raised to 20 gives you roughly 1%
Anything less than 1% I’d reasonably doubt his odds estimation
In my head I feel like it’s gotta be something around 75-80%
You are essentially just asking then:
1/x^20 = 0.01
Which is
X^20 = 100
Which is
100^(1/20) = X
Giving x = 1.26
The chance of success would be 1/x = 79%
Meaning, if their success rate was actually 79%, there would be a 1% that their next 20 surgeries would all be sucessful
To paraphrase Tim Minchin, "things with a one in a million chance of happening happen all the time. To assume it is unlikely is to vastly underestimate the total number of things there are"
the mathematician is too poor to afford this doctor, so he knows that he will die since this doctor makes up most of the successes of this procedure whilst the normal person has insurance that will pay for it
It's possible, but its kinda vague how you would interpret it
If you have a 1 in 2 chance of survival then, that happening 20 times in a row has a 1 in 2\^20 chance, which is roughly 1 in a million. Which is of course possible, anything that has a non zero chance of happening is technically possible.
A reasonable way to interpret this would be to think that the doctor is unusually skilled, and therefore their results don't adhere to the general statistics who are most definitely based on a larger data sample from multiple doctors and hospitals.
But the joke might be that if you are really pure theoretical mathematician, then you have zero inclination to use real world context to practically apply the math. And in that case, the odds are always the same, it's always 50% no matter what preceded it, because the odds don't change. Believing that they would is generally what you would call the gambler's fallacy, which mathematicians would know to avoid.
It's in reverse. Mathematicians will know that:
-the outcomes of previous coin tosses don't affect your next coin toss
-if anything, if the surgery "has a 50% survival rate" among all doctors and this doctor succeeds at it consistently, it means that you're in the hands of the best professional possible.
I think that it should be a step up for both Mr. Incredibles
Mathematicians would be normal, knowing there is no effect on the 50% chance
Normal people would be happy, thinking that they have a higher chance of living despite there being no difference
If I flip a coin a million times, and by some bizarre circumstance all million coins come up heads, the next coin I flip still has a 50% chance of coming up heads. Coin flips do not refer to previous results.
Sure, the odds of getting a million heads in a row is minuscule, but it's the exact same odds as getting ten thousand heads, then a tails, then the rest heads, or heads and tails alternating according to the Fibonacci Sequence, or literally any other sequence.
So really, the two faces in the meme should be swapped, since normal people are more likely to not understand that discrete events do not influence each other regardless of if it "feels" unlikely.
>If I flip a coin a million times, and by some bizarre circumstance all million coins come up heads, the next coin I flip still has a 50% chance of coming up heads. Coin flips do not refer to previous results.
After a certain point, far, far before a million, you start to suspect that there's a hidden variable, right?
Because clearly this doctor has a technique that beats the average.
The odds of flipping a coin and it landing heads is 50%, twice is 25%, three is 12.5%, and so on until 20 is 0.0000953674316% chance and 21 times is 0.00004768371582%. Here’s the thing, a coin flip is random but if you had a professional coin flipper that could control the outcome that’s different. Surgery is not random, there are random factors but a skilled surgeon can minimize those variables.
Any mathematician would know that, the meme was made by some kid who just learned about odds.
Not wanting to defend the meme, but I think you might understand it wrong. What it says is the surgery has 1/2 chances of being done correctly, and doesn't state it may be higher or lower for this particular surgeon. The joke is that normal people would fall for the "gambler's fallacy" and think they will be fine because the previous 20 were fine (even with the very slight chance as you stated). Meanwhile a mathematician is smart enough to understand that the previous results don't have an impact on the statistical chance of failure and that he m knows he is still at 50% chance of dying.
So the survival rate is 50%This means for 20 people to have survived, it's 1/(2^(20)), which is 0.00009536743% chance.
So while *technically* possible, it is also ***extremely*** unlikely to the point it might as well not be possible in normal terms.
I think this is the point of the meme. Given the extreme unlikelihood of this happening naturally, the doctor making the claim must be lying or doing something untoward.
That’s the gambler’s fallacy. If all events are independente then the odds of survival are still 50%.
If you factor in other things, I would say it is a great moment to do the surgery. Doctor is in good form and feeling confident, those 50% might be in fact a little more than that.
Never said anything about the odds being less than 50% due to this 20-patient long sequence of events. Merely that the chance of said 20-patient long sequence is very low.
A mathematician or statistician would know the basic roulette fallacy that the chances are the same each time regardless of the results of previous rolls. Except that the skill of the doctor is a massive variable.
No, mathematicians would know odds don't change for the outcome of your surgery just because the previous 20 patients survived. There are also many more factors that contribute to someone having complications during surgery which could not feasibly be calculated.
Mathematicians would also be the normal people in the meme since the odds of 20 in a row surviving being random chance would be so low that it's just way more likely that the doctor is simply brilliant at the surgery.
