Eli5: How do the odds of flipping a coin work?

Question

I know, 50/50 heads tails right? But help me understand the next step – each coin flip has a 50/50 shot of heads or tails. What I don’t understand is how the likelihood of the next flip doesn’t change. For example if I flipped a coin 10 times and every time it flipped heads, the next flip would be 50/50 tails. Wouldn’t the likelihood of flipping a coin 11 times and having it be heads every time be really low? 0.5^11 = 0.048%?

Here’s the origin of the question. I was at a roulette table and the guy said “it’s been black the last 8 rolls, the next one has to be red.” At first I thought, the next roll will be ~47% black, ~47 red, ~6% 0 or 00 you fucking imbecile. Then I thought to myself, what are the chances that there are no red rolls in 9 rolls, which is well below 1%.

Am I the imbecile?

In: 215

Answer 1

>What I don’t understand is how the likelihood of the next flip doesn’t change.

What’s the difference between flipping one coin 10 times and flipping 10 coins all at once?

Because flipping a coin does not significantly impact the coin *itself* one flip doesn’t impact the next because each flip doesn’t “know” any other flip occurred.

A roulette table, one that’s not rigged, anyway, is the same way. Nothing happens during a spin that will impact the mechanism itself so each spin is functionally identical to the very first spin. The ball doesn’t remember.

Probabilities like the odds of flipping a heads or getting a red after 8 blacks are calculated by taking all possible results and counting how many times the specific result you’re looking at happened. You’re only looking at one possible attempt. The more attempts you make the more likely what you’ll see is in accordance to the odds because that’s what the odds *are.* All possible attempts. (for extra funsies, look up the “galton board” for a great example of how *lots* of random = consistent)

You’re not an imbecile. You’re human. This is what’s known as the “gamblers fallacy” and it’s one of the ways our brains take shortcuts that are “good enough” most of the time but fails when you really take a close look at what’s actually going on.