A roulette wheel has a 49% chance (or something i can’t remember but for the sake of this discussion we can just call it 50%) of landing on either black or red. i feel like every time it lands on red, the odds of it landing on red again next spin go down, but also logically i know the odds reset for each spin because the numbers still add up to 50%. Why is it not the former? What is this magic?
In: Mathematics
I think the math is straightforward enough and other people have explained it anyway. You ‘know’ they’re independent, but it seems like you’re more asking why they don’t ‘feel’ independent. Which seems more like a psychological question than a math one.
Our big meaty human brains don’t really like random things. We like patterns and will go out of our way to find those patterns and significance in them. That’s really what it boils down to. Once you spin the wheel once, that has no impact on the second spin. But you can’t draw patterns from just one spin like you can from a whole series of spins. So even though it’s still a 50/50 chance you’ll get a red on that second spin, your brain is still trying to look at it in context of the other spins because that lets it make more patterns.
We also have weird notions of what ‘feels’ random. Ask people to pick a number between 1 and 10, and you’d be surprised how many 7s you get. It’s not even, it’s not on the edge, it’s not right in the middle, and it’s not a perfect square. None of those should matter if you’re just picking a number randomly, but it does because your brain doesn’t like random. It’s trying to find patterns in things that it shouldn’t. Ask them to pick a second number, and most won’t pick the same number that second time because that also doesn’t feel random.
So on a similar note, getting red twice in a row feels less random than getting two different colors. It’s because we sort of think about it backwards. A 50/50 chance *should* mean we get one red and one black. Thats not random, but it’s what would feel random. It feels like a “random” pattern because it’s different and conforms nicely to the probability. So even though two reds is just as likely as red then black, we just wind up putting a bigger emphasis on the pattern that feels more significant.
So the tldr; we don’t like looking at things independently because that makes it harder to draw patterns. And because we try to find patterns in random things, we expect non-random things when we shouldn’t and weight certain outcomes more heavily than others.
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