The probability you’ll get 50 heads and 50 tails is just under 8%. The change in probability to getting H51 and T49 or H49 and T51 is only about 2%. That is to say you’re nearly twice as likely to get either 49/51 or 51/49 as you are to get 50/50. The probability of exactly 50/50 decreases as you increase the number of coin flips, and interestingly the likelihood of something near to 50/50 increases as you increase the number of coin flips too.
What you end up with when you calculate all probabilities for all outcomes is a probability distribution - the most famous example of this being the “normal” or “Gaussian” distribution, (the “bell curve”). They signify that you’re far more likely to get a similar number of heads to tails than you are to get much more of one than the other, but they also signify that you’re actually likely to get more of one than the other a certain number of times on average i.e. the amount of times that you will get a significant amount more heads than tails is also calculable. There is even a mathematical way to detect fraud by the difference between what humans perceive as “looking random” and what random actually looks like, with far more edge cases than looks random to people.
So it’s neither random that you’ll get edge cases, nor is it the case that we ignore randomness - we actually have a whole science behind “randomness”, called Stochastics. Unless you mean the layman, in which case yes - they are very bad at detecting or replicating “randomness”, even ordering it to an extent to look “properly” random to themselves, and they don’t like things that don’t fit their expected patterns - an example of this being this thread. Few people here really seem to understand what randomness is, how much is known about it and what isn’t it, and that’s probably where a lot of the suspicion of Determinism comes from.
But the above isn’t even representative of the Natural Sciences - it’s Statistics. All science can be analysed statistically, but a main difference between the Natural Sciences and things like Social Sciences (where statistics are pretty much as far as you can go without Natural Science to support it), is the degree to which they study qualitative phenomena. In Physics, for example, you don’t need to worry about how a coin feels to work out its motion when subjected to whatever physical forces. If you calculate the force of the flip, the resulting angular momentum, the coin’s mass and spatial dimensions, air resistance, take into account the surface it’s landing on etc. you can work out if you’ll get heads or tails 100% of the time. At everyday scales, Newtonian Physics model what might as well be a deterministic world - even if it somehow turned out that Determinism was false, it still operates as though it is - and the Natural Sciences study this. You have to get to really extreme cases to find discrepancies with the Newtonian - like how Einstein fine-tuned things when you get close to the speed of light, or when you get all the way down to quantum scales. You don’t need to care whether Determinism is “true” or not - I don’t - but the quantitatively measurable world genuinely operates as though it does.
At everyday scales, you don’t get someone jumping into orbit “every so often” as a statistical anomaly. Whilst probabilistically, eventually you’ll get 1 million heads in a row, no number of jumps will get you into orbit.
This isn’t to say you can’t get into orbit by other means, nor that gravity ceases to affect you once you do. The hard part is achieving escape velocity, so you aren’t just taking a huge jump only to come back down again. Gravity will still be pulling you back down to earth - that’s why the moon keeps orbiting the earth. The effects of gravity even provably go interstellar, though they get weaker the further you go - the “special” guy who made this thread actually thinks astronauts “defy gravity” as though his “Free Will” overcame it, or as if he’s some sports commentator. The lack of education is just shameful. Satellites are “falling to earth” constantly, but moving sideways so fast that as soon as they fall far enough, they’re to the side of the planet and “missed it”, and continue missing it. This is where the Hitchhiker’s Guide to the Galaxy’s joke comes from - about how to fly: “throw yourself to the ground and miss”.
So in short, “one instance of H2 and T0” is absolutely not “enough to prove the cosmos prefers H” to the determinist. It used to be fashionable to think the cosmos was 100% orderly, but now we know that science is an ongoing improvement to model reality “as though it was Deterministic”, which is not the same as “because it is Deterministic”.
The important thing to remember is that absence of evidence is not evidence of absence.
We appear to be able to improve our Deterministic models over and over, with less deterministically understood areas becoming more and more deterministically understood all the time. That’s not to say the trend will continue forever (the problem of induction) but nor is it to say that any slowing down or stopping is evidence of the absence of Determinism. Proof of Determinism requires that there are necessarily circumstances where it can be measured that no causation is occurring - that is how you falsify Determinism.
Saying “absence of evidence is evidence of absence, therefore Free Will” is just lazy “God of the Gaps” un-thinking - or “The Argument from Ignorance” fallacy. You don’t need to go there at all, except to understand properly why you don’t need to go there - which I highly support. It’s contradictory to be “both causatively influenced by the world in order to make an informed decision on how to causatively effect it, whilst simultaneously not being causatively influenced by it as a free agent” and you need to resolve the unresolvable mind-body problem, and to equate possibility with actuality - in order to justify Free Will.
It wouldn’t even matter if Determinism was proven false, because the above proves Free Will can not take its place. I keep coming across the False Dilemma fallacy when I’m asked to prove something about “Determinism existing in reality” (which isn’t even what I’m saying) in order to prove that if Determinism has a flaw (the Nirvana Fallacy) then Free Will must be valid (the False Dilemma fallacy). Free Will has an inherent contradiction, and insurmountable task and a conflation of different terms to overcome in order to be valid in the slightest - that ain’t gonna happen, sorry.