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?
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Getting head on the 11th toss after getting heads in all previous 10 tosses is not same as getting heads 11 times in a row. The former experiment has already established that 10 heads in row have been observed(which in itself is an astronomically rare event) and getting head in the next toss is always 50-50. If you consider the chances of getting 10 heads in a row in the first place, then you get the same chances as the latter case.
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