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this post was submitted on 04 Feb 2025
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Asklemmy
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Pretty much anything related to statistics and probability. People have gut feelings because our minds are really good at finding patterns, but we're also really good at making up patterns that don't exist.
The one people probably have most experience with is the gambler's fallacy. After losing more than expected, people think they'll now be more likely to win.
I also like the Monty Hall problem and the birthday problem.
The gambler’s fallacy is pretty easy to get, as is the Monty Hall problem if you restate the question as having 100 doors instead of 3. But for the life of me I don’t think I’ll ever have an intuitive understanding of the birthday problem. That one just boggles my mind constantly.
Lemme try my favorite way to explain the birthday problem without getting too mathy:
If you take 23 people, that's 253 pairs of people to compare (23 people x22 others to pair them with/2 people per pair). That's a lot of pairs to check and get only unique answers
Really? The birthday problem is a super simple multiplication, you can do it on paper. The only thing you really need to understand is the inversion of probability (
P(A) = 1 - P(not A)).The Monty hall problem... I've understood it at times, but every time I come back to it I have to figure it out again, usually with help. That shit is unintuitive.
Adding my own explanation, because I think it clicks better for me (especially when I write it down):
p(switch|picked wrong) = 100%), so the total chance of the remaining door being correct isp(switch|picked wrong)* p(picked wrong) = 66%.p(switch|picked right) = 50%, which means thatp(switch|picked right) * p(picked right) = 50% * 33% = 17%.p(don't switch|picked wrong) * p(picked wrong) = 50% * 66% = 33%(because of the remaining doors including the one you picked, you have no more information)p(don't switch|picked right) * p(picked right) = 50% * 33% = 17%(because both of the unpicked doors are wrong, Monty didn't give you more information)So there's a strong benefit of switching (66% to 33%) if you picked wrong, and even odds of switching if you picked right (17% in both cases).
Please feel free to correct me if I'm wrong here.
My explanation is better:
There's three doors, of which one is the winner.
First, pick a door to exclude. You have a 66% chance of correctly excluding a non-winning door.
Next, Monty excludes a non- winning door with certainty.
Finally, open the remaining door and take the prize!
My favourite explanation of the Monty hall problem is that you probably picked the wrong door as your first choice (because there’s 2/3 chance of it being wrong). Therefore once the third door is removed and you’re given the option to switch you should, because assuming you did pick the wrong door first then the other door has to be the right one
Thanks for the help, it was easier this time 😅
The birthday problem is super easy to understand with puzzles! For example, how does laying out the edges increase the likelihood of a random piece to fit.
One of my favourite pages on wikipedia:
https://en.wikipedia.org/wiki/List_of_cognitive_biases
The thing about that is that it's a little too complete. How can there be both negativity bias and normalcy bias, for example?
To make any sense, you'd need to break it down into a flowchart or algorithm of some kind, that predicts the skew from objectivity based on the situation and personality tendencies.
I think they probably appear in different types of situations, not all at once. And maybe different types of people/thinking are more prone to some than to others.
Exactly. I feel like just listing them out is of limited use because of that.
It's extremely useful, because it's an index to all the known things that might be useful in a given situation. The point is not to assess all of them, the point is to not miss ones you're unfamiliar with that may be important in your situation.
I imagine psychologists can do more with it, but in practice the main thing I see formal fallacies used for is as something to shout during a debate, and it never seems to convince anyone.
If you can catch yourself using one, that's good I guess.
I work in the risk assessment space, so they are kind of critical to be aware of, for me :)
Related to gambling: being "pot committed"
Pot committed is more a math reality with a small amount of sunk cost fallacy. There's always a non zero chance someone is bluffing. A 99% chance to lose $11 is better than a 100% chance to lose $10 if you can win $100 on that 1%.