Never mind that all the percentages your permutilation calculations predict are falsified by my program, every single one basically. Forget it, because it is such a tangled mess. Start with the simple, and answer the above.
Question: Is a coin more likely to flip tails if it has already flipped heads a bunch?
Test: count incidence of tails when more heads than tails have been flipped.
Answer: yes.
By the way, we strenuously protest the changing of the “of” in “of it has already flipped heads a bunch” to “if.”
Flipping 9 heads in a row is a bunch. Does the next flip have a greater than 50% chance of being tails? NO!
There is a 0.09765625% chance of flipping 10 heads in a row.
If you flip 9 heads in a row (which is a bunch), the 10th flip has a 50% chance of landing on tails.
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In other words, at the start of 10 flips there is a 0.09765625% chance of flipping 10 heads in a row, and a 99.90234375% chance that you will flip a tails on any one of the 10 flips.
The more flips that land on heads the greater your chances of achieving 10 heads in a row, and the lower the chance of landing a tails during the 10 flips.
8 heads in a row means there is a 25% chance of 10 heads in a row and 75% chance of landing a tails for the next 2 flips.
9 heads in a row means there is a 50% chance of landing 10 heads in a row and 50% chance of landing on tails.
The percentages for getting a tail lowers the more heads you get. It started at the beginning at 99.90234375% chance that you get a tail on one of the 10 flips. When you have already landed 9 heads in a row there is only a 50% chance of landing a tails on the last flip.
Chances of getting Chances of getting
10 heads in a row a tails in 10 flips
Start 0.09765625 % 99.90234375 %
1 head in a row 0.1953125 % 99.8046875 %
2 heads in a row 0.390625 % 99.609375 %
3 heads in a row 0.78125 % 99.21875 %
4 heads in a row 1.5625 % 98.4375 %
5 heads in a row 3.125 % 96.875 %
6 heads in a row 6.25 % 93.75 %
7 heads in a row 12.5 % 87.5 %
8 heads in a row 25 % 75 %
9 heads in a row 50 % 50 %
That’s a paper excercice.
When you actually flip them and count, you find that it is likelier to flip one side if the other has been overepresented.
One important thin about my program is that it treats every tail heavy flip as an individual instance.
The question is not overall, though it is answered overall. The question is per flip. Now that we have arrived at this tail heavy state, what do we flip? We could stop there. At any rate, we record that result. Then we go to the next tail heavy flip, and record that.
In a 10 million flip set, which we would expect on the whole to give a 50 50 result (and in practice bears this probability out), select all tail heavy instances. All of them. It is important that we keep all the others, because that maintains the overall, naturally occuring 50 50 balance. We didn’t generate those flips on purpose to et that 50 50 balance, that is the way they were actually generated. This is how we know there is a legitimate 50 50 probability.
So, within a verifiably 50 50 set, we take all outstanding results, all results that deviate from the 50 50, on one side, the tails side. So we keep the raw data, we discard nothing, and we select a segment within that data, all of what segment of that data, meets the criteria for the overall question we are trying to answer: “of it has already flipped a bunch.” So we get the altered, non 50 50 segment we wanted, and we keep the total, 50 50 data that ensures we are within the realm of truth.
In all of those individual instances, all of those single flips, what are the odds. If odds didn’t shift per flip, then we would expect perhaps, well, if you think about it we would expect a perfectly variable result, but let’s say you expect a 50 50 overall distribution, because every flip is 50 50. But you don’t get that. Instead, when you compare them to the set that is complete, no cherry picked data, the 50 50 10 mill set, you find that heads happen more likely, representing, each of those flips individually, an instance where the odds are not 50 50. Per that flip, per flip. Not for the segment, which is still a 50 50 segment, as much as we can detect.
So, by looking only at individual weighed flips, and counting each, we determine that each of those flips had a bias towards flipping heads.
By the way, I’m not trying to be a dick, I’m not.
