
01-24-2025, 03:37 PM
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Planar Protector
Join Date: Jan 2023
Location: Felwithe
Posts: 5,149
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Quote:
ou’re onto an interesting thought process here, but let's break it down a bit.
1. Coin flips are independent events.
A coin flip is (assuming it's a fair coin) independent of all the flips that came before it. That means, on each flip, the probability of getting heads or tails is always 50/50, no matter what’s happened up to that point.
So if you’ve already flipped 40 heads in 40 flips (wildly unlikely, but not impossible), the odds of the next flip being tails are still 50%. This is where the gambler's fallacy comes in—thinking past outcomes influence future probabilities in independent events. They don’t.
2. Outcomes over 50 flips.
If you flip a coin 50 times, on average, you’ll get 25 heads and 25 tails, but that doesn’t mean it will always land exactly like that. Probability allows for a range of outcomes:
It’s very rare to get something extreme like 50 heads or 50 tails, but it’s not impossible.
The most likely outcome is something close to 25 heads and 25 tails, but the exact distribution will vary with each set of 50 flips.
The more flips you do, the closer the ratio of heads to tails is likely to get to 50:50 (this is the law of large numbers), but over small numbers of flips, you’ll see more variation.
3. What about 40 heads in 40 flips?
This is insanely improbable but not impossible. The probability of flipping 40 heads in a row is:
(0.5)40=1 in 1,099,511,627,776
(0.5)40=1 in 1,099,511,627,776
So if you're seeing that, you're either:
Very lucky (or unlucky).
Flipping a rigged coin.
But even then, the odds for the 41st flip are still 50/50 if the coin is fair.
TL;DR:
Coin flips are independent.
On average, you’ll get close to 25 heads and 25 tails in 50 flips, but it’s not guaranteed.
The gambler’s fallacy explains why we feel like tails would be "due" after seeing 40 heads, but mathematically, the odds remain the same: 50/50.
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someone taught this thing TL;DR lol.
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