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
Here’s a perspective that clicks for me: After the roulette table lands on black 8 times in a row, the probability that it happened *is now 100%*, because it’s already happened. The chances of the next spin landing on black (or red) is 47%, as you say.
Every time something happens, you can think of its probability resolving to 100% since now it’s in the past and you know the outcome.
That doesn’t conflict with the idea that landing on black 8 times in a row is a very low chance (0.47^8). The trick here though, is to realize that *any* combination of 8 red/black outcomes also has this same 0.47^8 chance of happening. There’s nothing special about it being 8 blacks. A sequence of RBRRRBRB has the same tiny chance to occur, we just don’t focus on it because it’s not so nice of a pattern.
Latest Answers