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Is there any luck in a chess game?

That isn't luck over the board though, that's luck of the draw in terms of strength of schedule. You can't think of rating as being the same as your play over the board. The play hasn't changed, the caliber of your opponents has. You aren't able to inflate your rating against weaker opponents. So against a stronger strength of schedule, you have a lower rating. That's not any sort of statistical anomaly at all, it's expected. So in that sense, the only 'luck' is the luck of the draw on how strong your schedule is.

You might also 'luck out' and get someone with an inflated rating and find an easy game. hahah

And those instances of random moves getting lucky, or finding yourself in an unexpected line that looks bad but happens to work out in your favor because of miscalculation from the opponent...these things could indeed be considered 'lucky' but in reality it can't truly be defined as 'luck' because there were possibilities to accurately calculate and avoid such things. Also finding the 'right line' by a lucky guess could boil down to intuition, which again is still not 'luck' it comes from seeing similar positions time and time again. Sometimes you just grab the right move based on your gut.
I would like to differentiate between luck and oversight. There can be good oversights where things work out, there will be bad oversights with a big "whoops!"

If you missed something, or if the opponent missed something, or if both sides missed something, they simply missed something. Error in judgement or oversight on something about the position, like variations or piece placement, is simply just that: error and oversight.

KEYPOINT: Anything that happens in chess happens as so because a) we cannot foresee, b) we mistaken foresight, and c) we did not foresee.

So where does that leave us with the idea of luck? Let's define it a bit, so we can see if it does or does not exist.

FEW SCENARIOS: Let's say a car hits your game of chess. Is that unlucky? What about when you win a game of roulette? Is that lucky? There are odds a car would hit you. There are also odds in a gamble with roulette. I would define luck as such.

Are there odds in a game of chess?

Statistically, yes. Statistically so with the runaway car and scoring at roulette.

SIMPLIFICATION: What about flipping a coin? Heads or tails? Can you call it luck if the side you advocate appears after a flip?

Can you improve the odds of your success with coin flipping without manipulating the governing rules of this game? Probably not.

What about roulette? Can you somehow better your odds of success? Sure, but you still lose in the long run if you bet everywhere.

How about getting hit by a car? Yes. Don't play on the highway.

KEY POINT:
So if luck is based on the idea that which may happen, that is the "odds" or probability of an event, cannot be more (or less) likely to occur, then luck may be attributed to such occurrence.

What about chess itself? If you study openings (knowledge). If you study your opponent's play (competitive intelligence). If you train your senses to detect patterns (tactical prowess). If you make sure you play an online game with a perfectly functional computer (technical). It seems it is possible to reduce the odds of losing the game, and increase the probability of winning it.
I don't agree with your simplistic characterization of luck simply applying to anything with statistical odds. Everything has statistical odds, so that would imply everything boils down to luck. If there is a randomizing element, then luck becomes involved. Otherwise it's simply a matter of skill. A car hitting your chess game involves luck only because the player at the chess board has no control over that outside force. In roulette, the game itself involves little more than the randomization element (provided it isn't rigged) in which case it's all luck. The way we define luck is whether or not we have control over the situation.

Some games blend skill and chance, like Risk, where there are randomizing elements (dice and cards) that effect the outcome and can't be controlled (unless rigged). Even if one plays perfectly, luck can ruin their day. However, there is still a lot of skill involved in how one takes advantage of the random elements. So while there is luck present, it is still considered a game of skill.

In games of chance like Texas Hold'em Poker, the game itself is a game of chance, the cards themselves are a randomizing element. But there is some amount of skill present in assessing probabilities and the like. However, even if one properly assesses the probabilities in the situation, one can still lose. Hence while there is skill involved, luck is the main factor involved so it is called a game of chance.

Chess, however, is a game purely based on skill. There is no randomizing element, thus, we have all the control over the odds based on picking the right moves. The natural result from the starting position should always be a draw if both players play all the "right" moves. However there are complex lines that can make it difficult to find all the "right" moves and therefore wins and losses occur. But they do not do so at random, they arise from our choices. So, no, there is no luck in chess simply because there are statistics involved.
I simplify the idea of luck to define it as: something impossible to control.

You can't improve the odds of winning at coin flipping. But you can improve your odds of winning a game through practice.

Not quite sure what you mean by roulette involving a little more than "randomization element". What do you mean?

I'm not sure about risk, but the games that has an element where you cannot improve your odds of winning on, and relies on its outcome in order for you to win the game itself, I would say: has luck.

Of course, since luck is uncontrollable, if all else the same, then skill determines your long-term outcome.

The same goes for chess, except I argue there is no luck.

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