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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The Gambler's Fallacy makes sense logically, but it feels so wrong emotionally. (lemmy.world)
submitted 9 months ago by alt_total_loser@lemmy.world to c/showerthoughts@lemmy.world
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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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[–] Silentiea@lemm.ee 4 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?

[–] Iamdanno@lemmynsfw.com -2 points 9 months ago (1 children)

The host's intentions are irrelevant. Numerically, there are only two choices. That makes it fifty-fifty.

[–] Silentiea@lemm.ee 7 points 9 months ago

You think that even in the hundred-door case? Test it. Hell, even test it in the 3 door case. It is empirically not 50%.

If the host had an even chance to show you either door, you'd be right, but since the host always shows you a goat, the two events (picking a door and choosing whether to switch) are no longer independent, since if you pick a goat it forces the host to pick the other goat.