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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Think of it this way: Let’s say that last week you were unlucky enough to be hit by lightning, then developed a rare disease. That doesn’t mean you can drive without a seatbelt on the way home thinking “Well, nothing else bad can happen to me.” Your chances of a car accident have nothing to do with whether you have the disease or were struck by lightning.
Now, two weeks ago, we would have said “The chances of you getting hit by lightning, developing a rare disease AND being in a car accident in a two week period is really really small.” But, once the first two of those happen, the accident doesn’t become any less (or more) likely to to happen.
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