Chess by design is a game of skill. But, a players skill rarely matches the depths and richness of the position. Sometimes even the very best must follow their intuition and their best guess. They may get lucky.
For instance, a couple of days ago I sacrificed a pawn simply to offer my opponent two ways to proceed, neither being the drawish rook maneuvers we had been doing for several moves. He chose a clearly wrong reply. But, even the better reply was dead lost. It took me a considerable investment of time in postgame analysis to see that even the move I thought retained near equality was dead lost.
My move was desperate effort to avoid a repetition. It turns out that it was far stronger than I imagined. There is an element of luck that I timed it perfectly.
For a GM, my sacrifice may be routine. For me, it was a desperate act that involved superficial calculation. A beginner might play it as a blunder (failing to see that a pawn is offered).
calculation none the less which means it was not random chance and not due to anything other then your own action. Such as randomly dealt cards or a dice roll. To imply otherwise is uninformed.
Which is apparent with Lee, and which Optimissed rightly pointed out, since we must have different definitions of the word luck or we must have a different interpretations of the question posed by the OP, therefore we can not have an honest debate.
Calculation?
The beginner’s calculation that fails to realize that a pawn is being given up?
My mis-calculation that considered only the exchange of pawns and believed that I was not gaining anything? Calculation that was wrong. Even the pawn exchange is winning.
A GM would see further in this position.
White to move
Level of calculation is level of skill. not luck. Just admitting it was a calculation, takes luck out of the equation.
The point: calculation barely came into play, and where it did it was in error (assessing, incorrectly, that the position was still close to equal).
Oh wow, with the kind of hint I'm looking at d5 of course... and if that's the solution it's a pretty cool idea.
Far cooler than I realized. That’s my argument for luck arising: intuition, or in this case desperation, sometimes works out very well. Other times it blows up in ones face.
What seems like a fairly simple and drawish rook endgame reached a position where White could strike a decisive blow and did so, but did so without understanding. However, when Black took the free pawn, White was back in his sphere of knowledge and ruthlessly exploited the advantage of being able to cut off Black’s king from the action.