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
BEFORE you start flipping, the odds of a run of 9 heads (say) are (1/2)^9. But.
If, at some point, you’ve already flipped 8 heads in a row, well – it’s now a fact. There’s no chance it didn’t happen. Its probability is 1. The chance NOW that you will complete a run of 9 is the chance of a run of 8 which has already happened, multiplied by the chance of another head. 1 x 1/2, i.e 50%.
The gambler’s fallacy is, basically, failing to recognise that the probability of something that has already happened is 100%. It doesn’t matter that what has already happened was, at one point, extremely improbable. It’s happened. It was improbable back then; now it’s not only not improbable, it’s a certainty. And the dice (etc.) don’t have memories, and don’t care.
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