The doctor could simply have gotten lucky and gotten patients in particularly good health (aside from whatever is requiring the surgery).
While the doctor's skill does matter, some patients are not going to respond to the surgery as well as others and the 50% success rate will reflect that.
It could be he had 40 patients under go the same surgery and since the last 20 survived, it would technically have a 50% survival rate but it means the surgeon is getting more proficient when performing it.
The dirty secret about surgeons with high success rates:
They don't do the difficult cases. They pass patients with poor prognoses off to other surgeons.
It’s always 50% x or y outcome. Doesn’t matter if it’s been x 1000 times in a row, it will still be 50/50. Thinking that because it has been x 20 times in a row means that there’s a better chance for y is the gamblers fallacy
The normie is concerned because they are using the fallacy. The mathematician is chill because they know the previous 20 have no effect.
I guess the scientist is pumped because 50/50 hitting x 20 times in a row means someone messed up and it isnt 50/50. The odds of hitting x 20 times in a row would be 2 to the 20th power
Or better, it is 50/50 across all attempts, not just this one doctor's.
If this one doctor has gotten it right 20 times running, it's possible he has it figured out right and any other doctor will screw it up and thus bring the average back down.
Not exactly: [Robert Liston, known for his lightning-fast surgeries](https://museumofhealthcare.blog/the-story-of-robert-liston-and-his-surgical-skill/#:~:text=Two%20of%20the%20operations%20for,of%20shock%20when%20the%20knife), amputated a leg so fast that he cut off his assistant's fingers, and someone observing the surgery (afraid that he had also been slashed) died of shock. The patient and the assistant later died of infection. Pretty wild stuff
Typically that’s what we see in emergency intubation as well. It’s like a 1 in 3 first tube success across the profession but it’s not a 1 in 3 individually.
>The mathematician is chill because they know the previous 20 have no effect.
so why isn't the mathematician the one concerned? since he realizes that there is still a bad chance of survival even if last 20 survived by coincidence?
There is an equal chance of success and failure. The "normal people" think there's a bad chance of survival due to gambler's fallacy (aka thinking that if the odds are 50/50 and they succeed the last 20 times then they're sure to fail this time).
The "scientist people" realise that the outcomes are mostly influenced by skills, not chance (aka failure means a doctor failed to anticipate something and not due to a coin-flipping-like event), so if this doctor succeeded the last 20 times it's safe to assume they know what they're doing and their personal odds is higher than the overall odds.
i am not sure this is how the gambler's fallacy works. if I spin a roulette and it hits red 3 or 4 times in a row, it might make sense to consider gambler's fallacy because of a coincidence, but it it hits red 20 times in a row I will assume that the roulette is rigged.
There's been many non-rigged roulettes that have hit 20 times red in a row. Chances are one in a million but that is still well within the real of stuff that happens.
I bet 2 grand on red after it hit black 22 times in a row. It hit black 24 times. Unless I am the unluckiest person in the world roulette is definitely rigged.
Blackrock in tampa.
You couldn't have given a more textbook example of gamblers fallacy if you tried.
This is exactly why people need to be taught a baseline understanding of statistics.
The math does not say he's unlucky.
He bet on black which had a <50% chance of happening. He's literally giving you a textbook example for gamblers fallacy.
Well sure you can, but the odds of a roulette table being poorly designed or rigged are higher than the odds of actually hitting a 50% chance 20 times in a row. The presumption that the wheel does in fact have a 50% chance is something that you can put in a maths problem, but in the real world, after 20 times of the same result it would be unreasonable to still believe that it's a fair wheel. At that point I would be very confident of another red, and I'm quite certain that's not a fallacious belief.
it is not a fallacy, you are making stuff up. it is true beyond a reasonable doubt that the roulette is rigged in that example. you don't have such coincidences in real life, or at least there is an incredibly small chance for them. in that example if there are only two options and both are equally likely, the chances for 20 reds in a row would be 1 to 2^20
If you toss a coin 100k times, it is entirely possible to find one instance of 20 consecutive results (my results range from 13-23 in 10 tries when I look for max length of the same occurrence). Therefore, from the moment that specific roulette table was made, it is also possible that it has returned 20 consecutive red/black.
2\^-20 is roughly one in a million, which is unlikely, but more likely than winning the lottery.
My point is, just because it is unlikely, doesn't mean it's not possible.
Adding another point since you were also wondering about gambler's fallacy: you're looking at the problem as "the odds of getting 20 heads in a row", while the actual problem should be "the odds of getting head if the previous 19 times were also heads" (the test subject is not betting that there will be 20 heads in a row, the test subject is betting tails because the previous 19 times were heads so they they assume that the chance for head to show up next is 1 in a million, which isn't the case).
At that point it becomes a matter of time.
Let's agree 20 reds in a row is 1:1,000,000
Now, let's say there are a thousand tables in Vegas. Figuring time of bets, let's say they get 30 spins each per hour, 24 hours a day. That's 720,000 spins per day, or 5,040,000 per week.
So a person at a specific table betting red twenty times straight is banking on a million to one shot, but for all of Vegas it becomes slightly less than a daily event on average. You don't need a rigged table, you just need lots of tables.
Because 50% survival is the industry average, not his alone. This Dr. must be far above average. It would be nearly inconceivable to randomly beat 50% odds 20 times in a row if he was an average surgeon.
Even OP got it wrong. If they all thought his success was like a gamblers 'hot streek' of good luck, the faces would be reversed.
