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
You are talking about the probability of a single event versus a series of events.
The probability of 20 heads in a row is .5^(20) but then you’re asking about just the next flip it’s still 50/50. If that 21st flip is tails, you would have a pattern of 20 heads and then 1 tails. The probability of those exact 21 flips is .5^(21)
It helps to remember that the odds of a spin ending up with 8 black and 1 red or 9 black and 0 red (sequentially) is the same.
You are not the imbecile.
Those tiny chances that it happened 11 straight times are dependent on specific outcomes over the course of 11 instances.
Each individual flip of a coin is 50/50, and that should be particularly apparent.
Another way to think about it is that if you land heads 10 times straight, then the odds that you’ll land heads 11 times straight are RIGHT NOW 50/50. The hard part of the math has already happened.
The coin has no memory. The odds of flipping 11 heads in a row is 0.048%, but the odds of flipping 11 heads in a row **given that you already flipped 10 heads** is back to 50/50
The individual odds of each flip is always 50/50. It always is that way those are just your two options.
Now the odds do change when you talk about stringing MULTIPLE flips together.
For example let’s say you flip the coin twice, the odds of getting two heads are 1/4 or 25%. For each individual flip it is still 50/50, but to get that specific whole string of flips it is 25% because you could get:
Heads-heads
Heads-tails
Tails-heads
Tails-tails
There are 4 possible outcomes for a two flip string, meaning each outcome has a 25% chance of happening.
>What I don’t understand is how the likelihood of the next flip doesn’t change.
What’s the difference between flipping one coin 10 times and flipping 10 coins all at once?
Because flipping a coin does not significantly impact the coin *itself* one flip doesn’t impact the next because each flip doesn’t “know” any other flip occurred.
A roulette table, one that’s not rigged, anyway, is the same way. Nothing happens during a spin that will impact the mechanism itself so each spin is functionally identical to the very first spin. The ball doesn’t remember.
Probabilities like the odds of flipping a heads or getting a red after 8 blacks are calculated by taking all possible results and counting how many times the specific result you’re looking at happened. You’re only looking at one possible attempt. The more attempts you make the more likely what you’ll see is in accordance to the odds because that’s what the odds *are.* All possible attempts. (for extra funsies, look up the “galton board” for a great example of how *lots* of random = consistent)
You’re not an imbecile. You’re human. This is what’s known as the “gamblers fallacy” and it’s one of the ways our brains take shortcuts that are “good enough” most of the time but fails when you really take a close look at what’s actually going on.
In what way does the result of the previous flips affect the next? You flipped heads 10 times, stood up, walked out and somebody else came in. They know nothing about you or your coin flips. They just see a random coin and do a flip. What would they expect the odds of their single flip to be?
In order to modify the odds of another event, *something* has to tangibly change. An outcome must be added or lost. If your coin doesn’t change the number of sides or suddenly grow some tiny wings to steer itself midair, it’s still gonna be “one out of two options”.
Same with the roulette. It sure is a tiny chance to hit the same result 9 times, *but you already did 8 times*. Those are settled. You are *already* in an extremely low probability branch, but the next roll is independent – it just decides between the three even lower probability branches you’re about to enter.
Or take it like this: 9x black is very rare, but 8x black plus 1x red is exactly the same rarity.
Flipping a coin has a 50% chance of heads and a 50% chance of tails.
The sequence of ten heads in a row seems unlikely, but it’s actually just as likely as any other individual sequence, because they’re all made of the same 50/50 shot taken ten times in a row. A sequence doesn’t actually affect the next thing in the sequence because it’s all random chance.
If you watch your buddy flip a coin ten times and it’s heads every time, you would think tails for the next time. But if you DIDNT see the previous ten flips, you’d know it’s just a 50/50. Random chance never actually ‘sees’ (or cares about) the first ten flips, so it knows it’s just a 50/50.
The reason the probability does not change is the coin does not have a memory. How it lands will be a result of how exactly you throw it and with a well-balanced coin both sides have equal probability. You can’t control how you throw the coin to get hea or tails.
It could be the case that if the count is not balanced or someone have a coin with a head on both sides. So cheating is always a possibility
You can change it to 100 people in a row that flip a coin without showing the result or anyone else. There is not reason that the result of one person depends on the result of the people around them.
Instead of flipping the coin 10 times, you can ask the 10 first people in the line their results.
One thing to consider when you talk about probability went the question is asked.
If you ask it before you start then it is very unlikely that you get 11 heads in a row. But if you ask the question after you have got 10 heads in a row the chance of getting another one the change is 50/50.
The Unlikely 10 heads in a row has already happened. The probability for what did happen is 1.
If you flip a coin 10 times, there are 2^10 sequences that you could end up with. So while it may be true that the most probable outcome is to end up with 5 heads and 5 tails, it’s only because more of those unique sequences tally up to those values. If you do end up with a 5/5 distribution, the exact sequence that got you there is still the same as flipping all heads or all tails.
So yes, flipping a coin 11 times and having it land on heads every time is 0.048%. But it’s the exact same probability of following the exact sequence of heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads. The higher probability in the ending tally being more evenly distributed is only because we lump the sequence together with other sequences.
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