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
I understand it’s contra-intuitive, but every single event has its chance independently from the previous ones.
Imagine you are tossing coins 8 times. One such run could be something like HHHTHTTH. You would probably call it a kind of realistic run. Even though the first 7 times you had slightly more heads (4H vs. 3T), it’s kind of okay to have yet another H.
Now imagine you exist in 256 parallel universes, and in the first universe you have a run such as HHHHHHHH. In the next one you have HHHHHHHT. Then HHHHHHTH, or HHHHHTHH, eventually HTHTHTHT etc. Of course there will be such “random” looking runs like HTTHTHTT, which is kinda the thing you expect.
Now those alteregos of yours where your coin did a “weird” run, they would think that this is impossible (or unlikely), and for example after 7 H’s there is more likely for a T to come. But in fact there will be only one universe where after 7 H’s in fact a T comes.
It’s because each exact run (even each regularly random looking run like HTTHTHTT) has only one chance out of 256. And each “weird” one has the same 1 in 256.
So when you are tossing the coin and have already 7 H’s, you can always imagine that you are one of your alteregos in 256 parallel universes, and one yourself will get a H, the other yourself will get a T. You just don’t know which one you really are, that’s why it still remains 50-50%
If this is not convincingly for you, you can always ask another question. If the coin (or roulette or whatever) has memory, how long is this memory?
Let’s say you have a coin and you already have 7 H’s. Let’s assume that for some reason a T has a higher chance now. For how long does this higher chance for T exist? Within an hour? Within a day? What if you never have the chance to toss the next time, but someone else does it for you? Is it okay to always have H’s, if you change the coin, because you “exhaust” the heads in one coin but have some left in the other? If you can exhaust a coin, what happens if you give it away? Can you cheat a coin toss (like the beginning of a football match for example) by exhausting a coin of heads and then tossing it because now it is surely tails?
If the odds are not linked to a coin but to a person (so you exhaust *yourself* of heads), what happens if two people meets and do a common coin toss; if one has had only heads previously and the other has had tails?
As you see if the luck had any memory it would create a super weird world.
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