this post was submitted on 11 Feb 2024
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Showerthoughts

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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.

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I can accept the fact that on a Roulette wheel (as long as there are no defects or imbalances in the wheel or ball) that the odds are the same each spin and previous spin outcomes have no influence over the current spin. However, if I see black come up 32 times in a row I am betting on red for the next spin.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

The Gambler's Fallacy is Really Odd

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[–] Feathercrown@lemmy.world 23 points 9 months ago (1 children)

You're wrong, but you're in good company. It's a very counterintuitive effect. One technique that can be helpful for understanding probability problems is to take them to the extreme. Let's increase the number of doors to 100. One has a car, 99 have goats. You choose a door, with a 1% chance of having picked the car. The host then opens 98 other doors, all of which have goats behind them. You now have a choice: the door you chose originally, with a 1% chance of a car... or the other door, with a 99% chance of a car.

[–] june@lemmy.world 9 points 9 months ago (3 children)

Oh that’s so weird. I get it from a proof perspective but it feels very wrong.

My brain tells me it’s two separate scenarios where the first choice was 99:1 and after eliminating 98 there’s a new equation that makes it 50:50.

[–] Silentiea@lemm.ee 10 points 9 months ago* (last edited 9 months ago) (1 children)

The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.

Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?

[–] june@lemmy.world 5 points 9 months ago

Your first paragraph made it click. Thanks!

[–] Feathercrown@lemmy.world 1 points 9 months ago

Yeah it's very counterintuitive