I mean, look, I get a lot of this is semantics; I would not disagree, at least, that those wins you got would be unlikely to happen much in the future. I guess I just think that that fact is a different, moot point; it doesn't "de-legitimize" the win that you did get. It doesn't de-humanize the win. But with a coin toss, I would say a win or loss isn't really a human thing; it's like the gods just do a bunch of things and then we arbitrarily decide that someone wins. Any win you get at a coin toss has nothing to do with you.
Luck in Chess

"Its totally reasonable to call such an experience luck. But nobody was rolling dice so it wouldnt be probaility in any mathematical unambiguous sense of the term. you are again simply confused over semantics...the fact that 'luck' is a word with multiple nuanced meanings depending on your perspective."
A fair point. I agree this is about maybe 80% semantics, but not necessarily 100%.
Not much luck in chess
Every time I win I feel lucky - my opponent was not obliged to make all those mistakes, but nevertheless he made them.
Your "feeling" tells you nothing about what made your moves better than your opponent's moves.
My moves were better for 2 reasons - skill and luck. Skill sets probability of mistakes at certain low level, luck manifests itself when in this particular game those probabilities (of my and his mistakes) turned to my favor.
Here is an example of luck and skill just like that found in some chess games (actually mine).
https://www.youtube.com/watch?v=4guiyiwyXrg

Suppose you follow a mathematical proof closely and find that it is valid. Is the theorem 100% true then? You could say that there is a non-zero chance of you, the author, and everyone else who read it fucking up. The more people you get to check it, the more likely the theorem is to be true. Theoretically, the theorem is proven; there is no chance involved. Practically, there is.
There is a similar distinction with luck in chess. There is no internal luck inherent to the game. Of course there is some practical external luck assosciated with the particular imperfections of the players. It's misleading to conflate these and say that chess has just as much luck as backgammon and poker.
Suppose you follow a mathematical proof closely and find that it is valid. Is the theorem 100% true then? You could say that there is a non-zero chance of you, the author, and everyone else who read it fucking up. The more people you get to check it, the more likely the theorem is to be true. Theoretically, the theorem is proven; there is no chance involved. Practically, there is.
There is a similar distinction with luck in chess. There is no internal luck inherent to the game. Of course there is some practical external luck assosciated with the particular imperfections of the players. It's misleading to conflate these and say that chess has just as much luck as backgammon and poker.
Nobody is saying that chess has as much luck as backgammon and poker. But it has much more luck than math. You bring a very good example - mistakes in math proofs that happen from time to time. But after being corrected they are interesting only to historians as math curiosities. They don't belong to math theory, math books etc. They won't be taught to students.
It's not same with chess mistakes. They can't be undone. They can be analyzed in post-mortem, but the game itself and its result are there to stay forever. Chess books are filled with games which are filled with mistakes. They are inherent to chess between humans. Without mistakes chess would be boring. And at least partially those mistakes were made due to some random factors.

They are not made due to random factors. If I say "I want to play move x because of y," then I make a move, I find out it was a mistake, that move nevertheless had a clear motive: just like with any move, I decided I wanted to play move x, for y reasons.
You are pretty much saying only perfect skill is skill (a pretty lame definition). But that's not the point of skill. The point of skill isn't to be right all the time. The point of skill is to base your decisions off of things, so if you are to be wrong, it's because of some problem with your reasoning. If on the other hand you lost a coin toss, no one would criticize your reasoning.
Elubas, when you miss a tactics - it's not because of some problem with your reasoning. You know the pattern, you've seen it many times, you've used it many times. But in this particular game you miss it - this happens all the time. It's not about reasoning, it's about seeing or not seeing things. What's your explanation for this? My explanation is that your skill level always leaves some chance of this kind of mistake. It's random, it's probability at play, it's luck - good or bad.
Of course there is other face of our skill - the rationalizing, the thinking method, the reasoning, acquired knowledge - but that defines other kind of mistakes IMHO.

Yeah it is because of reasoning. I'm still thinking about something no matter what move I make, and then I decide I want to play that move. That does not change regardless of the outcome.

It's simply the human element. No one is perfect and people miss things and make mistakes. Some people call it luck.

