Right, the point I was trying to show is that prior to 100 flips you have to make a prediction of how many flips will land on heads and how many will land on tails. Once that prediction is made, of say 50 heads 50 tails then you have to complete the ENTIRE 100 flips in order to finish the set of flips. Making the claim that every flip has a 50-50 chance is not relevant to the 100 flip scenario.
If there really is a 50-50 chance of heads or tails then it should be roughly 50 heads and 50 tails for 100 flips. If 75 of 99 have shown to be heads then it stands to reason that the last flip should have a greater probability of being tails, because overall out of the 100 flips it should be closer to 50-50 than 76-24.
Your “probability” is really just a fancy word for calculated prediction. You already claimed your prediction is 50-50 for every flip. That is worthless unless you actually flip the coin and find out the outcome. When you flip you find your prediction is wrong 100% of the flips.
The other side of the coin, pun intended, to the gambler’s Fallacy is the Hot Hand Fallacy.
People prone to gamblers fallacy think a streak of, say, black on a roulette table makes red more likely to come next, while Hot Hand Fallacy peeps think the streak of black means you should bet on black again.
I think gamblers fallacy is far more common though. Although hot hand is usually less about coin flips or roulette tables and usually applied to other situations entirely, like athlete performances and stuff.
You did not interact in the least with what I wrote. Nothing about causation, for example, and how the previous tosses change future flips. Nothing, nada, noll.
And you were obviously writing to some other person, with whom you’d had more exchanged posts, since you referred to things we had not had with each other.
Are you the kind of person who just pretends obvious things are not there?? Because then there’s no point in talking to you.
Yes, I did not answer your question because your post did not respond to mine.
I don’t know what you are trying to say here.
I’m not sure why you feel the need to say this, but I agree.
It could be many possible results.
and you still haven’t interacted with what I wrote about, for example, causation.
Your “50-50” chances are simply 1 flip with 2 possible outcomes. You are claiming there is a 50% chance the coin will land on heads and 50% chance it lands on tails. With multiple flips your “50-50” becomes irrelevant, because the discussion is about how many flips out of 100 will be heads and how many will be tails. It is how many out of 100 will it land on heads, not how many possible outcomes are there.
Again, there are two different discussions and bets:
What percentage is there for the coin to land on heads or tails, which is your whole discussion, that there is a 50% chance of landing on heads and 50% chance it lands on tails.
How many times out of 100 flips will the coin land on heads.
So again for the third time, how many times out of 100 flips will the coin land on heads? What is your prediction?
You can’t answer that because of your limited scope of “There is 2 possible outcomes, heads or tails.” (rolls eyes)
No, that doesn’t follow. If you witnessed 75 of 99 flips being heads, you should update your prediction. Your original prediction doesn’t bind the set of flips. The coin doesn’t know anything about your prediction, nor about the previous flips. There are two outcomes on the last flip, and they are still equally likely.
There’s a difference between a set of flips where we know that there will be a 50-50 outcome (e.g. the ‘deck of flips’), and a set of flips where we predict there will be a 50-50 outcome. It seems like you reject that difference.
If you tell me you’re going to flip a coin 100 times, and you give me an even payout option to either bet it will be a 50/50 result, or some non 50/50 result, I’d bet on it not being 50/50.
In other words, I think most sequences of 100 flips of a fair coin are not split perfectly even, 50/50.
It’s not about my prediction or the coin somehow knowing what the previous flips were, it’s about the fact that roughly 50% of the flips should be heads and roughly 50% of the flips should be tails. So out of 100 flips, roughly 50 of them should be heads. No, you don’t get to “update your prediction” because it’s not about your prediction. On any given set of 100 flips, roughly 50 of them should land on tails. Will it ever be exactly 50-50? Heck no, maybe never. But it’s a better bet that the numbers will be closer to 50-50 than 99-1. Surely you wouldn’t bet it will turn out to be 99-1, would you? Your bet would be that it is closer to 50-50 than it is 99-1. Because it is more likely that roughly 50% of the flips will be heads than it is for 99% of them to be heads.
What do you mean I can’t answer? I did answer. There are many possible outcomes. The odds are it won’t be 50/50 even. And it’s a poorly worded question since we cannot know the answer in advance.
For the third time, you didn’t interact with what I wrote. Nothing about causation. You managed to say what I didn’t write and I suppose you think that’s interacting with what I did write.
Yes, make up an response that I didn’t give and throw in a grammatical error. Continue to avoid admitting your first response to me was confusing my post with someone else’s post. Keep not managing to make the slightest response to what points and responses I did make.
You have a serious integrity problem. I’ll ignore you and let other people keep pointing out how you are wrong. Though I feel sorry for them, since you probably don’t respond to what they write either.
You’re on of those archetypes on the internet. Someone who keeps repeating their position and can’t manage to interact with what other people write.
You can’t answer because you’re stuck on every flip having two possible outcomes, heads or tails. Really? Is that all you’ve got? So when I ask you your prediction of how many out of 100 will be heads and how many will be tails, you reply with “there are two possible outcomes for each and every flip, heads or tails!”
But the question is how many out of 100 will be heads? Remember?
If the question is, “If a fair coin is flipped 100 times, is it more likely to come out 50-50 or 100-0?”, then I agree it’s more likely to be 50-50.
If the question is “I’ve just flipped a fair coin 99 times and they were all heads, is the next flip more likely to be heads or tails?”, then I don’t agree that the next flip is more likely to be tails.
Do you see a contradiction between these answers? Do you agree they are different questions?
Why do you think it’s more likely to be 50-50 than 100-0?
You just said it’s more likely to be 50-50 than 100-0, so you must agree that it is more likely to be 99-1 than 100-0, right?
They are definitely different. The contradiction is that you agree that 50-50 is more likely than 100-0, but in the next breath you don’t agree that it is more likely to be 99-1 than 100-0. How about 89-11? Is that more likely than 100-0? How about 71-29? Is that more likely than 100-0? How about 58-42? Is that more likely than 100-0? How about 51-49? Is that more likely than 100-0? Is it that you think 50-50 is more likely than 100-0, but anything different than that all bets are off?
If it’s 2 flips of a coin, exactly half of the permutations of flips are 50/50 evenly split.
If it’s 4 flips of a coin, it’s 6/16 - 6 of the 16 possible permutations of 4 flips are 50/50 (37.5%).
If it’s 100 flips, it’s closer to 8%. There’s an 8% chance that 100 flips will end with a perfectly even 50/50 split of heads/tails.
But that’s not what Carleas is focusing on anyway. He’s focusing on the question: if we’ve already seen 99 flips, and we have yet to do the final 100th flip, what can we say about this last flip?
And his answer, of course, is – it’s the same as any other flip, 50/50, regardless of what happened 99 flips previously. Coins don’t remember their results.
That’s it. Carleas is of course on the money, coins have no physical memory of what they flipped previously, a coin has no mechanism to care if it flipped 75 heads and 24 tails in the last 99 flips.
The final flip is 50/50 regardless.
Of course I could write a program to test it, but that doesn’t seem necessary.