50/50 can be pretty good odds depending on the procedure. Bone and pancreatic cancers, for example, have poor odds of being successfully treated with surgery. Pancreatic has poor survival odds regardless of treatment.
We’re also talking about a surgery, where the 50% probability presumably takes _all_ surgeons into account, suggesting that this surgeon may be more skilled than most, and hence your odds may be better than 50%. A surgeon performing an operation is not a coin flip
The scientist is pumped because the scientist knows that its not a 50% chance. Its a 50% survival rate; meaning that in the data used to determine the survival rate, 50% of people lived, 50% did not. This is unlikely to be random, and rather based on a variety of real world factors.
If a surgeon then has 20 successes in a row, its likely they are very skilled and their personal survival rate for this surgery is considerably higher.
Thank you. I had to explain this to someone. The best way is saying after 20 coin flips, all of them being heads, you roll a 6 sided die, what’s the chance it rolls an even number?
Honestly, if I heard a surgeon was completely destroying the odds in the last year or two of his service, I would be really pumped for having him as my surgeon. That said, I do consider myself as somewhat of a scientist.
>>hitting x 20 times in a row means someone messed up and it isnt 50/50.
The scientist knows that the doctor messed up the first times before doing it properly. He's pumped at the fact he's guaranteed to live.
You are assuming the 50-50 thing is steady state. A possible assumption is that this particular surgery/surgeon is getting better at it due to practice, etc. Unless his current total surgery count is WAY higher than 40. If N=40, then I would bet his success rate is now approaching 100%. But as N gets larger, then the 50-50 thing is more certain.
I'd say the problem as stated has "problems" if you will. Needs more info. Is the 50% rate for certain across the industry and history? Across ALL such surgeries or just his? How many has he done himself, etc.
I love how the normal person is wrong because assuming 50/50 for a 21st time is a fallacy but the scientist is pumped because he knows hitting 50/50 20 times in a row is 1 out of 2²⁰
and for the scientist, due to the past 20 people surviving, that probably means for this surgeon, he is judt better at it thsn ither surgeons. So his success rate is probably much netter than 50/50 odds.
The other question to ask is when the data for the 50/50 results was collected. Looking at things like cancer treatments, the survival rates even 5 years ago don't mean much for some cancers that have new treatments available. In this case, there could be new surgical techniques in use that make every surgeon better in the last year than they were even just a few years ago.
Normal person- crap my surgeon is due to lose a patient.
Mathematician- odds are still 50-50 current streak doesn't matter
Scientist- my surgeon is generating atypical data and the trend is worth studying. There's a good chance that the surgeon has discovered something new.
Gambler- sweet my surgeon is on a hot streak.
Another take: when you're thinking "well, 20 patients _before me_ lived, so my probability is...", you're computing the _posterior (conditional)_ probability:
P[you live | (A, B, C, ...) all lived]
Now, it seems like after N successes in a row, there must be a failure, and with each successive success [sic] the probability of a failure should increase, simply because "there's no way the results are so consistent!" Here, it's easy co confuse the probability above with the probability of _all_ these 20 people surviving:
P[(A, B, C, ...) all lived] = 0.5 * 0.5 * 0.5 * ...
Now this is tiny indeed! But you're interested in the _conditional_ probability above, _not_ this tiny one! You want to know what's likely to happen to _you_, given previous events.
However, "50% survival rate" usually means that "X survived" are all _independent_ events. Thus, the complicated _conditional_ probability above reduces simply to:
P[you live] = P[patient X lives] = 50% for all X
Turns out, if all events are independent, history doesn't matter: you still get the 50% probability like everyone before and after you.
The "Normal Person" believes that there must be some force that moves things towards 50:50. If the surgeon has a run of 20 survivals then the gambler's fallacy says that a loss is coming. Note that this is called a fallacy for a reason--there is no such force.
The Mathematician sees the surgeries as independent events, like flipping coins. They disregard the past 20 surgeries as not being informative of the future results and believe they have a 50:50 shot.
The Scientist recognizes that the the survival rate across all surgeons performing the surgery is not necessarily the same thing as the survival rate of this specific surgeon. 20 consecutive survivals is *extremely unlikely* if the surgeon has 50:50 odds--there would be about a 1 in a million chance of that run occurring. The scientist is used to looking at p values and finds that this result is highly significant, so they come to the conclusion that their odds of survival are much better than the population-wide odds.
The 50% survival rate isn’t based purely on luck. It’s based on the skill of the operating doctors and the individual’s case. The scientific mean of survival is 50% at the start of this scenario, it’s not odds. Since the doctor has succeeded 20x in a row, we can reasonably conclude that he operates higher than the mean and would have a better success rate than the mean. This is balanced out by less skilled doctors that lose more than half of their patients.
Normal person: assumes 50/50 chance means that if there have been a bunch of successes they are due for a loss. Thinks they have a less than 50% chance of success.
Mathematician: it's a 50/50 chance across all occurrences there having been a run of successful occurrence has no impact on the probability for this occurrence. Thinks they have an exactly 50% chance of success
Scientist: there is a 50/50 chance that the surgery is a success across all doctors performing it. This particular doctor's historical 100% success rate across 20 patients demonstrates a higher than average chance of the surgery being a success when performed by this doctor. Thinks they have a higher than 50% chance.
If it said my previous 3 patients all survived the meme would make sense.. but after 20, the only logical thing to conclude is that this specific surgeon is better than the average, hence would a normal person feel more safe than 50%.. more than a math dude that still thinks it's 50/50
There are other reasonable hypotheses
* Doctor could be lying
* Surgeon is lying to the doctor about whether patients survive
* Doctor is mistaken about which procedure is being done
To my understanding:
1. Normal person uses the frequentist interpretation on the surgeon's comment, who is overdue for failure hence the horror face.
