Because there’s far less ways to flip 99 heads than there are ways to flip 50 or 10 heads
if you include the order of the heads/tails, then each possible outcome is equally likely, whereas if you include just total number of heads/tails then each outcome is not equally likely, as to flip 99 heads in 100 throws theres 100 choose 99 (100) ways of getting 99 heads out of 100 throws, whereas theres 100 choose 50 1.0089134 x10^29 ways to get 50 heads out 100 throws
Occam says: the coin has two heads.
It’s surprising because, while there are zillions of permutations of a 99 coin sequence, only a handful out of those zillions are something memorable, or we regard as a strict pattern.
It’s in the odds of getting one of those strict patterns on the first go.
I would be surprised if you predicted a specific sequence of a hundred flips (HTTHTHHTTTT…) and then flipped that.
This is the best answer so far, I think, but if I might, maybe an example can make it a little better?
If you put all possible sequences of 99 flips in a hat, draw one out, and bet money on it, you might pick one with a discernible pattern, like alternating sets of 11 heads, and 11 tails, all heads, or all tails, or you might pick one with no pattern. Each one has a 1 on 99 chance of being drawn.
If you then actually flip a coin and bet money that 99 flips will match the sequence you drew, the chance that the flips and the drawn sequence will match is the same whether there is a pattern to the sequence or not.
When you specify the odds of something, it matters whether you are talking about the event before or after it happened. Asking what the odds are after an event happened is different from asking what the odds were that it might have happened, unless you set up specific conditions (for example, you decided beforehand that you were going to flip the coin exactly 99 times, the odds don’t favor 99 heads-- if you decided you were going to flip it 10,000 times, then look for a sequence of 99 heads, the odds are actually fairly good you’ll find one). If you look at the obituaries, and see that someone has died on his birthday, and say what are the odds? what is the actual question? that someone (in the range of that paper’s obits) who died that day would also be having a birthday? that the particular person who died would die on his birthday in some year? in that specific year? That there would be something remarkable in the obits? (this is the kind of thing, as someone else said, psychics count on).
Anyway, if you flipped some discernible pattern, like all heads, or all tails, or alternating heads and tails, you brain recognizes the pattern, and tricks you into thinking because it’s a patterns you are familiar with you specified it ahead of time. But you didn’t.
(I still think Kolmogorov complexity is a key clarifying concept.)
Your overall point is valid but …
Nitpick: Even if you flip a fair coin a trillion quadrillion times, the chance of 99 consecutive heads is still much less than 1% by my reckoning.
The expected length of the longest run of heads of a random sequence of length n is log[sub]2[/sub]n - 1. (Yes, I do know this off the top of my head. Well, the log part. I had to check if it was +/-1.) For 10,000, this is a bit over 12. Extremely unlikely to find a run of 99 heads.
Again, non-random stuff is a lot less common than you think. Ergo, the content of most Internet message boards.
OK. If you have a sequence of 10,000 flips, and a sequence of 99 flips, you will have better luck finding a run of 99 heads in a row somewhere in the 10,000, than in the 99.
Not quite 8 percent, according to a binomial calculator with:, number of trials = 100, probability of success in one trial = .5, and successes = 50. 92 percent sounds like ‘far more likely’ to me.
Basically, to your human brain, 99 heads in a row has some special significance because we have an instinct to look for patterns. To the laws of chance 99 heads in a row is no more or less special than any of the many other possible outcomes of flipping a coin 99 times.
So, random is as random does, as Gump said: before the fact, the odds of 100H are as good as [insert pattern here of 100 flips].
Then, to significance and the search for it:
I
You don’t see any obvious significant pattern (“surprising” or “not-surprising”–your call), you can
and continue to scan the numbers (another 100 flips say), searching and testing for patterns, perhaps noting rejected ones–now over 101, 102, etc.–may be part of some other signifying pattern. Psychology reaches, at apex, insanity of the kind portrayed in the character of John Nash, in the movie A Noble Mind, which is a symptom of schizophrenia in thought patterns in general, but here reduced to symbolic unease, the same unease, regrettably, that is at the heart of OP (and me).
The thing is, that after the very next 100 flips, the pattern of the first 100 could repeat (like the opposite of the usual definition of Jewish Luck in the lottery cited above). Then the madness purports to show a method.