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
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.
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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
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