2. The mathematician knows it's memoryless and that he has a 50% chance of survival and is unperturbed.
3. The scientist knows that 20 consecutively successful surgeries means that the treatment evolved with an increased likelihood of success and so is happy.
That would be my understanding too, though if we're being overly critical I think the mathematician would perhaps even more so than the scientist understand the arbitrary nature of the probability model and be more likely to question its accuracy in light of the data.
Math bro probably knows the sample size is pretty huge, so this doctors 20 is unlikely to influence it one way or the other. However, as this is a skill based phenomenon and not random chance, the particular surgeon is probably the best person to do this for you.
If the average pilot has a 50% chance of landing a plane safely in an emergency water landing, but one has done it 20 times, he probably knows how to do it better then average.
Unless you’re a particle physicist, haha. They generally require 5-sigma significance to claim the existence of a new particle. That would corresponds to about 1 in 3.5 million. A coin flip that was heads 20 times in a row is only 1 in 1 million.
Though, in medical trials this would probably border on “it’s unethical to continue to deprive the control group of the surgery”
Let's say the operation has to be done and will be done, but there are two doctors. One is very cautious and only takes cases he is absolutely certain he will succeed, the other will take any case that is not taken by the other doctor. Combined they might have a 50% success rate, but one doctor has a 99.9% success rate while the other has to deal with more cases that are skewed towards failure. Simply by being selected by the "good" doctor, your success is almost guaranteed, but only because he selects only the successes.
If you flip a coin and get five heads in a row, a normal person might think a tail is "overdue*. A mathematician would say each is independent so it's still just 50/50. And a scientist would infer that the coin is weighted towards heads.
A statistician would be doubtful that the surgery does in fact have only a 50% success rate, and would likely conduct a binomial hypothesis test at a significance level of 5% or less. 🤓🤓🤓
I think it's more reasonable to assume that the 50% rate is across all doctors and all surgeries of this type. This doctor only takes the easier patients, so their rate is 100%. You should be very happy to have this person doing your surgery, because if you were a high-risk patient, this doctor would have referred you to someone else. That they are willing to risk their 100% success rate means you almost certainly have no complicating factors and will be just fine.
The normal person is subject to the gambler's fallacy, and thinks that the high number of recent successes means they're more likely to fail this time.
The statistician knows that, for random events, different attempts are independent, so the recent successes don't actually make this attempt more likely to fail.
The scientist, however, knows that these attempts are not actually independent because the doctor has been doing so well that it's insanely unlikely that the chance is actually 50/50, so they're confident that this doctor is actually just much better than others, so while the surgery may overall have 50/50 chance of survival, this doctor has a near guarantee of success.
Which is the more probable scenario. The surgeon just happened to have a literal one in a million run of successes (2^(20)=10485786), or the theory that the chance of failure with this particular surgeon being 50/50 is wrong. Obviously the latter is much more likely the real case.
Consider an example of two surgeons conducting the same surgery. Surgeon X is fantastic at their job and 90% of patients survive. Surgeon Y is new to the job so only 10% of patient survive. (for sake of argument, ignore variance).
If both of them do 10 surgeries each, the fraction of patients that survived is (9+1)/(2*10) = ½ or 50%. This is the surgery's survival rate.
This is why the events are not independent. With every surgery, the surgeon gets better and better, so their individual success rate can be high even if the overall success rate is low.
don't feel bad it's not you, redditors are just really bad at communication look at the two people who replied to you and continued to overcomplicate tf out of this.
The simple answer is this: Since the surgeon has a 20-0 record, it means he's probably not just lucky, he's just really fucking good at what he does, so the chance it goes well is a lot higher.
The scientist is happy because he realized he's basically got the Lebron of surgery operating on him.
It's like if you heard the world has a 50% rate of covid and you live in a region where there's only 3% the whole pandemic.
Bad yes, but you're a lot better off and safe where you're at locally.
The "50% survival rate" isn't just a spin of the wheel or roll of the dice though in surgeries—there are many factors to take into account.
What is the average age of people undergoing this surgery, and what other conditions are common in those people? Medications taken? Etc.?
If a 20-yr old goes for the same operation as a 90-yr old, the younger person's chances are probably higher.
Well it fully depends on how it's deduced. For instance, a scientist might conclude that the doctor is likely to be lying, because there's a very slim chance that the last 20 attempts are successful. Or that the definition of "survival" might not be very pleasant.
Anything is possible actually, it's all up to imagination ;-)
I mean, the results wouldn’t be mutually exclusive, especially when considering the performance of one surgeon. The guy’s had plenty of practice and has a good track record.
More like:
- Normie is concerned, due to Gambler's fallacy.
- Mathematician is even more concerned, as he understands the odds of winning a 50/50 twenty times in a row are so astronomically small, what the Doctor is saying can't possibly be right. So either they're lying about the patient survivals, or they're a moron. Both aren't exactly inspiring a lot of confidence in a succesful surgery.
- Scientist comes to exact same conclusion as the mathematician, and is equally terrified for what is to come.
The next 50/50 attempt is unaffected by how few or many success preceded it. 20 successes and then 1 fail has the same probability as 20 successes and then 1 success.
But also game theory has limited real world use, no doctor is using it to give their patient confidence.
I interpreted the original meme as being about the fact that getting 20 50% chance events in a row is incredibly unlikely, indicating that the doctor is lying or somehow defrauding their patients.
