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
From the standpoint of statistical probability, yes, every coin flip is an independent 50/50 event, and the likelihood of 11 heads in a row is 1/2048 or .048%. This means that for any given flip, you have no reason to expect one outcome more than the other; but if you record the outcomes of 2048 sets of 11 coin flips, there is reason to expect that nothing but heads will show up just once.
The probability of 8 fair American roulette rolls in a row coming up all red is (0.474)^8, or about 1/392. So yes, it’s not going to happen often, but the person running the table can safely expect to see it happen every now and then.
More importantly, though, keep in mind that it’s this person’s job to discourage players from feeling as though these are independent events as much as possible. If the previous eight rolls hadn’t been all red, the person running the table would have described the situation in terms of whatever the most unlikely recent sequence had been. Maybe the last six came up even numbers; or maybe the last five were all in the third column. So no matter what happens, there’s almost always going to be a way to describe the current sequence as uncommon.
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