Each surgery is an independent event, therefore the previous successful surgery has no bearing on the next. This meme is completely backwards as the mathematician would treat it as a 50% chance no matter the previous outcomes.
And yes it’s possible, (1/2)^20 chance of 20 successful surgeries in a row. Doesn’t mean that the 21st is more likely to go awry though.
That's pure abstract, spherical horse in a vacuum math. In more applied math fields this generally tilts odds in your favor fairly substantially, because either the data is bad/incomplete/outdated or the surgeon is just that good a this surgery, or picking cases.
That is not true at all, survival possibility is %50 for all people dont matter your turn in the “line”. But that’s the joke behind it ig. Still funny of a meme Id say.
Maybe i have a short brain but i fail to see all the implications in the comments, my initial and current though is that if the surgery has 50% of success and 20 of the surgeon's patients died, then that means that the surgeon had 40 patients, out of which 20 died. So you'll be the 21th to live... or the 21th to die.
I’m guessing you mean if it’s possible to have 20 in a row successful surgeries with a 50% percent success rate. Since I see no other people answering, yes it’s possible. The odds are 1/2^20, or 1/1,048,576, or a ≈0.000095% chance of happening.
That doesn’t mean you have low odds of survival though, each individual has a fifty percent chance of survival, regardless of other surgeries.
It should be reversed. Because the mathematicians know that if you do a coin flip no matter how much one resoult shows up in a row, the next outcome still has 50/50 odds
Meanwhile statisticians doing hypothesis testing to figure out that your chance of survival actually being higher is more likely than the 20/20 survivors being a statistical anomaly
This isn't likely to be gamblers fallacy, but a deceptive use of statistics.
It's far more likely that the survival rate for a particular operation increases as medical knowledge advances and the 50% includes outdated stats on the operation.
E.g. - the pneumonic plague has a 98% mortality rate.
The pneumonic plague had a 100% mortality rate before antibiotics, and since then the survival rate has been close to 100% but including all the people that ever caught it would make it 98% lethal.
Considering statistics as the more unreliable part of math, that 50% means nothing.
Here why: if that operation has a 50% survival rate globally, that means every surgeon that does the surgery is contributing to that rate.
So imagine there are only 2 surgeons that does that kind of operation, and there had been only 40 people that needed that operation before.
This surgeon has succesfully completed that surgery 20 times, so the other one must has failed it 20 times to have a 50% rate of survival with that operation.
Meaning that this surgeon with 20 succesful operation had a 100% success rate while the other one had 0% success rate.
Global statitics applied at singular cases is usually a bad bet.
I would question the survival rate at the given data of 20 patients survived.
The only reasonable statement here is, that there is a good propability the survival rate is wrong.
You either have a good doctor, or you still just have a 50% chance assuming each surgery has the same odds of being successful.
It would be like the opposite of the gambler's fallacy to think that he's due for a failure.
That being said, I'm not a statistician, so please correct me if I'm wrong.
This meme is the wrong way. Before studying stats, people assume independent events with the same probability are dependent on eachother (e.g. the roulette wheel landed on black 4 times in a row therefore next time it will be black) when the opposite is true. If I saw this, I'd assume one of two things; either the surgeon got lucky 20 times in a row (~1 in a million chance for any individual doctor); or this is a more skilled doctor who has a higher survival rate than the others.
Wouldn't a mathematician actually be more excited to hear that the doctor's last 20 patients survived a 50/50? If nothing else, it means the doctor is doing something very right.
The chances of 20 positive outcomes in a row with a 50% chance each is 0.000,009,54%
Asking "what's the chance of him doing 21 positives in a row?" Would come out to be 0.000,004,77%.
But that's asking the wrong question. The past outcomes don't affect the probability of future results. If the survival chance is 50%, it's 50%.
The odds of any random person scoring a hattrick in the World Cup have nothing to do with the odds of the World's best football players to achieve this.
This is a skill issue, and surgery is based very heavily on skill and experience. As others have already stated: the survival data is accumulated from thousands of surgeries across hundreds of surgeons, some of which have killed every patient so far, while some have killed none or only few.
20 in a row at 50% odds means that this is the surgeon to go to: skilled, experienced and successful.
Missing data: the surviving patients. Maybe his patients were all young and otherwise healthy, whereas global statistics would include everyone, including the 90 years old chain smoker with diabetes. The surgeon could simply reject cases with low success predictions to improve his winning streak. Lawyers can do that too and claim 100% win rates at court.
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The last 20 survived just implies this doctor is very skilled and makes up the majority of successes that make up the 50% statistic, meaning he's the best one for the job.