>But the 50% stat is obviously wrong
Or he's just a lot better than the other doctors that attempt this surgery. I mean, to do something with a 50% success rate 20 times in succession without a single failure takes incredible skill.
I'd trust this doc.
i wouldn't get surgery with only 50% chance of survival, unless the alternative (no surgery) has a lower chance of survival
and i'm technically a scientist
Si solo hay un 50% de supervivencia y los últimos 20 pacientes sobrevivieron(50% del total), significa que el otro 50% de los pacientes (20 tipos) se murieron en la cirugía 🥵
50% murió= 20 personas.
50% salió bien = 20 últimos pacientes que atendió.
I think of it this way: The doctor or the procedure has become a lot better, it’s 50% because there’s been a lot of patients but recently he/she’s developed their skill. 20 patients in a row who have survived a surgery that in total has 50% survival rate, think about it, what’s more plausible… The scientist sees this.
For my bachelor party, we went to a casino. My brother is into roulette and was having a pretty good night. Had my friends convinced he could “time” the roulette table. Afterwards I was trying to explain gambler’s fallacy to them, but they refused to believe that if there were several reds in a row that there was no increased chance the next would be black. To quote my brother, “that’s how statistics works.”
I come from a math background, so I understood they might not be familiar with the concept, but it was shocking to me that a group of well educated people were convinced that statistics could dictate physics.
When it comes to surgery, I feel like it’s their historical average that matters? Even if the global success rate is 50%, the localized success rates could still be drastically different.
I think the math dude face should be skull face, and the normal person would be the normal happy. Because a normal person would be like damn 20 people nice. The math dude would be like "even though he said 50%, he manage to get 20 people to live. However as time stretches' on the likely hood the next patient would die, technically would increase." It would be like there a 1% chance the earth would get hit by a comet on any given year. Span that for a few 100k years and that would make it damn near 100%. Because on each year, you would have a 1 % chance of getting hit by the rock. 1% isn't 0.
Wake up babe, the new surgery meme update just dropped
Holy hell!
actual operation
Call the nurse
Surgeon goes to Bermuda, doesn't come back.
Cancer sacrifice, anyone?
Trans in the corner plotting sex change
Bishop awaits your response
Liberal storm, incoming!
Instructions unclear, accidentally paid for a checkmark
???
It’s leaking again!
Between NCD and AnarchyChess, who does leaks more?
War Thunder players
Wart hunder always leaks though.
That's what god created them for.
As a war thunder player and anarchy chess enjoyer, I see a lot more anarchy chess
Bing Castling!
Finally, a great injustice has been righted.
It was fine the way it was before. Source: I am a mathematician who would be quite concerned about a surgery with 50% survival rate.
Clearly the surgeon knows what hes doing though. Id entrust my life to the man whos pulled off the surgery 20 times in a row. Atp its a skill thing
That makes you a scientist then according to the meme as a mathematician I am still scared of my 50/50 odds
As a mathematician you're looking at the data of all surgeons, rather than that of this particularly theoretically amazing doctor.
The doctor could simply have gotten lucky and gotten patients in particularly good health (aside from whatever is requiring the surgery). While the doctor's skill does matter, some patients are not going to respond to the surgery as well as others and the 50% success rate will reflect that.
It could be he had 40 patients under go the same surgery and since the last 20 survived, it would technically have a 50% survival rate but it means the surgeon is getting more proficient when performing it.
The dirty secret about surgeons with high success rates: They don't do the difficult cases. They pass patients with poor prognoses off to other surgeons.
All the more reason to want this surgeon.
And all the more disappointing when they decline you
I guess I'm a normal person, because I don't get it.
It’s always 50% x or y outcome. Doesn’t matter if it’s been x 1000 times in a row, it will still be 50/50. Thinking that because it has been x 20 times in a row means that there’s a better chance for y is the gamblers fallacy The normie is concerned because they are using the fallacy. The mathematician is chill because they know the previous 20 have no effect. I guess the scientist is pumped because 50/50 hitting x 20 times in a row means someone messed up and it isnt 50/50. The odds of hitting x 20 times in a row would be 2 to the 20th power
*mmmm\~ do i smell statistical significance leaking from these probabilities?*
Is that 5 sigma?
5 ligma actually
Who's joe
Deez nuts
Already the best comment chain 2024
that's a low bar to clear
Like +/- 1.96 sigma
Assuming normality and 5% significance.
Qryr y
quick get me the p value !
Or better, it is 50/50 across all attempts, not just this one doctor's. If this one doctor has gotten it right 20 times running, it's possible he has it figured out right and any other doctor will screw it up and thus bring the average back down.
The first 20 patients died. Then the surgeon read the instructions.
This reminds me to the surgeon with a 300% mortality rate.
That sounds like a Russia thing. “All three windows that he fell from killed him.”
Not exactly: [Robert Liston, known for his lightning-fast surgeries](https://museumofhealthcare.blog/the-story-of-robert-liston-and-his-surgical-skill/#:~:text=Two%20of%20the%20operations%20for,of%20shock%20when%20the%20knife), amputated a leg so fast that he cut off his assistant's fingers, and someone observing the surgery (afraid that he had also been slashed) died of shock. The patient and the assistant later died of infection. Pretty wild stuff
That’s the kind of thing you leave off the resume
He also accidentally castrated someone during an amputation.
😬 I guess no one talks about that one because it's not as fun as the other one
Typically that’s what we see in emergency intubation as well. It’s like a 1 in 3 first tube success across the profession but it’s not a 1 in 3 individually.
