Out of Pod Experience

A streak is just a simple way of referencing any repeating pattern for any long duration. Such things do exist.

it does not have to be repeating, it just an unbroken series of events.

i guess eg. wining every hand can be seen as a repeating pattern.

As the previous post suggests, what constitutes a pattern is largely subjective.

For example:

10001 11111
10001 00100
11111 00100
10001 00100
10001 11111

If a random generator produced the above content, an observer would probably quickly notice that it says "HI". As far as the machine stringing the bits together is concerned, that was no more likely than any other combination of the same length. But because we see something unique in it, we consider it special or significant. On some other planet,

00111 01011
01110 11011
11100 01110

Might mean the same thing. To us, it's just pseudorandom stuff, easily lost amidst all the other random output. It's only when we recognize something that we pay attention to its occurrence.

Those are simple and short patterns mr Floppie. This is about long repetitious events being consistently generated from random events. Like: 1111111111111111111^2 or 00000000000000000000^2 or 101010101010101010^2 or 11001100110011001100^2 or 111000111000111000111000^2

For protracted periods of time (look up what protracted means)

Nope.
It's about the number of possible combinations that INCLUDE at least one streak of at least 7 heads anywhere within.
Whether that turns into a more-than-7-heads streak or multiple separate 7-heads streaks is completely irrelevant. You still got the 7 heads you were looking for within that series of tosses. You can't discard that.

Or do you want to tell me that if I got a streak of 8 or more heads in a certain trial run I somehow miraculously FAILED to get a 7 heads streak anywhere in that exact trial run ?
That's ludicrous beyond belief.
You HAVE to include those too.

There's 2^20 = 1,048,576 possible combinations to throw a coin 20 times.

The following is ONE of those 1,048,576 possible combinations : 01011111111110110101

Answer a simple YES/NO question : DID I MANAGE TO GET 7 HEADS IN A ROW DURING THAT PARTICULAR SET OF 20 THROWS ?

...

It's really simple, dude.
If you were sitting next to me and ringing a gong as soon as I got 7 heads in a row, would you ring that gong for that sequence ?

...

Here's a hint : 01011111111110110101
Yes, yes I did manage to get 7 heads in a row.
I actually managed to get 10 heads in a row. But that doesn't matter. What matters is that I did manage to get 7 heads in a row.

Here's ANOTHER of those 1,048,576 possible combinations : 111111110011111111
Did I manage to get 7 heads in a row ? YES I DID.
I actually managed to get 8 heads in a row, twice. But that doesn't matter. What matters is that I did manage to get 7 heads in a row.

Now count all the combinations out of those 1,048,576 possible in which I do manage to get 7 heads in a row.
You'll get more than 40k of them.
The combined chance to get 7 heads in a row in 20 throws is over 3.9%.

Nope. Try again. Over 40k. And the first 12+k are even spelled out in post #126. Just go back up this very page and read.

If I have 1,048,576 pieces of paper, on over 40k of them the word "SUCCESS" is written somewhere, while the rest have "NOPE" written on them somewhere, what's the chance to randomly pull out a paper which says "SUCCESS" on it ?
Here's a hint, it's 40+k/1,048,576 ~= 3.9+% chance to pull a paper that says "SUCCESS".

Those 1+ million papers are all the possible combinations of 20 throws of a coin, each paper has a different combination of 20 throws, and all possible combinations are written exactly ONCE.
Those 40+k papers that have "SUCCESS" written on them somewhere alongside the 20-throw combination are the ones for which the corresponding combination contains 7 heads in a row somewhere inside.

Pulling a paper at random is exactly the same as making that particular set of throws.
If the paper says "SUCCESS" on it, it means there is a 7 head streak present on the paper.
Hence, ~3.9+% chance to get 7 heads in a row in 20 throws.

VERY SIMPLE. All you had to do was count.

I would prefer not to stray to far away from the OP. So I will just respond and then get back to the point at hand (because we were making some progress).


If you have randomly generated 7 in a row you have achieved something that had a certain probability.
If you have randomly generated 8 you have achieved something that had a smaller probability.
If 8... and continue on forever.



You CAN do it the way that you are saying, but what is the point? What intrinsic value does NOT distinguishing the difference between 7 and 8 have when both outcomes have a distinctly different probability of occurring? It may compute and it may be a fun academic exercise but it does not make any sense.

Let's test the ABSURDITY of your approach with a PRACTICAL example.

Tell me, in your opinion, what is the chance to get a streak of 2 heads when you make 200 throws ?
According to your previously stated approach you took for the 7head-20throw case, it should be 198 : 2^200 = almost zero.

Now throw a coin 200 times and tell me you didn't manage to get at least 2 heads in a row at least once.
What do you know, something your math says should almost never happen manages to happen almost always.
Obviously your approach is flawed.