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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Gambler’s fallacy: a random event is influenced by past results.
Truth: no matter how many heads or tails in a row occur, the probability of either occurring on the next toss remains 50/50.
What *does* change is the *liklihood* that such a runs of a particular length are seen over an infinite number of tosses.
So if you were to toss a coin 1,000,000 times, you would expect to record far more discrete instances of 4 heads occuring in a row than 40 heads occuring in a row.
Each toss has a 50/50 chance of going either way. But the frequency (and liklihood) that a sequence of all heads occurs decreases as the length of the sequence increases.
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