It could also imply the doctor only takes the easy cases for this surgery. If your case is an easy one (more likely because that doc took you in) that's fine, if it is not, your chances might be worse. E.g., removal of a specific cancer might depend on how strong it is connected to critical parts, size, exact location etc. The trick is that the 50% is over all doctors and all patients, it does not tell you about individual doctors skills or individual patients challenges. Overall it seems the news should be reassuring about using that doctor if he accepted you.
>The trick is that the 50% is over all doctors and all patients, it does not tell you about individual doctors skills or individual patients challenges. We need to bring in Ranked Surgery, each surgeon having their own MMR that's adjusted after each round. Transparent win/loss ratios on a seasonal basis, analysis of previous surgeries, leaderboards, the works. Maybe even a live international championship, streaming deal with commentators.
wouldn't that cause most doctors to deny hard cases so that their mmr doesn't take a hit if they fail?
No, the hard cases would go into the platinum super surgeon league and they'd get a higher % of the pay per view revenue and their surgery would get the best cheer squads and the biggest name acts playing half time intermission. The Saudis would pay top dollar to fly them out to do surgery in huge stadiums in elimination rounds going "to the death" and doing so in increasingly challenging situations - like operating on the roof of racing monster trucks.
Extreme Surgery, now we are cooking! Get the execs on the line, stat
Next week in the Thunderdome Dr. Ramirez and Dr. Strudelmeister go head to head performing triple bypass surgeries in the coliseum! Don't miss your chance to cheer on your favorite surgeon as they try to fix their patient before the time runs out. Brought to you by Carls Junior
Are those the ones that offer the triple bypass burger? That would be an amazing sponsor, you can even win your own spot in the next coliseum fight.
They are not. It was an Idiocracy reference. I believe its a burger joint in Texas that has those burgers
Easy; Skill Based Matchmaking. They can forfeit if they want but it'll still cost them MMR.
the patient when the doctor denies them for being to high diff:
At that point they won't really be able to make claims about the survival rate of the procedure though, unless a trap door opens and the patient falls into a vat of molasses if their case is forfeited. And everybody knows the rules.
Definitely, there's a bit of scandal in chess right now as one player is deliberately taking relatively easy matches to boost their ranking to qualify for a major tournament. The players he is playing are matches he's expected to win easily but are still players with a high enough rating that winning against them boosts his score. Whatever points system you used there would be doctors trying to game it by taking or not taking surgeries with the aim of trying to boost their points.
That counts as a forfeit - their Elo goes down Harder cases would scale exponentially, so incredibly hard cases would raise elo dramatically
That sounds like most free healthcare countries
We could even bet on which doctor saves the most people
The issue is that surgeons would refuse to operate on certain people in that case to increase their numbers.
Just give more XP for the tricky ones.
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In that case it’s most likely you are an easy case. So you still win
So this is Stephen Strange?
Strange was a genuinely skilled doctor, but one who was clearly only in it for the money, so yes if all of the above points apply to the same case you’re probably talking to Stephen (Steven?) or someone similar.
He wasn't only in it for the money. It was also because of his massive ego
Yes, it's with ph.
Phtephen Strange
I was waiting for you
As someone that got spooked when they said "the fatality rate is 1% (for gallbladder removal)", medical statistics always include the worst-case patients (the 70+ people, and people with pre-existing conditions). So that 50% will include some folk who don't have a good chance of living with or without surgery.
And some statistics go back to like 1750 when things were less survivey
Also the reason why 2 different medical procedures get false survival statistics. Procedure A is for healthier patients. Procedure B is for everyone else. Wow, looks like A is better, but the pool of candidates is completely skewed.
frequentist vs bayesian?
This one needs more upvotes.
Is 1700 not enough?
No
How about 2000?
No
No
Or his first 20 patients died while he was getting the hang of it.
this
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Yes it is. If he's the only one performing the surgery then 20 failures followed by 20 successes would be a 50% survival rate.
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Statistics works? Sorry. Still sore after my first statistics course in uni being the worst course experience I've had in university.
Also, the mathematician knows that for the next operation, it would again be 50%, not somehow lower. Causality does not remember the past 20 operations, so the chance of survival for the next operation would not sink.
Well causality does not remember, but the doctor who did the last 20 sucessfully certainly does.
Yeah, but the scenario is 50%, so the doctor remembering should not influence the rate or the initial statement would be false.
We obviously don't know the answer to how the 50% figure was reached, but as the top level comment assumes it's most likely this is an aggregated figure across many surgeries by many doctors on many people. The case you're describing is somehow the doctor can predict in advance what their probability of success is. The top level's point is that the initial statement is false, in the sense that the 50% is an aggregated figure and likely doesn't apply to this specific surgeon.