Chessmaster and two time world backgammon champion Bill Robertie makes a strong argument that there is luck in chess and compares the probability factor in it to backgammon. Very interesting. It starts at the 35:41 mark in the video.
Luck in chess is like luck in poker...
Yeah it is because of reasoning. I'm still thinking about something no matter what move I make, and then I decide I want to play that move. That does not change regardless of the outcome.
Pattern recognition and intuition are subconscious, they go without reasoning. Often mistakes are made because a player doesn't see the pattern, not because of his reasoning about some other moves not related to this pattern.

It still doesn't matter. Whether you recognize something consciously or subconsciously, it's as much you as anything. That is, for me to see pattern x is just as cognitive as me reasoning about a move I want to make.

Erubas, uri65 is correct. I don't see what you mean by "They are not made due to random factors. If I say I want to make a move x because of y, then I make a move." Or "yeah, it is because of reasoning. I am still thinking of sonething when I make a move."
It looks like you think thay since Chess is chess is what's called a "Complee Information Deterninistic Game" there is no chance involved. Of course when you analyze the game afterward you will see all of the cause and effect interaction. But this in no way eliminates probability. Even the computers, if they're set to think no more than x moves deep have to resort to some sort of pattern algorithms because the patterns are there in the first place to help increase chance of winning because a certain response from the opponent is expected but not determined. If there were no probability in chess , which is chance, then the game could be considered fully solved but since it isn't there are patterns that are based on projected responses.
There are even moves that are based on probability change. For example some players may tend to make moves that expand the move options and which force the opponent to make a guess at what type of attack will take place. If he could see exactly what type of attack is coming he'd be able to defend much more effectively. So, making moves that do not give out the plan but expand the possibilities is advantageous to the player who has more options. You could clear out the minor pieces on both sides of the king with the intent of having the option of castling on either side. Until you castle the opponent will either be forced to wait until finalizing the plan, or to make a guess and choose the side of attack hoping he guessed correctly on which side the castling will occur.
There you go. That is an example proving that statistical probability in chess exists and therefore what we call "chance" is present in the game.

lol, flexibility is chess strategy, not probability. For example if you don't know where the other guy's king will be, there is a correct way of going about things: play in a way that would likely be good against either.
There is no guessing correctly in your example: the opponent won't castle on a side that he doesn't want to. You would only attack on one side of the board if the opponent going on the other side wasn't a valid option, or if it wasn't worrisome to you. You wouldn't "just hope" that he castles on the side that you're trying to attack on. I mean sure, you'd hope, but you'd prepare for him not to.

if you don't know where the other guy's king will be, there is a correct way of going about thingsplay in a way that would likely be good against either.There is no guessing correctly in your example: the opponent won't castle on a side that he doesn't want to. You would only attack on one side of the board ifhope" that he castles on the side that you're trying to attack on. I mean sure, you'd hope, but you'd prepare for him not to.
You're still ignoring my point that I might play someone 500 points superior to me and by good fortune he plays straight down a line I was studying last night, where there is a trap he isn't aware of. If he played 499 other lines, he would win but he played that one. Try arguing that that isn't luck!
Yeah but he didn't play those 499 lines. So he lost. It's worth pointing out that skill isn't a completely easy measure: you are, in fact, more skilled than him as regards some particular positions; so when you reach those particular positions it may be you that wins instead of him.
I think people confuse this kind of thing with "overall" measures of skill. I would say, yeah, you won with skill, but that doesn't mean it's logical to think that you are "overall" more skilled than him, when observably he can do many things in chess that you can't, which is why in many different situations he does beat you.
So, yeah, there is a lack of predictability in this example, and hey, I get why people would want to call it luck. Am I just being difficult? Maybe, but it does seem like there are a lot of chancy elements in poker for example that are not in chess, yet if we just put poker and chess under the exact same label, we will not realize that there are different forces that go into the result. So, yeah, your move is still your move; you might not have known what it would be, but there is some kind of special force that goes into your move nevertheless; there is some kind of power the "your-ness" of your decision carries, that transcends your thoughts/beliefs about what will happen.