this post was submitted on 09 Oct 2024
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So...
Did I get it right?
The mathematician is probably feeling fine because he is computing the conditional probability of survival (otherwise fuck no I am not taking a surgery that has a %50 chance of killing me, that is way too much).
Depending on what you're treating, 50% sounds pretty good.
I remember when I went for my last surgery and I was signing all the consent forms, my doctor was emphasising the 17% chance of this known lifelong complication, and the increased 4% chance of general anaesthesia fatality (compared to 1 in 10,000 for general public).
My mum was freaking out because when she had the same surgery she'd been seen much earlier in the disease process, she wasn't expecting such a "high" risk of complications in my care.
But all I was hearing is that there's an over 80% chance it will be a success. Considering how limited and painful my life was by the thing we were treating, it was all no brainier, I liked those odds. Plus my condition is diagnosed 1 in 100,000 people, so how much data could my surgeon really have on the rate of risk, the sample size would be laughable.
Still the best decision of my life, my surgeon rolled his skilled dice, I had zero complications (other than slow wound healing but we expected and prepared for that). I threw my crutches in the trash 2 years later, and ran for the first time in my life at 27 years old after being told at 6 years old that I'd be a full time wheelchair user by 30.
That's awesome. I'm glad everything went so well. Here's to a healthy and long life! Even the idea of going under is terrifying to me. You definitely had some courage with that attitude and that's really admirable.
It helps that I'd had several previous surgeries, so I'd had practice at keeping my cool. Plus my surgeon was in discussion with me for months with multiple consultations to really understand the issue, I don't think I could have possibly been in safer hands.
the gambler's fallacy is the opposite of what applies to #1
#2 is an optimist? A glass half full type of guy maybe.
#3 i'd guess is inferring that the statistics are based on an even distribution where the failures are disproportionately made up of by the same select few surgeons. or maybe that's #2 and the scientist actually know the theory of how the procedure works in addition to what #2 knows about statistics and distributions.
1 in 100,000 not 10,000 (anaesthesia deaths)
Well either it's 1 in 10,0000 in my country, or the department of health, my surgeon and GP are all missing a zero... which isn't more likely because there's no way our risk would be that much higher than the UK, and the NHS public health resources is 100,000.
I can't load that page so assuming it just says 1 in 10,000. That does seem like an insane difference and actually quite a high risk imo given how many people undergo surgery.
10 points to Gryffindor
Yay!
If the surgeons been successful the last 20 times, then they're probably doing something different or much better at it than the pool of surgeons the data was pulled from.
Yeah. The odds of 20 coinflips coming up heads is 1 / 2^20, 1 in 1048576. Meaning, it would take over one million tries of 20 coinflips to get one that comes up all heads on average. Our surgeon has done the surgery 10000 times, you say. That's 500 runs of 20 coinflips. The surgeon could do 2000 times the amount of surgery they've already done and not expect a given run of 20 surgeries to succeed. Granted, odds are slightly higher looking for a string of 20 successes in one run of 10000 than looking for one successful run of 20 in 500 runs of 20, but I don't believe those odds are higher by one or more orders of magnitude. I don't remember enough of my statistics class to calculate it though and I'm too lazy to look it up. In any case, either that last 20 is an INSANELY lucky run, or the surgeon has improved drastically, and it's far far farore likely the surgeon has improved or found a way to improve the procedure.
The difference between this and the gambler's fallacy being it's not using past results to justify the next, we're using past results to make a hypothesis that the conditions have changed. If you have a slot machine with a 1% chance to pay out, going 200 or 300 pulls without winning wouldn't really be unusual. If it didn't happen for enough tries that you reach the same odds as the surgeon hitting that 20 coinflips run, I'd say your 1% chance slot machine is broken or faulty -- you're so far out of the normal distribution your data points is in a different zip code
Gamblers fallacy does go both ways. There's also a thing in gambling, not part of the gamblers fallacy, more of a superstition thing, that there can be runs of, what is more or less luck. The gamblers fallacy would have you believe that after 20 successes, a failure is "due to happen". According to math, that's not the case, and in the event of something that requires skill to execute, almost nothing is just luck or statistics.
So the last one isn't so much the gamblers fallacy, if anything it would be the superstition that the run of successes will continue; however scientists will look at this more as a game of skill. While 50% of all patients who have the procedure do not survive, or whatever, the last 20 of this doctors patients have survived. Clearly their skill for the procedure is above average. Even from a statistics perspective the rate might be 50% but you're in the hands of a doctor pushing that number up to 50%, rather than dragging it down to 50%. So on all fronts, if you hear this, bluntly, you have an unknown risk level, somewhere between 50% and 0%.
Gamblers fallacy or law of large numbers...
law of large numbers does not imply gambler's fallacy