Out of Pod Experience

100 (or more) in a row are unlikely to ever be seen by a single person due to the infinitesimal chance of it happening with a realistic number of flips.

1 : (1*1,267,650,600,228,229,401,496,703,205,376) = 1 : 2^100 odds for a single set of 100 flips
3 : (2*1,267,650,600,228,229,401,496,703,205,376) = 3 : 2^101 odds for a single set of 101 flips
8 : (4*1,267,650,600,228,229,401,496,703,205,376) = 8 : 2^102 odds for a single set of 102 flips
20 : (8*1,267,650,600,228,229,401,496,703,205,376) = 20 : 2^103 odds for a single set of 103 flips
...and so on and so forth.

Notice however how the first number in the odds of actually getting at least 100 heads in a row quickly increase with added flips, while the second number multiplier grows at a slower rate.
The overall odds become better and keep getting better the more throws are made.

Eventually, the first number becomes more than 1,267,650,600,228,229,401,496,703,205,376 times larger than the second number used as the multiplier, and the odds become better than even to throw 100 or more heads in a row.
Granted, the number of throws is a lot larger than the number of throws likely to be possible for a single person to ever make during his expected lifetime, but that's a different story (and one that explains why you don't see anybody claiming he made 100 heads in a row).

Then the odds keep going up afterwards.

After some consideration with regards to your explanation of regression to the mean, it seems like it is saying that after a streak of 10 in a row, there is an an inclination for the streak to end, although that is not definite. The static 50:50 does not change, but this principle of distribution will tend to apply.


Is this not so?

Ok now this is what I mean by applying relativity to statistics. If I get this wrong I will just let it go so thx for bearing with me. You surely know your stuff.


But…


The odds of a streak ending in 3 more throws is 12.5 % from the perspective of the observer BEFORE he ever tosses the coin. This applies to the ending of a streak of any previous length, or any size and for any duration if you take into account general relativity before the coin is tossed. The static 50:50 of each toss does not have to change.


General Relativity being applied to statistical theory.
I guess you explained my idea for me.

Your think about after you toss
I am thinking about before you ever even started.


Maybe there is a reason we are not communicating. The past has no relevance to the future if you are still standing within it.

Let me put it another way, I am thinking about before you even tried to flip it X times (relative to the observer) you are thinking of it before and after each toss.

But before I toss anything what are the odds of me generating a 3 heads or tails streak? from where I am standing relative to the observer? According to you it has an odds of ending of 87.5%

It depends on how many throws you want to make in total.
And the chance to get a 3-heads streak in the remaining throws constantly changes as each subsequent throw is made.

Chance to get 3 heads in a row in the next 3 throws if previous throw was tails or this is the very first throw ? 1:8.
Chance to get 3 heads in a row the next 2 throws if previous throw was heads ? 1:4.
Chance to get 3 heads in a row the next throw if previous two throws were heads ? 1:2.

50% chance to end in very next throw, 50%*50%=25% additional chance to end in exactly 2 more throws, 50%*50%*50%=12.5% additional chance to end in exactly 3 more throws -> 50%+25%+12.5% = 87.5% combined chance to end in 3 throws or less.
And a 12.5% chance to continue the streak at least 3 more throws.
And a 6.25% chance to continue the streak at least 4 more throws.
And a 3.125% chance to continue the streak at least 5 more throws.
And so on and so forth.
Regardless of streak length so far.

Limit of sum(0.5/x) for x going from 1 to infinity equals 1, so a p=1 (or if you prefer 100% chance) for any streak to end in "infinity" throws or less.
Anything less than infinity additional throws and the chance for a streak to end is BELOW 100%.
Not much below, but still below.

Descending probability to continue an existing streak in increasing number of tosses, but NOT reaching 100% chance to end a streak in any FINITE number of tosses.

Also

Descending probability to get a streak given a FIXED number of tosses and an increasing streak length.
Which nobody is disputing, but is hardly relevant.

And

ASCENDING probability to get a streak given increasing number of tosses and FIXED streak length.
Which is telling you that a streak of any fixed length X is possible (even if very improbable) if you make at least X tosses, and it gets increasingly likely with additional tosses (never reaching 100% chance, but always increasing with additional tosses).

Not really relevant to the discussion.


A probability that never reaches zero for any finite number.
Which means that there's still a chance to continue a streak for any finite number of additional tosses.


Also not very relevant to the discussion.