I am really surprised at how bad at statistics and compound interest really smart people can be.
Example 1: Not so good with statistics.
Me: There's about a 5 chances out of 6 this six-sided die will roll above a one.
Them: ok ...
Me, rolls die: It's a 1.
Them: You are bad at statistics, and can no longer be trusted.
Me: ... I said this could happen.
Them: You said the other was more likely, and this is what actually happened.
Example 2: Not so good with compound interest
Me: A times B ^ T times C is the same as A times C times B ^ T
Them: No, because having C happen after the interest accrues means the output is larger.
Me: ....
These were both from real smart people. It's a humbling moment, as I realize I assuredly have similar blocks.
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Failing a die roll when I have an 80%+ chance of success sometimes feels like being cheated, even while I go "Well, that's gonna happen sometimes" intellectually.
ReplyDeleteAnd I suspect the intellectual habit there is me heading myself off at the pass to avoid saying exactly the kind of thing you've noted above, motivated by not wanting to look stupid by saying it.
Them: I lost 10% and then I made 10% so I should have all my money back.
ReplyDeleteMe: no
Do you know the puzzle about the family with two children?
ReplyDeleteFact 1: There is a 50/50 chance that all children are born either boys or girls. (Clearly this puzzle was invented some time ago)
Fact 2: One of the children in this family is a boy.
Question: what are the odds that the other child is also a boy?
My favourite real example I was around for of really intellectual people going mad about stochastic basics:
ReplyDeleteArbitor for distributing housing areas: there is a lottery ticket for everybody to see which ground you get.
Them: but it's unfair. I can only come in the evening to pick my lottery ticket and the best areas might be already gone. People who come early have an advantage.
Arbitor: it doesn't matter in which order the tickets are drawn.
Them: I call my lawyer.
Lawyer: everybody should draw their ticket at the same time. Change your procedure.
I once gave an impromptu lecture to my friends in a high school math class about conditional probabilities. I didn't know my math teacher was standing behind me while I did it. She startled me when she told me I did a good job.
ReplyDeleteWhat she didn't know was that I'd played poker for snacks since elementary school and could win consistently enough at blackjack that when my parents threw BBQs for their friends, which always included a group playing blackjack, at least one person there would hand me money to play for them so they could go sing karaoke.
Brian Ashford I do. You want to walk us through it?
ReplyDeleteWe're all so bad at everything.
ReplyDeleteBrian Ashford You also need to know that the gender of different children within a family are independent. That's essential.
ReplyDeleteWorth reading if you care about such things:
ReplyDeleteTversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105-110.
... illustrated by the responses of 84 professional psychologists to a questionnaire concerning research decisions ...
We’ve gotten a little better since then professionally, but people are just bad intuitive statisticians.
People in a gaming group I hung around with used to hang around with, would say things like: "If I'm rolling twelve d6, and looking for 4+, then I'm statistically guaranteed six successes".
ReplyDelete