By the way, a 2,000 flip deviation in a 10,000,000 set, a 0.0001% deviation margin, means that the instances of imbalance within the set will be so very few, so far in between, and so small, of necessity, that to nail it at any particular point of imbalance, and to have that same imbalance instance spontaneously repeat itself within the set so that you can note statistical incidences of that case of imbalance, is almost impossible.
To write a program that could do it, one would have to be some kind of genius.
And, when you do do this, two things you will see:
Again, sometimes more tails, sometimes more heads, rarely perfectly balanced.
But tails heavy heads will still fairly often have a percent that’s higher heads than overall heads percent. But it’s not surprising, it’s what you’d expect anyway. To get to that point, you had to get to +1000 tails, so you’re already inherently in a data set that’s light on heads, and you’re counting a new data set that isn’t necessarily going to be light on heads.
If each flip was 50 50, you would expect at least 50% of instances of 10 mill flips where the state just stays heavy forever. It has no reason to go back. If you predict a “boundary,” it’s because, necessarily, you predict the tail heavy flips will be heads heavy, because it would have to to get back to the “boundary.” If each flip is a perfect 50 50, there is no need for any trend to exist, it could just go tails heavy forever, exponentially, just as easily as go back to the boundary.
But, miracle of miracles, it always goes back. And, God himself must be doing this, it goes does about the same on the other side at about the same rate so that, somebody must have forged this, each individual flip probability will have shifted to give every single 10 mill sample an almost perfect 50 50 composition.
I was hoping you guys would eventually formulate this yourselves, so that I wouldn’t have to make you look foolish. But:
Each individual flip cannot be 50 50 and at the same time overall flip composition be 50 50. If a break from overall 50 50 happens, and individual flips remain 50 50, there is no reason it would trend back to balance. In f act, it might be likelier to just stay on the twisted path it entered. Of course, even this wouldn’t hold, what would hold is a kind of unpredictable perfect variance with no possible predictable overall composition.
Anyway, I’ve run the test and confirmed, yes, when you get to +1000 tails, you’re just as likely to go even more tails afterwards as you are to go more towards the center/heads
Thanks bro! I bet it would pass a code review too. You know there are places online to get free code reviews? You should submit your code there, or allow me to on your behalf.