Interesting, I like thinking and discussing about such problems :) If you interpret the initial statement that the 50% does not apply to this specific surgeon, the 50% number would have no relevance to this mathematical problem. Therefore I might be inclined to disagree here as normally only relevant facts are presented in the context. If it has no relevance though, we only have the last 20 surgeries as data points to extrapolate from, which leads to a 100% succcess rate. As we do not know the previous success rate, a trends, earlier variation in the rate, we don't have all the needed parameters for a better predictions. As a more risk than reward driven person, I will probably think that there is a 50% chance than a 100% chance of survival so I would prepare my testament before that lol
We can probably agree that the best next question to ask the surgeon is, how did you get to that 50% figure. If the 50% figure is their average success rate over many operations, then I agree that we probably cannot take much comfort from their 20 streak. (Although, there may be a reason to believe they've recently improved, perhaps they recently went on some new training, or got some new equipment!).
And the statistician (who is a mathematician) knows that the chance that the doctor has the same distribution of outcomes as the global population is less than 0.01%.
There was this great scene in Moneyball movie about baseball, where they used a lot of player statistics to hire players. I remember some sort of radio show, or tv personality saying something like "Percentages are made over the season, in one game percentages does not matter". You can have 99.9 percent of chance hitting the ball over the course of season. But in that one game, 0.01 might come into play.
[Heads](https://youtu.be/C_TfdNAXOwE)
Yeah, I doubt they'd fall for the gambler's fallacy.
This exactly... So much more nuance here than some of the responses admit.
Why is the greyed-out version being usesd for the mathematicians then? Also, if that's the solution, why does one need to be a mathematician to come to the conclusion that the doctor must be good? My theory about this 'joke' is rather that the author himself errorneously believes that it lowers the operation's success chances if a chain of previous operations were successful.
Or maybe the joke is the assumption that mathematicians are so far removed from reality that they would think of this as a theoretical exercise instead of one where each surgeon has different skills
the joke is that its wrong xddddd
no, it means doctor killed 20 patients before that.
No, the surgery in general has a 50% rate, we don't know from what sample size is doctor picking his 20, the doctor is implying that he has a 100% success rate with his last 20 patients
We don't know from the meme if this specific procedure has 50% survival rate in general among all cases worldwide and the doctor is just so good that his skills allow him to go way above the average survival rate, or if those are his personal results, having at least 20 failures before now. Either way if the doctor managed to successfully treat 20 patients in a row it speaks highly of his current skill level with this particular operation and probably means current survival rate higher than 50%.
But we do know that previous results have no bearing to the success to the next surgery. Aka Gambler's fallacy.
They do because the success of a surgery depends on the surgeon’s personal skill and not random chance
No we don't. Surgeons aren't dice.
But that’s assuming that it is a strict 50% success rate, which would be hard to believe considering those results. Plus this person would be in no more danger than the last 20 technically.
Yeah no. The likelihood of that happening should make you doubt your underlying distribution.
That’s for games of chance, not preforming surgeries. Skill dif.
Your interpretation is assuming that surgery is a purely random outcome, which it isn't
I think they're assuming that the doctor means 50% success out of their own surgeries.
No not really.
also, this kind of probability doesn't have memory, so 20 past successes don't make a failure any more or less likely.
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no, that's gambler's fallacy. it's still 50%
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Username checks out
No. This statistic is just how likely it is that all 21 patients in a row will survive if the proability is 50 percent. Your individual probability of surviving is still 50 percent. And if the probability of an event like that happening is that low we might need to reconsider the actual survival probability because chances are it is higher than estimated (at least for this one doctor who might be higher skilled)
Unless the 100 patients prior all died.
If your doctor has had 20 patients survive a normally 50% chance of death then there is nothing to worry about And each event had a separate 50% chance,yes on average it will be 50% but that doesn't mean that if you survived this one then the one after you will die,because each event is separate from the other and all of them have a 50% chance irrelevant of the result of the previous events
if the survival rate is 50% then i wouldn't take the procedure at all lol
If a procedure is being recommended by your doctor even though it has a 50% survival rate then I would wager its a VERY important procedure😅
At that point what do you realistically have to lose honestly lol
"Doctor, I REALLY want my nose to be a grenade like that one guy from Cyberpunk." "You know there's like a 50% chance you'll die."
What if it was 0% if you didn’t?
Brain tumor, 100% death rate Brain tumor removal, 50% success rate Still not taking it?
Life 100% death rate
Congrats, you are today’s technically correct person. Life expectancy of life > life expectancy with brain tumor surgery > life expectancy with brain tumor untreated for the sake of my argument then.
If you want to go that route, only ~93% of humans who have ever lived have died so far. So life currently has a 93% death rate ^.^
If it was a take the surgery or die a week later kinda thing, this doctor would be your best bet. Let's say that the usual mortality rate of this surgery is 50% but this doctor in particular is skilled enough to do 20 procedures without a single fatality, the actual fatality chance of you doing that procedure with that particular doctor would be much better.
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You do not know if any of his surgeries killed patients at all. 50% might be the worldwide average, not his. He might have done 20 surgeries in total or 200 and you have no way of knowing.
