So in a set that includes only instances of aaax, and nothing in between, with a fair coin, you would not say that the odds of getting a within any particular iteration of x is 50 50?
You aren’t describing the scenario rigorously enough for me to give you a clear answer. How in the world would a fair coin output a set that includes only instances of AAAX?
Same as it would any other random set.
You are not wording your question clearly, at least not for my standards. I don’t even know what you’re asking me.
But I am curious if you’ve taken the time to see my link on the Gamblers’ Fallacy, and particularly as it pertains to coin flips.
Incidentally, this is part of why I write software correctly the first time more often than my colleagues. My colleagues will take vague instruction and try their best. I’ll hear vague instruction and say “that’s not clear enough, you need to go into more detail”.
Check it.
In a series of aaax, and only aaax, there is a given probability that x will be a, and another that it will be b.
If you repeat only instances of aaax, you would expect that probability to bear out.
If you repeat only instances of aaax, and nothing else, and you assume the probability for any individual flip is 50 50, then you would expect the occurrence of b to be greater than a.
Ah, so not always, I see.
How in the world is someone “repeating instances of AAAX”? Do they have a magic coin that always flips 3 heads and then a random? What is the scenario you’re imagining? I have no clue what you’re talking about.
Origami.
You seem to be under the bizarre impression that if you get a million heads, statistically, it’s more likely that you’ll get tails the next time.
You have lost all hope when you have to resort to authority (especially Wiki).
You’re phrasing it like it’s a choice.
Just pick up a fair coin and repeat instances of AAAX. It’s just a choice man, can’t you just make that choice? Come on it’s easy, just pick up the coin and repeat those instances.
That’s what it sounds like you’re saying. Like you can just will AAAX iterations into existence. It doesn’t make sense, your wording is not rigorous enough.
He said it’s the cornerstone of statistics. I’m taking his appeal to authority and pointing out that (a) there’s been no evidence that it is the cornerstone of that, and (b) that I have clear evidence that authorities call this reasoning an explicit fallacy.
If you flip the coin 100 times, and get 75 heads, you would expect to get around 25 heads the next 100 flips, on average.
If you have flipped 75 tails that second time, you would expect to get heads the next flip, and all remaining flips.
There will of course be a margin of error that decreases with every repetition.
This is literally the same fallacy that all these experiments should have rid you of by now.
Fair coin flips from a fair coin are independent. I don’t think that you would expect 25 heads the next 100 flips, in fact I think that’s pretty friggin unlikely.
Who gives a shit about wiki.
The logic is simple.
You can have an infinite number of heads on a coin that’s not weighted.
Tell me this obsrvr.
(I like number theory only now… not into solving problems anymore… philosophy of numbers)
Why is it impossible in statistics to never get tails forever?
Why is flannel wrong?
Statistics already implies repetition. If a coin has 50 50 chances to be heads, it means that in 100 repetitions, it is likely to be heads about 50 times. If it is much more than 50, and we still believe the 50 50 odds, then we would expect that exaggeration to be balanced out by an exaggeration of tails within a wider selection, say of 1000.
Origami, I played along with your goalpost moving many times. I changed my experiment to match your descriptions, multiple times, and the results always came back: the X of an AAAX series is just as likely to be heads as it is to be tails.
Are you at least close to changing your mind yet?
Do you at least have a bit of doubt that MAYBE, AAAX might have a 50/50 chance of being heads/tails at the end? Is there even a sliver of doubt after all of this?