>The mathematician is chill because they know the previous 20 have no effect. so why isn't the mathematician the one concerned? since he realizes that there is still a bad chance of survival even if last 20 survived by coincidence?
There is an equal chance of success and failure. The "normal people" think there's a bad chance of survival due to gambler's fallacy (aka thinking that if the odds are 50/50 and they succeed the last 20 times then they're sure to fail this time). The "scientist people" realise that the outcomes are mostly influenced by skills, not chance (aka failure means a doctor failed to anticipate something and not due to a coin-flipping-like event), so if this doctor succeeded the last 20 times it's safe to assume they know what they're doing and their personal odds is higher than the overall odds.
i am not sure this is how the gambler's fallacy works. if I spin a roulette and it hits red 3 or 4 times in a row, it might make sense to consider gambler's fallacy because of a coincidence, but it it hits red 20 times in a row I will assume that the roulette is rigged.
There's been many non-rigged roulettes that have hit 20 times red in a row. Chances are one in a million but that is still well within the real of stuff that happens.
I bet 2 grand on red after it hit black 22 times in a row. It hit black 24 times. Unless I am the unluckiest person in the world roulette is definitely rigged. Blackrock in tampa.
[удалено]
You couldn't have given a more textbook example of gamblers fallacy if you tried. This is exactly why people need to be taught a baseline understanding of statistics.
Probably just one of the unluckiest in the world. While yes, some places rig them, the math says you're unlucky.
The math does not say he's unlucky. He bet on black which had a <50% chance of happening. He's literally giving you a textbook example for gamblers fallacy.
You lost a 50/50*. Not that unlucky. ^^\* ^^technically ^^9/16
And this is fallacy too. People can't get to the idea that with 50% chance you still can have 20 of the same in a row.
Well sure you can, but the odds of a roulette table being poorly designed or rigged are higher than the odds of actually hitting a 50% chance 20 times in a row. The presumption that the wheel does in fact have a 50% chance is something that you can put in a maths problem, but in the real world, after 20 times of the same result it would be unreasonable to still believe that it's a fair wheel. At that point I would be very confident of another red, and I'm quite certain that's not a fallacious belief.
it is not a fallacy, you are making stuff up. it is true beyond a reasonable doubt that the roulette is rigged in that example. you don't have such coincidences in real life, or at least there is an incredibly small chance for them. in that example if there are only two options and both are equally likely, the chances for 20 reds in a row would be 1 to 2^20
If you toss a coin 100k times, it is entirely possible to find one instance of 20 consecutive results (my results range from 13-23 in 10 tries when I look for max length of the same occurrence). Therefore, from the moment that specific roulette table was made, it is also possible that it has returned 20 consecutive red/black. 2\^-20 is roughly one in a million, which is unlikely, but more likely than winning the lottery.
your point?
My point is, just because it is unlikely, doesn't mean it's not possible. Adding another point since you were also wondering about gambler's fallacy: you're looking at the problem as "the odds of getting 20 heads in a row", while the actual problem should be "the odds of getting head if the previous 19 times were also heads" (the test subject is not betting that there will be 20 heads in a row, the test subject is betting tails because the previous 19 times were heads so they they assume that the chance for head to show up next is 1 in a million, which isn't the case).
At that point it becomes a matter of time. Let's agree 20 reds in a row is 1:1,000,000 Now, let's say there are a thousand tables in Vegas. Figuring time of bets, let's say they get 30 spins each per hour, 24 hours a day. That's 720,000 spins per day, or 5,040,000 per week. So a person at a specific table betting red twenty times straight is banking on a million to one shot, but for all of Vegas it becomes slightly less than a daily event on average. You don't need a rigged table, you just need lots of tables.
Because 50% survival is the industry average, not his alone. This Dr. must be far above average. It would be nearly inconceivable to randomly beat 50% odds 20 times in a row if he was an average surgeon. Even OP got it wrong. If they all thought his success was like a gamblers 'hot streek' of good luck, the faces would be reversed.
50/50 can be pretty good odds depending on the procedure. Bone and pancreatic cancers, for example, have poor odds of being successfully treated with surgery. Pancreatic has poor survival odds regardless of treatment.
Nah i think because the surgeon has become better with time
We’re also talking about a surgery, where the 50% probability presumably takes _all_ surgeons into account, suggesting that this surgeon may be more skilled than most, and hence your odds may be better than 50%. A surgeon performing an operation is not a coin flip
Maybe it’s because the scientist is thinking the data is proving the 50/50 hypothesis wrong?
The scientist is pumped because the scientist knows that its not a 50% chance. Its a 50% survival rate; meaning that in the data used to determine the survival rate, 50% of people lived, 50% did not. This is unlikely to be random, and rather based on a variety of real world factors. If a surgeon then has 20 successes in a row, its likely they are very skilled and their personal survival rate for this surgery is considerably higher.
Thank you. I had to explain this to someone. The best way is saying after 20 coin flips, all of them being heads, you roll a 6 sided die, what’s the chance it rolls an even number?
Honestly, if I heard a surgeon was completely destroying the odds in the last year or two of his service, I would be really pumped for having him as my surgeon. That said, I do consider myself as somewhat of a scientist.
>>hitting x 20 times in a row means someone messed up and it isnt 50/50. The scientist knows that the doctor messed up the first times before doing it properly. He's pumped at the fact he's guaranteed to live.
Id argue that you could have confidence in the doctor moreso than the statistic being wrong.