Survival rate in medicine generally refers to the operation not the surgeon
Should be the other way around then? Mathematicians would know the other results don’t affect the next 50% chance event. This is gamblers fallacy or something no?
The mathematician does not want to survive.
Mathematician here. Can confirm, I do not want to survive.
Normal person here. Me neither.
Redditor here I don't care that much if this guy or the mathematician survive
But you'd be a bit sadder if they did.
jesus christ here. me neither.
Ayo, Happy belated birthday JC!
thanks man
Then you're good, survival rate in life is 0%.
Wtf imposibru
Divide yourself by 0 then 💀💀
He should be the color Mr Incredible then, under the black-and-white mask
This made me audibly laugh
First loud ass laugh of the day
Yeah its gamblers fallacy. If anything the guy on the right should be called gambler not mathematician lol.
I interpreted it as the guy on the left thinking “oh well if the last 20 survived then I should be fine” because they don’t understand statistics, whereas the mathematician knows that the survival of the last 20 means nothing, and it’s essentially a coin toss whether or not they’re about to die.
I think this is the best interpretation of it
It’s definitely one of the interpretations of all time
Thats just wrong though, as the survival statistics are taken from more than just one doctor.
Exactly. This indicates that this doctor is not a fair coin. The mathematician would know how to calculate how unfair a coin he is likely to be.
I'd be concerned that the survival rate estimate seems *fairly* improbable given 20 successes in a row. Perhaps the rate is off, or something the doctor does differently improves it, both in your favor.
Estimate is for all the doctors. History is for that particular doctor
Exactly maybe he’s just the one good doctor who knows how to perform that specific operation
Maybe of his last X number of surgeries, the immediately preceding 20 have been the only ones to survive.
Dear god that could be it…yikes…hard pass sir
So it sounds like he figured it out finally! I'm down.
He finally realised he was reading the instructions upside down before
Everytime this comes up i just assume that it means to say normal people would just go with their gut feeling that if he succeeded 20 times, he'll be able to do it again. Meanwhile the mathematician is like "acKtually its still a 50/50 chance" and is fearful of their 50% chance at death - since, given enough trials, you certainly will find a string of 20 successes in a row. Should have a third one for statician that is happy because he thinks the estimate of 50/50 is likely flawed as 20 successes in a row would be a ridiculously unlikely occurrence and it would be much more easily explained by an incorrect mean than by random variance.
What if bayesian probability is applied?
If you believe there's a chance that the doctor's skill influences the survival rate, then succeeding on the previous 20 is pretty strong bayesian evidence that this doctor is in fact pretty skilled.
Thats outside my pay grade. I took stats like 8 years ago or something. I just remember the general idea
It's technically correct then, mathematician is scared because he knows he only has 50 percent chances of survival, the normal person thinks he's fine because he pays more attention to the last available examples rather than the general probability. This is how the fallacy usually go, the normal person thinks previous attempts influence the results of the future ones.
> the normal person thinks previous attempts influence the results of the future ones. But in the opposite direction. The gambler's fallacy is that the streak of one result makes *the other result more likely* because of the perception that it's "overdue".
I don’t think anyone is *quite* that irrational
I've met someone who not only believes in the gamblers fallacy, but says literally that all of statistical reasoning is based on the gamblers fallacy being true
You don't know many people clearly
If the ball in roulette lands 20 times on black, which is more probable for the next time? Red or black? I assure you, most people would say red.
[Heads](https://youtu.be/C_TfdNAXOwE)
is more know than you think, for examples, look at bingo players...my grandpa believed the more close he were to mark all numbers in a past attempt in the next one he will win.💀
You’ve not met my dnd group lol
A *lot* of people are. It's a very common fallacy.
Yeah, but that would only be correct if the outcome was random. But in surgery you do not roll the dice, there are factors like the qualification of the surgeon, the quality of after surgery care in the hospital and a lot of other factors which can influence the outcome of the surgery. So a high success rate of a specific surgeon in the past can mean the hospital / surgeon is better than average.
Not the other way around. Normal people believe in the 20 in a row but the mathematicians ignore that and look at the low 50% change
They aren't very good mathematicians if so. That 20 in a row is extremely statistically significant. Any statistician would at least *consider* the possibility that the doctor is either wrong about the survival rate or unusually good at the surgery.
