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
In what way does the result of the previous flips affect the next? You flipped heads 10 times, stood up, walked out and somebody else came in. They know nothing about you or your coin flips. They just see a random coin and do a flip. What would they expect the odds of their single flip to be?
In order to modify the odds of another event, *something* has to tangibly change. An outcome must be added or lost. If your coin doesn’t change the number of sides or suddenly grow some tiny wings to steer itself midair, it’s still gonna be “one out of two options”.
Same with the roulette. It sure is a tiny chance to hit the same result 9 times, *but you already did 8 times*. Those are settled. You are *already* in an extremely low probability branch, but the next roll is independent – it just decides between the three even lower probability branches you’re about to enter.
Or take it like this: 9x black is very rare, but 8x black plus 1x red is exactly the same rarity.
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