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
Probability doesn’t have the capacity to tell you what is going to happen next. This is always true, even when you toss a coin repeatedly.
Probability tells us that at some point in the future, after a significantly large number of tosses of a perfectly balanced and impartial coin, you will eventually have tossed an equal amount of heads and tails.
This is mainly because of how probability works — it is descriptive of the past, it isn’t technically predictive of the future. It can never tell you what is actually going to happen to a single event, or a single coin. It approximates the aggregate events, and does it reasonably well with large numbers but poorly with small numbers. We don’t know what’s going to come up next. We don’t know how many tosses it will take to achieve the perfect distribution either. However, given enough assumptions and some abstraction, we use the probability predictively for practical things.
This is usually just fine for whatever we are doing, including tossing a coin, but it is never predictive of the outcome of the coin toss in the strict sense.
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