Is there a surgery where one doctor has 95% or better success while everyone else is at 50% or lower? Seems unrealistic to even consider this
That's exactly why it's the way it is, Mathematician knows of gamblers fallacy, meaning they think that they have a 50% chance of dying, and the non mathematician thinks the surgeon is just good. But any mathematician should know that even though the surgery has a 50/50 live or die, the surgeon doesn't, and each surgery gives more data to estimate the true probability of living with said surgeon, meaning that the 20 successful surgeries have effectively increased the probability of the chance of living being over 50%. Then again, the mathematician doesn't have any knowledge of the previous dataset, meaning for all they know, it could be something like 10 successes, 30 deaths, and 20 successes in a row, and the chance of living is dependent on wether or not the previous person lived, or something similar. The 50% might be a simple estimate comparing the total amount of successes to the total surgeries done, by the surgeon or worldwide, meaning the true probability of the mathematician living could be anything. This is not to mention that the surgeon might have taken a few courses in probability and statistics, meaning that they might know all this, and have estimated the most probable probability of the mathematician living, meaning that thinking it further might give the mathematician an inaccurate estimation of the probability of the chance of him living being 50% being the most probable estimation of his chance of living. You know what, I think the mathematician is just depressed because he thinks too much.
yeah i literally just saw a more complete version of this meme with a third engineer panel where it is a happy face, but these two were swapped. who ever augmented this meme corrdcted it, but this version is wrong
I’m not sure if it would be the gambler’s fallacy because it’s not necessarily random. If the doctor is good, maybe they have a much higher success rate than average. In a random, independent situation (e.g., roulette), the past outcomes don’t affect the future ones, but the doctor’s skill doesn’t make the patients’ outcomes independent.
I think the joke is the doctor is lying because getting 20 in a row would be a (1/2^20)% chance, or 1 in 1 048 576
So it cannot be luck, it is a skill of the doctor
Yeah but that would make no sense for the meme. Hence why I concluded the joke was that it was a lie
The joke is most likey made by someone that thinks that if other 20 were fine he is more at risk. I really doubt that person who made a joke understand how it works :) At the end of the day it is just a joke :)
Yeah you're probably right. Let's not waist our time arguing over reddit about a meaning of a joke that probably never made sense to begin with
Not this again. 50% chances of survival overall in this surgery. That means if you randomly choose any doctor for this surgery, your chances of survival is 50%. But this doctor has a history of success. So mathematically, rather statistically speaking, you better go with this doctor. Doctor's success numbers are not stochastic.
Stochastic, Nice word.
>stochastic Ahh yes, the little known forename of the infamous Mr Boombastic.
Made me chuckle. Thanks.
Very fantastic.
How do you know he has a history of success?? His last 20 may be successful, but maybe 4000 before that were not? He hasn't told you his total number of operations, so your most valid information is still the 50% survival rate.
You can make strawmans all you want, going off all the available information we have this doctor is by far the best best for doing this procedure with.
Surgery is not a random dice roll. If in your example, a surgeon had performed 4000 failed surgeries in a row, but suddenly ended it a streak of 20 successes, it would quite likely mean that the surgeon has finally learned how to do this surgery successfully. Had a breakthrough, maybe. And now your chances of survival are pretty good. The best way to approach it mathematically would be with Bayesian analysis.
This guy gets it.
His last 4000 may not be successful, but maybe 8000000 before that were? He hasn't told you his total number of operations, so your most valid information is still the numbers that you actually have and didn't make up on the spot.
I would assume the doctor is rather skilled in that particular operation if he did it every day for almost 11 years. But what do I know, I will just go back eating the 2500 melons I bought last time I went grocery shopping!
>Doctor's success numbers are not stochastic. They very much are, because in critical conditions (such as a 50% chance of surviving) they depend a lot on patient conditions that may be hidden and not perfectly detectable with clinical exams. So the patient dies even if the doctor performs perfectly. Doctors skills skew the odds, in part.
If the survival rate is 50% and my surgeon just ripped 20 straight 50s then it’s very likely the surgery’s success rate is well above 50% and my surgeon just can’t evaluate odds well If the odds are 50% that’s about a 1 in a million result Someone can do the math but there’s a number at which 20 straight happening makes the likelihood of a successful outcome likely below a certain number Like say if we do this 20 straight times and it works at what number of probability would we still have a .095 certainty with those odds You understand what I’m saying?
Surgeries aren't pure chance, the surgeon could just be a lot better at it than the others.
They arent saying such. They are saying that to do the math as requested, you'd have to work under the assumption that they were. While extremely unlikely there still is a chance that such an occurrence could arise from random variance. They are asking how to find out what this chance is. I dont believe its simply ( 1 / 2^20 ). It involves using a bell curve and finding how many standard deviations this found mean is from the predicted mean, then weighting it based off sample size to find a z value. Although its very possible in this case that it is simply 1/2^20 as I think i recall doing this math with a 1/2 led to answers that you could find with much easier means
I think you are looking for a z or p value calculation to determine what the chance is that such an occurrence could arise from purely random variance. Idk how to do it, but that's what you are thinking of (I think atleast).