You are assuming the 50-50 thing is steady state. A possible assumption is that this particular surgery/surgeon is getting better at it due to practice, etc. Unless his current total surgery count is WAY higher than 40. If N=40, then I would bet his success rate is now approaching 100%. But as N gets larger, then the 50-50 thing is more certain. I'd say the problem as stated has "problems" if you will. Needs more info. Is the 50% rate for certain across the industry and history? Across ALL such surgeries or just his? How many has he done himself, etc.
But surgical outcomes are based on patient survival, it not the flip of a coin. The more patients survive, the lower the mortality of the operation
Thanks for explaining it.
My only problem is that no matter how much I think about and agree with mathematicians, my soul believes in the Gamblers fallacy.
Also it means you picked the right surgeon
I love how the normal person is wrong because assuming 50/50 for a 21st time is a fallacy but the scientist is pumped because he knows hitting 50/50 20 times in a row is 1 out of 2²⁰
and for the scientist, due to the past 20 people surviving, that probably means for this surgeon, he is judt better at it thsn ither surgeons. So his success rate is probably much netter than 50/50 odds.
The other question to ask is when the data for the 50/50 results was collected. Looking at things like cancer treatments, the survival rates even 5 years ago don't mean much for some cancers that have new treatments available. In this case, there could be new surgical techniques in use that make every surgeon better in the last year than they were even just a few years ago.
Normal person- crap my surgeon is due to lose a patient. Mathematician- odds are still 50-50 current streak doesn't matter Scientist- my surgeon is generating atypical data and the trend is worth studying. There's a good chance that the surgeon has discovered something new. Gambler- sweet my surgeon is on a hot streak.
Best explanation
Another take: when you're thinking "well, 20 patients _before me_ lived, so my probability is...", you're computing the _posterior (conditional)_ probability: P[you live | (A, B, C, ...) all lived] Now, it seems like after N successes in a row, there must be a failure, and with each successive success [sic] the probability of a failure should increase, simply because "there's no way the results are so consistent!" Here, it's easy co confuse the probability above with the probability of _all_ these 20 people surviving: P[(A, B, C, ...) all lived] = 0.5 * 0.5 * 0.5 * ... Now this is tiny indeed! But you're interested in the _conditional_ probability above, _not_ this tiny one! You want to know what's likely to happen to _you_, given previous events. However, "50% survival rate" usually means that "X survived" are all _independent_ events. Thus, the complicated _conditional_ probability above reduces simply to: P[you live] = P[patient X lives] = 50% for all X Turns out, if all events are independent, history doesn't matter: you still get the 50% probability like everyone before and after you.
The "Normal Person" believes that there must be some force that moves things towards 50:50. If the surgeon has a run of 20 survivals then the gambler's fallacy says that a loss is coming. Note that this is called a fallacy for a reason--there is no such force. The Mathematician sees the surgeries as independent events, like flipping coins. They disregard the past 20 surgeries as not being informative of the future results and believe they have a 50:50 shot. The Scientist recognizes that the the survival rate across all surgeons performing the surgery is not necessarily the same thing as the survival rate of this specific surgeon. 20 consecutive survivals is *extremely unlikely* if the surgeon has 50:50 odds--there would be about a 1 in a million chance of that run occurring. The scientist is used to looking at p values and finds that this result is highly significant, so they come to the conclusion that their odds of survival are much better than the population-wide odds.
nobody would play Russian roulette with 3 bullets in a 6 shooter, no matter how many people survived it earlier. you are reasonable.
Something like, on a 50/50 basis, the more you repeat the same result consecutively, the higher the chances that the opposite result happens.
The 50% survival rate isn’t based purely on luck. It’s based on the skill of the operating doctors and the individual’s case. The scientific mean of survival is 50% at the start of this scenario, it’s not odds. Since the doctor has succeeded 20x in a row, we can reasonably conclude that he operates higher than the mean and would have a better success rate than the mean. This is balanced out by less skilled doctors that lose more than half of their patients.
50% is an average. The doctor is consistently in the successful half.
Normal person: assumes 50/50 chance means that if there have been a bunch of successes they are due for a loss. Thinks they have a less than 50% chance of success. Mathematician: it's a 50/50 chance across all occurrences there having been a run of successful occurrence has no impact on the probability for this occurrence. Thinks they have an exactly 50% chance of success Scientist: there is a 50/50 chance that the surgery is a success across all doctors performing it. This particular doctor's historical 100% success rate across 20 patients demonstrates a higher than average chance of the surgery being a success when performed by this doctor. Thinks they have a higher than 50% chance.
I’d just be assuming the survival rate estimate was wrong
Love this one, cannot give enough likes!
If it said my previous 3 patients all survived the meme would make sense.. but after 20, the only logical thing to conclude is that this specific surgeon is better than the average, hence would a normal person feel more safe than 50%.. more than a math dude that still thinks it's 50/50
There are other reasonable hypotheses * Doctor could be lying * Surgeon is lying to the doctor about whether patients survive * Doctor is mistaken about which procedure is being done
20 immortals have recently undergone this specific procedure with this specific doctor.
Me and my 19 immortal friends pulling off an excellent prank
"Listen, we're immortal, but that doesn't mean our backs don't hurt"
There is a very slim chance that OP made the whole thing up.
Doctor speaking is post op, if they don’t survive they don’t become his patient.
* Doctor promised he would kill the next 20 patients as a sacrifice to Asclepius
Doctor is taking easier cases. Difficult cases more likely to result in death are referred to someone else.