When Carleas says it is unintuitive, I can relate. That is how everything appears before you begin to properly study statistics and probabilities. It seems like a sacrilegious insult, like that famous book title “lies damn lies and statistics.” Maybe because I had already had the experience of something fucking up my whole intuition to arrive at a rationally correct understanding: chess.
In chess, everything intuitive is a trap waiting to ensnare you. You have to play a thousand million games, break your intuition, and then let it build back up with actual, realistic, real world strategies that are rational. That intuition eventually develops, and I can see things on a board that someone with less experience will be insulted by. Not only not see, but be insulted by.
I once checkmated a guy and he said something like “ah, but it only worked because for that one square on the file there was that tiny momentary opening.”
But an experienced chess player knows that this is what you aim for. I had been cultivating that weakness the whole game, and maneuvering all my pieces to exploit it. A good chess player doesn’t seek a favourable pattern, he seeks an unavoidable pattern.
The answer, then, is to never give your intuition a blank check.
Like all indicators, intuition has to be kept in check.
Carleas and I are trying to keep the intuition that you’re correctly counting tails-heavy flips in check. We have a better way.
I’m not talking to you anymore man, you have no honesty that I can detect.
But we appreciate the enthusiasm and the participation.
If that’s what keeps your ego in tact
My ego is a diamond.
But it does keep my energy not wasted.
Wouldn’t want to waste any energy questioning your assumptions or intuitions
Thanks, I knew you’d understand.
Please stop addressing me if at all possible.
Thanks.
I can post in this thread as much as I please. You have no obligation to reply.
The last thing I will say on the subject is that, because you are a moderator, I don’t get the option of muting you like I would another user.
so while your point of “I can say whatever I want” is well taken, I would like there to be some leeway or rope for me considering that, normally, you would just be muted.
You should consider the possibility that we’re just disagreeing with you, because we think you’re incorrect. You keep making it personal, and it’s entirely unwarranted.
Carleas focuses on your ideas and your program. I focus on your ideas and your program. You focus on me and Carleas and what kind of vices you like to imagine we have.
That’s not the most honest approach to philosophy. I recommend you switch it up. Focus on ideas, not us.
Thanks Flannel Jesus.
I see that you addressed me and I am just posting in reply to mention that I didn’t read any of what you wrote.
Certainly, that may be. But I shared two programs in my last post that confirm my intuitions. At the end of this post, I’ll share a couple more that show that your intuitions are mistaken.
As a wise man once said, “maybe your intuition is off”.
Part of why you find this so galling is that you’ve framed it tautologically. But you aren’t trying to argue for a tautology. It’s true that your program “counts tail-heavy instances”, because “counting tail-heavy instances” is term you coined to describe what your program does.
Rather, we disagree about whether a “count of tails-heavy instances” is a good way to test if a flip stops being 50-50 under certain conditions. It is not.
Moreover, because your progam’s output is expected under an assumption of 50-50 flips, at best it fails to distinguish between your intuition and mine.
But we aren’t stuck with your program!
(I think both of these were originally suggested by @Flannel_Jesus, but any mistakes are my own)
Here is a program that samples one flip from a bunch of permutations, in order to avoid the th-sequence problem. For each permutation, it flips coins and counts heads and tails. If tails ever exceeds heads by a random amount between 0 and 100 (to make sure we aren’t only looking at tails=heads+1), it flips one more coin and increments thHeads or thTails.
As I understand your position, this should show the same result as your program. It does not. All of the counted flips are flips where we’ve “already flipped [tails] a bunch”, but there is no pattern of flipping more heads than tails in those conditions.
Here’s another program. This one similarly looks at a subset of thFlips, but instead of taking a random sample of individual flips, we wait for the balance to get to +100 tails, and then we tally the next 100 flips as thHeads and thTails respectively. All of these are tails-heavy, but we avoid the boundary effect.
As it the last one, there is no pattern in the results, thHeads and thTails are equally common.
If you think these programs don’t conflict with your position, I’d ask you to clarify your position: Why is your program finding an effect and these programs aren’t?