I think origami is stuck thinking that the “flipper” is affected by prior events.
If the flipper or coin is “fair” - it can’t matter about anything of the past - else it wouldn’t be a 50/50 toss each time - and if it IS a 50/50 toss each times - then guess what - it is 50/50 - every time.
There is actually a culture (village) of people who are incapable of abstract thought. It’s considered the second most difficult language to learn on earth.
Their language doesn’t use numbers. They have no concept of object permanence … when someone walks around a corner, they cease to exist. Then they come back from non existence when seen again.
My point is… there are lots of ways to see life.
I ask you again.
If everytime you flipped a coin, the stakes were non existence if a tail ever came up for you… we know that by having this discussion, a tail never came up.
In fact, with those stakes, we even know that a tail will never come up before trying to flip…
The point is this, and why it matters that the program be well written and not some half-assed get-it-out-of-the-way thing.
If when you subtract the rest of the series from the aaax’s you don’t get a 50 50 distribution, then what you have in the aaax’s is also not an equal distribution. Effectively, your instances of aaax are not a 50 50 flip, there will be a greater than four to one chance of getting heads for each of the individual flips within the comination.
If you had a set of a’s and b’s where the occurrence of a is much higher than the occurrence of b, would you say that the odds of getting a within any particular iteration is 50 50?
"If after tossing four heads in a row, the next coin toss also came up heads, it would complete a run of five successive heads. Since the probability of a run of five successive heads is
1
/
32
(one in thirty-two), a person might believe that the next flip would be more likely to come up tails rather than heads again. This is incorrect and is an example of the gambler’s fallacy. "