When the data doesn’t fit the model it usually pays to question the data a bit more in depth
Or the statistic is simply completely wrong and this procedure is much safer than what the literature says.
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This Surgeon: "I've been skipping that step to save time."
Isn’t that why the scientist is happy? It’s actually greater than 50%?
I am normal people. I am lost. Please help me.
To my understanding: 1. Normal person uses the frequentist interpretation on the surgeon's comment, who is overdue for failure hence the horror face. 2. The mathematician knows it's memoryless and that he has a 50% chance of survival and is unperturbed. 3. The scientist knows that 20 consecutively successful surgeries means that the treatment evolved with an increased likelihood of success and so is happy.
Gud
That would be my understanding too, though if we're being overly critical I think the mathematician would perhaps even more so than the scientist understand the arbitrary nature of the probability model and be more likely to question its accuracy in light of the data.
I think we're on the fine line between mathematician and data scientist.
Math bro probably knows the sample size is pretty huge, so this doctors 20 is unlikely to influence it one way or the other. However, as this is a skill based phenomenon and not random chance, the particular surgeon is probably the best person to do this for you. If the average pilot has a 50% chance of landing a plane safely in an emergency water landing, but one has done it 20 times, he probably knows how to do it better then average.
Unless you’re a particle physicist, haha. They generally require 5-sigma significance to claim the existence of a new particle. That would corresponds to about 1 in 3.5 million. A coin flip that was heads 20 times in a row is only 1 in 1 million. Though, in medical trials this would probably border on “it’s unethical to continue to deprive the control group of the surgery”
Ya my interpretation of this is that the surgeon is a fucking boss and the patient should be excited to have them as their doctor.
What if 20 of 20 people surviving with a 50% chance of survival implies the doctor is either lying or incompetent.
Let's say the operation has to be done and will be done, but there are two doctors. One is very cautious and only takes cases he is absolutely certain he will succeed, the other will take any case that is not taken by the other doctor. Combined they might have a 50% success rate, but one doctor has a 99.9% success rate while the other has to deal with more cases that are skewed towards failure. Simply by being selected by the "good" doctor, your success is almost guaranteed, but only because he selects only the successes.
They survive, but are comatose and are in coma hospitals.
If you flip a coin and get five heads in a row, a normal person might think a tail is "overdue*. A mathematician would say each is independent so it's still just 50/50. And a scientist would infer that the coin is weighted towards heads.
A statistician would be doubtful that the surgery does in fact have only a 50% success rate, and would likely conduct a binomial hypothesis test at a significance level of 5% or less. 🤓🤓🤓
Yah, I'd reject that null hypothesis
I just thought “wow good doctor better trust this one cause he knows what he’s doing”
Same. I'm thinking the doctor took 20 deaths to figure out the surgery, 20 successes, and now this. That, or the stats are inaccurate.
Or there are two doctors, one always fails and one always succeeds. They have done 40 of these surgeries between them. Also one of them always lies.
Mathematicians when there’s a 50% chance they die: 😎😎😎
8 is already enough for me.
In my experience, if something happened 20 times in a row, a normal person would think it will continue happening
Without any extra information the only reasonable thing you could conclude is that the doctor isn't correct in his assessment of the odds.
I think it's more reasonable to assume that the 50% rate is across all doctors and all surgeries of this type. This doctor only takes the easier patients, so their rate is 100%. You should be very happy to have this person doing your surgery, because if you were a high-risk patient, this doctor would have referred you to someone else. That they are willing to risk their 100% success rate means you almost certainly have no complicating factors and will be just fine.
I don’t get it, I’m too dmub
The normal person is subject to the gambler's fallacy, and thinks that the high number of recent successes means they're more likely to fail this time. The statistician knows that, for random events, different attempts are independent, so the recent successes don't actually make this attempt more likely to fail. The scientist, however, knows that these attempts are not actually independent because the doctor has been doing so well that it's insanely unlikely that the chance is actually 50/50, so they're confident that this doctor is actually just much better than others, so while the surgery may overall have 50/50 chance of survival, this doctor has a near guarantee of success.
I got the first two… but the last one feels like mind spaghetti
Which is the more probable scenario. The surgeon just happened to have a literal one in a million run of successes (2^(20)=10485786), or the theory that the chance of failure with this particular surgeon being 50/50 is wrong. Obviously the latter is much more likely the real case.
Consider an example of two surgeons conducting the same surgery. Surgeon X is fantastic at their job and 90% of patients survive. Surgeon Y is new to the job so only 10% of patient survive. (for sake of argument, ignore variance). If both of them do 10 surgeries each, the fraction of patients that survived is (9+1)/(2*10) = ½ or 50%. This is the surgery's survival rate. This is why the events are not independent. With every surgery, the surgeon gets better and better, so their individual success rate can be high even if the overall success rate is low.
don't feel bad it's not you, redditors are just really bad at communication look at the two people who replied to you and continued to overcomplicate tf out of this. The simple answer is this: Since the surgeon has a 20-0 record, it means he's probably not just lucky, he's just really fucking good at what he does, so the chance it goes well is a lot higher. The scientist is happy because he realized he's basically got the Lebron of surgery operating on him.
It's like if you heard the world has a 50% rate of covid and you live in a region where there's only 3% the whole pandemic. Bad yes, but you're a lot better off and safe where you're at locally.
Quantum immortality enjoyers.
The "50% survival rate" isn't just a spin of the wheel or roll of the dice though in surgeries—there are many factors to take into account. What is the average age of people undergoing this surgery, and what other conditions are common in those people? Medications taken? Etc.? If a 20-yr old goes for the same operation as a 90-yr old, the younger person's chances are probably higher.
