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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The usual model would say that 8 blacks in roulette do not change the probabilities on the next roll. LIkewise with coin tossing. For example, in two coin tosses, with the usual model, the following outcomes have equal probability: HH, HT, TH, TT. Getting a heads does not change the probability of getting heads on the next toss. Whether or not the standard models do a proper job of modelling reality is another question.
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