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
If you flip a coin 10 times, there are 2^10 sequences that you could end up with. So while it may be true that the most probable outcome is to end up with 5 heads and 5 tails, it’s only because more of those unique sequences tally up to those values. If you do end up with a 5/5 distribution, the exact sequence that got you there is still the same as flipping all heads or all tails.
So yes, flipping a coin 11 times and having it land on heads every time is 0.048%. But it’s the exact same probability of following the exact sequence of heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads. The higher probability in the ending tally being more evenly distributed is only because we lump the sequence together with other sequences.
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