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

Each flip, you have 50% of getting heads and 50% chance of getting tails. That is true.

The odds of achieving the sequence of H-H-H-H-H-H-H-H-H-H-H are the same as the odds of H-H-H-H-H-H-H-H-H-H-T.

It is not a 50% chance, though. As there are many other sequences possible, such as T-H-T-H-T-T-T-T-H-T-H. And if your calculation is correct (I didn’t check), then every possible sequence is .048% chance of happening.

Now, if you haven’t flipped any coin yet, it is a .048% chance of getting all heads in 11 flips. However, if you ALREADY landed on heads 10 times in a row, all those sequences that DIDNT start with H-H-H-H-H-H-H-H-H-H (10 heads) are no longer a factor and your odds of getting 11 heads in a row are 50% AT THAT POINT.

In fact, each time you land on heads, your odds are no longer .048%; it rises with each flip.

TLDR: You start with a .048% chance of getting 11 heads in a row. And with every successful flip, your odds increase. Eventually, it becomes a 50% chance when you’re on your final flip.

Edit: So, with the roulette, you are right. B-B-B-B-B-B-B-B-B has the same odds as B-B-B-B-B-B-B-B-R. The other guy is getting confused with the thought that getting 9 blacks in a row is a low chance IF he predicted that prior to any of the roulette rounds. And even then, guessing which one will be red is pointless.