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.
Each spin is completely independent from the previous one, so previous outcome doesn’t have any affect. You remember what happened on the last spin, the wheel and ball have no historic memory. Equipment is the same, technique is the same, odds of either outcome is the same.
The expected odd for it to continually land on red go down with each spin. The same is true with any specific outcome. The odds of all red are exactly the same as all black or the sequence rbbrrrbrbbbrrrbr as for any other combination the same length. This means that over time one would expect equal black and red rolls.
It isn’t the former because for individual trials, each trial has no impact on the next. Its like flipping a coin. You have a 50/50 shot of heads or tails each flip. If you flip a coin and get heads, and then flip it again and get heads, and then flip it again a minute later, an hour later, a day later, a year later, you have the same 50/50 probability of getting heads.
that is for INDIVIDUAL Trials.
The rules change a bit when you do GROUP trials.
Say you want to know what the probability is of getting heads three times in a row before you even start flipping. (emphasis on making the prediction before you start flipping).
Here the odds are (1/2 * 1/2 * 1/2) = 1/8 or .125. For each individual trail in that group the odds are still 50/50, or 1/2 or 0.5. But when you group them all together the probability does change because now the previous trials impact the next, because you cant get three heads in a row if the first or second trial has already landed tails.
So the probability of getting three heads in a row before you even start flipping is .125, but say you get the first two heads, and now you just need the last flip, that last individual flip is 50/50.
You’re mixing what’s called “conditional probability” (the probability of something happening *given that something else happened*) with the single-event probability.
The probability of red or black on *any* single spin is 50%. This is always true (on a fair wheel) regardless of prior results. The ball and wheel have no “memory”, nothing changes between spins. The odds of red on the next spin don’t drop if the prior spin was red, it’s still 50%.
But that is NOT the same as the probability of two reds in a row. That requires that the first spin be red (50% chance) *and* the next spin be red (50% chance). The joint probability is 25%. The probability of red on the second spin didn’t drop, it’s the probability of the overall outcome of two spins that is lower (because you’re specifying one outcome out of a possible four, rather than one in two).
Why would it matter? There is nothing in the roulette wheel that controls where the ball goes. The ball is not offended by falling into the same colour slot twice in a row. The second spin isn’t any different from the first from the wheel or the ball’s perspective.
Being lucky is just that – luck. There is no pattern, but your brain is wired to try and find patterns. Being able to predict and anticipate is a survival skill in the wild, but some things can’t be predicted. A short term lucky sequence of events may be noticed by your brain trying to find a pattern, especially since you want to win, even though over a long period of time it will not work out.
Also, the reason it’s 49% is because there’s the special green `0` and `00` positions on the wheel. These tilt the odds slightly in favour of the house. Betting $50 on red and getting red wins you $100 (you double your money), but with the odds being slightly *less* than 50/50, the math says you don’t break even in the long run. Which means the house wins.
It’s the same event with nothing changing so the odds stay the same.
Of course for it to keep happening the odds go up due to the odds of it hitting the same 50% repeatedly are unlikely when there is only 2 outcomes that are both equally possible
No each event is separate, previous results have no bearing on future results. For instance tossing a coin is always 50/50 head or tail if you have got three heads in a row the next toss is still 50/50 head or tail.
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