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
The odds of getting 10 heads in a row is the same as the odds of getting any other combination of flips. Consider that the first flip is as important as the last to get 10 in a row. And all the others. AND the odds of getting any other combination – 10 tails, or 5 heads and 5 tails, or alternating heads and tails, or 3 heads, then a tails, then 2 heads, then 4 tails – whatever – are all the same as the odds of getting 10 heads. You just don’t notice most of the other combinations because they don’t look significant. Same with something like playing the lottery with the numbers of your birthday – there’s absolutely nothing special about your birthday except to you, and the odds are the same as with any other numbers. You just notice the pattern so you think it’s rare, but the odds are the same as all the other patterns.
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