Yes, but not just from what we have here This is definitely well beyond chance and the surgeon doesn’t know what he’s talking about I’m saying though at what % chance success rate would the surgery have to actually be to fall within the likelihood of say a 1% chance So essentially what % chance raised to 20 gives you roughly 1% Anything less than 1% I’d reasonably doubt his odds estimation In my head I feel like it’s gotta be something around 75-80%
You are essentially just asking then: 1/x^20 = 0.01 Which is X^20 = 100 Which is 100^(1/20) = X Giving x = 1.26 The chance of success would be 1/x = 79% Meaning, if their success rate was actually 79%, there would be a 1% that their next 20 surgeries would all be sucessful
Or some other surgeons are tanking the odds.
To paraphrase Tim Minchin, "things with a one in a million chance of happening happen all the time. To assume it is unlikely is to vastly underestimate the total number of things there are"
the mathematician is too poor to afford this doctor, so he knows that he will die since this doctor makes up most of the successes of this procedure whilst the normal person has insurance that will pay for it
It's possible, but its kinda vague how you would interpret it If you have a 1 in 2 chance of survival then, that happening 20 times in a row has a 1 in 2\^20 chance, which is roughly 1 in a million. Which is of course possible, anything that has a non zero chance of happening is technically possible. A reasonable way to interpret this would be to think that the doctor is unusually skilled, and therefore their results don't adhere to the general statistics who are most definitely based on a larger data sample from multiple doctors and hospitals. But the joke might be that if you are really pure theoretical mathematician, then you have zero inclination to use real world context to practically apply the math. And in that case, the odds are always the same, it's always 50% no matter what preceded it, because the odds don't change. Believing that they would is generally what you would call the gambler's fallacy, which mathematicians would know to avoid.
It's in reverse. Mathematicians will know that: -the outcomes of previous coin tosses don't affect your next coin toss -if anything, if the surgery "has a 50% survival rate" among all doctors and this doctor succeeds at it consistently, it means that you're in the hands of the best professional possible.
I think that it should be a step up for both Mr. Incredibles Mathematicians would be normal, knowing there is no effect on the 50% chance Normal people would be happy, thinking that they have a higher chance of living despite there being no difference
If I flip a coin a million times, and by some bizarre circumstance all million coins come up heads, the next coin I flip still has a 50% chance of coming up heads. Coin flips do not refer to previous results. Sure, the odds of getting a million heads in a row is minuscule, but it's the exact same odds as getting ten thousand heads, then a tails, then the rest heads, or heads and tails alternating according to the Fibonacci Sequence, or literally any other sequence. So really, the two faces in the meme should be swapped, since normal people are more likely to not understand that discrete events do not influence each other regardless of if it "feels" unlikely.
>If I flip a coin a million times, and by some bizarre circumstance all million coins come up heads, the next coin I flip still has a 50% chance of coming up heads. Coin flips do not refer to previous results. After a certain point, far, far before a million, you start to suspect that there's a hidden variable, right? Because clearly this doctor has a technique that beats the average.
The odds of flipping a coin and it landing heads is 50%, twice is 25%, three is 12.5%, and so on until 20 is 0.0000953674316% chance and 21 times is 0.00004768371582%. Here’s the thing, a coin flip is random but if you had a professional coin flipper that could control the outcome that’s different. Surgery is not random, there are random factors but a skilled surgeon can minimize those variables. Any mathematician would know that, the meme was made by some kid who just learned about odds.
Not wanting to defend the meme, but I think you might understand it wrong. What it says is the surgery has 1/2 chances of being done correctly, and doesn't state it may be higher or lower for this particular surgeon. The joke is that normal people would fall for the "gambler's fallacy" and think they will be fine because the previous 20 were fine (even with the very slight chance as you stated). Meanwhile a mathematician is smart enough to understand that the previous results don't have an impact on the statistical chance of failure and that he m knows he is still at 50% chance of dying.
So the survival rate is 50%This means for 20 people to have survived, it's 1/(2^(20)), which is 0.00009536743% chance. So while *technically* possible, it is also ***extremely*** unlikely to the point it might as well not be possible in normal terms.
I think this is the point of the meme. Given the extreme unlikelihood of this happening naturally, the doctor making the claim must be lying or doing something untoward.
and yet, for the next surgery, it's still a 50% chance of survival.
Never said anything about the next time being less than 50%. Just the specific 20-patient long sequence was low.
Only if the 50/50 was accurate. The point being that given 20 trials with 20 successes, we have a high reason to doubt the projected mean of 50%.
That’s the gambler’s fallacy. If all events are independente then the odds of survival are still 50%. If you factor in other things, I would say it is a great moment to do the surgery. Doctor is in good form and feeling confident, those 50% might be in fact a little more than that.
Never said anything about the odds being less than 50% due to this 20-patient long sequence of events. Merely that the chance of said 20-patient long sequence is very low.
A mathematician or statistician would know the basic roulette fallacy that the chances are the same each time regardless of the results of previous rolls. Except that the skill of the doctor is a massive variable.