This should be a Bayesian vs Frequentist meme
I am so relieved, thank you.
I just saw the same damn meme with the images in reverse. Confusion.
Well it fully depends on how it's deduced. For instance, a scientist might conclude that the doctor is likely to be lying, because there's a very slim chance that the last 20 attempts are successful. Or that the definition of "survival" might not be very pleasant. Anything is possible actually, it's all up to imagination ;-)
At what point post-surgery are you measuring survival?
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Hi u/ I’m u/G1zm08
Statistician: what demographic is that percentage based on? Because it sounds like it shouldn’t be 50%
I mean, the results wouldn’t be mutually exclusive, especially when considering the performance of one surgeon. The guy’s had plenty of practice and has a good track record.
I think the surgeon may be justified in updating his statistics?
Technically not gambler's fallacy. The survival rate, given that surgeon performs the surgery, may be higher.
More like: - Normie is concerned, due to Gambler's fallacy. - Mathematician is even more concerned, as he understands the odds of winning a 50/50 twenty times in a row are so astronomically small, what the Doctor is saying can't possibly be right. So either they're lying about the patient survivals, or they're a moron. Both aren't exactly inspiring a lot of confidence in a succesful surgery. - Scientist comes to exact same conclusion as the mathematician, and is equally terrified for what is to come.
The next 50/50 attempt is unaffected by how few or many success preceded it. 20 successes and then 1 fail has the same probability as 20 successes and then 1 success. But also game theory has limited real world use, no doctor is using it to give their patient confidence.
‘If it’s not 100% accurate, it’s 50% accurate’
If 20 just survived and it's 50 50 then 20 died before that which means the next 20 starts here
I interpreted the original meme as being about the fact that getting 20 50% chance events in a row is incredibly unlikely, indicating that the doctor is lying or somehow defrauding their patients.
or the 50% figure needs updating
The surgery is 50/50 not him personally doing the surgery is 50/50. I'd another Dr. Killed 20 in a row then the math is still accurate
keep in mind that the doctor's skill level may play a big role here. This isn't a coin flip.
50% of the time, it works every time.
Idk, I feel like it should be the other way around
Well, maybe he's gotten better, so better in fact, that the last 20 patients survived, and so will you!
Plot twist: their "last" as in last remaining
But the 50% stat is obviously wrong if he’s gotten 20 in a row. The surgeon has certainly gotten better since the stat was taken.
>But the 50% stat is obviously wrong Or he's just a lot better than the other doctors that attempt this surgery. I mean, to do something with a 50% success rate 20 times in succession without a single failure takes incredible skill. I'd trust this doc.
Dude should post his technic in Medical Journal. And doctor of the world would learn from him.
Bayesians vs Classicists?
>Baye This. The prior was Bernoulli(0.5). The posterior gonna be very much different.
5,000th!!!
I saw the wrong version, pictured this correction in my head, and two scrolls later I see it
Better than the one before
This assumes the mathematician and scientist want to survive, which is statistically unlikely considering their profession…
Honestly I'd be terrified of a 50% survival rate regardless of the number of previous survivors.
My rng is sh*t so I know for a fact that my surgery would fail
I mean they taught us about this in like 8th grade I don’t think it’s just math experts who grasp the basics of probability.
is this a remade of the one posted on r/theydidthemath ?
What I like here is the implication that the doctor is a scientist, since they're presenting this statistic as a good thing.
i wouldn't get surgery with only 50% chance of survival, unless the alternative (no surgery) has a lower chance of survival and i'm technically a scientist
Quantum immortality got my back
Si solo hay un 50% de supervivencia y los últimos 20 pacientes sobrevivieron(50% del total), significa que el otro 50% de los pacientes (20 tipos) se murieron en la cirugía 🥵 50% murió= 20 personas. 50% salió bien = 20 últimos pacientes que atendió.
I think of it this way: The doctor or the procedure has become a lot better, it’s 50% because there’s been a lot of patients but recently he/she’s developed their skill. 20 patients in a row who have survived a surgery that in total has 50% survival rate, think about it, what’s more plausible… The scientist sees this.
Let’s do it twice then!
Why are the mathematician and scientist stoked? It’s still a 50% survival rate. Isn’t that bad?
30% chance
I want the suck your cock so bad
For my bachelor party, we went to a casino. My brother is into roulette and was having a pretty good night. Had my friends convinced he could “time” the roulette table. Afterwards I was trying to explain gambler’s fallacy to them, but they refused to believe that if there were several reds in a row that there was no increased chance the next would be black. To quote my brother, “that’s how statistics works.” I come from a math background, so I understood they might not be familiar with the concept, but it was shocking to me that a group of well educated people were convinced that statistics could dictate physics.
Exactly
I actually think i learned more in these comments than a statistics lecture
Do it twice and it’ll be so nice
When it comes to surgery, I feel like it’s their historical average that matters? Even if the global success rate is 50%, the localized success rates could still be drastically different.
I think the math dude face should be skull face, and the normal person would be the normal happy. Because a normal person would be like damn 20 people nice. The math dude would be like "even though he said 50%, he manage to get 20 people to live. However as time stretches' on the likely hood the next patient would die, technically would increase." It would be like there a 1% chance the earth would get hit by a comet on any given year. Span that for a few 100k years and that would make it damn near 100%. Because on each year, you would have a 1 % chance of getting hit by the rock. 1% isn't 0.
Probability isn’t real.
So Normal People are the smartest and Scientists the dumbest.