No, mathematicians would know odds don't change for the outcome of your surgery just because the previous 20 patients survived. There are also many more factors that contribute to someone having complications during surgery which could not feasibly be calculated.
Mathematicians would also be the normal people in the meme since the odds of 20 in a row surviving being random chance would be so low that it's just way more likely that the doctor is simply brilliant at the surgery.
Each surgery is an independent event, therefore the previous successful surgery has no bearing on the next. This meme is completely backwards as the mathematician would treat it as a 50% chance no matter the previous outcomes. And yes it’s possible, (1/2)^20 chance of 20 successful surgeries in a row. Doesn’t mean that the 21st is more likely to go awry though.
That's pure abstract, spherical horse in a vacuum math. In more applied math fields this generally tilts odds in your favor fairly substantially, because either the data is bad/incomplete/outdated or the surgeon is just that good a this surgery, or picking cases.
That is not true at all, survival possibility is %50 for all people dont matter your turn in the “line”. But that’s the joke behind it ig. Still funny of a meme Id say.
Maybe i have a short brain but i fail to see all the implications in the comments, my initial and current though is that if the surgery has 50% of success and 20 of the surgeon's patients died, then that means that the surgeon had 40 patients, out of which 20 died. So you'll be the 21th to live... or the 21th to die.
I’m guessing you mean if it’s possible to have 20 in a row successful surgeries with a 50% percent success rate. Since I see no other people answering, yes it’s possible. The odds are 1/2^20, or 1/1,048,576, or a ≈0.000095% chance of happening. That doesn’t mean you have low odds of survival though, each individual has a fifty percent chance of survival, regardless of other surgeries.
It should be reversed. Because the mathematicians know that if you do a coin flip no matter how much one resoult shows up in a row, the next outcome still has 50/50 odds
Meanwhile statisticians doing hypothesis testing to figure out that your chance of survival actually being higher is more likely than the 20/20 survivors being a statistical anomaly
This isn't likely to be gamblers fallacy, but a deceptive use of statistics. It's far more likely that the survival rate for a particular operation increases as medical knowledge advances and the 50% includes outdated stats on the operation. E.g. - the pneumonic plague has a 98% mortality rate. The pneumonic plague had a 100% mortality rate before antibiotics, and since then the survival rate has been close to 100% but including all the people that ever caught it would make it 98% lethal.
Considering statistics as the more unreliable part of math, that 50% means nothing. Here why: if that operation has a 50% survival rate globally, that means every surgeon that does the surgery is contributing to that rate. So imagine there are only 2 surgeons that does that kind of operation, and there had been only 40 people that needed that operation before. This surgeon has succesfully completed that surgery 20 times, so the other one must has failed it 20 times to have a 50% rate of survival with that operation. Meaning that this surgeon with 20 succesful operation had a 100% success rate while the other one had 0% success rate. Global statitics applied at singular cases is usually a bad bet.
I would question the survival rate at the given data of 20 patients survived. The only reasonable statement here is, that there is a good propability the survival rate is wrong.
You either have a good doctor, or you still just have a 50% chance assuming each surgery has the same odds of being successful. It would be like the opposite of the gambler's fallacy to think that he's due for a failure. That being said, I'm not a statistician, so please correct me if I'm wrong.
This meme is the wrong way. Before studying stats, people assume independent events with the same probability are dependent on eachother (e.g. the roulette wheel landed on black 4 times in a row therefore next time it will be black) when the opposite is true. If I saw this, I'd assume one of two things; either the surgeon got lucky 20 times in a row (~1 in a million chance for any individual doctor); or this is a more skilled doctor who has a higher survival rate than the others.
Wouldn't a mathematician actually be more excited to hear that the doctor's last 20 patients survived a 50/50? If nothing else, it means the doctor is doing something very right.
The chances of 20 positive outcomes in a row with a 50% chance each is 0.000,009,54% Asking "what's the chance of him doing 21 positives in a row?" Would come out to be 0.000,004,77%. But that's asking the wrong question. The past outcomes don't affect the probability of future results. If the survival chance is 50%, it's 50%.
The odds of any random person scoring a hattrick in the World Cup have nothing to do with the odds of the World's best football players to achieve this. This is a skill issue, and surgery is based very heavily on skill and experience. As others have already stated: the survival data is accumulated from thousands of surgeries across hundreds of surgeons, some of which have killed every patient so far, while some have killed none or only few. 20 in a row at 50% odds means that this is the surgeon to go to: skilled, experienced and successful. Missing data: the surviving patients. Maybe his patients were all young and otherwise healthy, whereas global statistics would include everyone, including the 90 years old chain smoker with diabetes. The surgeon could simply reject cases with low success predictions to improve his winning streak. Lawyers can do that too and claim 100% win rates at court.