What is "luck" in chess?

Sure if your opponent's mouse slips, or some other unforseeable circumstance, that would be "luck", but otherwise, how does one "get lucky"?

Buy her enough alcohol and tell her you really care.

It's an interesting question. I guess the idea is that if a master hangs something a beginner would easily see, allowing the beginner to win, the beginner didn't win through master-like skill, but won because of an unusual occurrence that was outside his control (he can control his own moves, but not those of his opponent).

So yes it seems like there is some nonzero probability that a person will win not primarily because of skill, but low probabilities are low -- it's also possible that I could type random keys for a few hours and they would just so happen to match Shakespeare's Hamlet word for word. Besides, not hanging a piece before your opponent takes some skill -- I would still say that if you could avoid that you played better than your opponent.

And sometimes things that look like luck aren't. For example just because your opponent makes a really simple mistake doesn't necessarily mean he is playing at a way lower standard than usual -- it could be that you had great control of the game, and when your opponent has a bad position it will be harder for him to avoid cracking under the pressure and blundering.

What dpnorman said.

I equate chess "luck" in two ways. (1) For example: You make a certain move in a sicillian with your knight, and black checks you with his queen, and you start to panic that you didnt see the move, but your piece that you thought he was going to take with his queen is actually protected, but when you played this knight move originally your criteria wasnt to necessarily to make it protected (you thought no attack was imminent).

(2) A certain combination from you or the opponent has an outcome this is favourable for one of you but neither saw this outcome originally through your calculations.

(1) and (2) have both happened to me and against me in an over the board match.

Luck in chess technically does not exist - there are no random variables - in the way that poker has. But as the mind is limited to understand all chess variations (obviously, more so at the amateur level), then chess luck is the outcome of certain moves that you did not intend to happen. 

I would argue though that "chess luck" seems to be of a more subjective, internal sort. What I mean by that is it's basically the uncertainty the player feels. I may play a move that is right but feel uncertain about it. But my uncertainty about the move doesn't affect its quality; all it does is determine how surprised or unsurprised I am when my move happens to work/not work. If I carried out a checkmate in one, then there's no debate about that, even if I didn't know it was checkmate when I played the move :)

Carelessness on the opponent's behalf. 

There is randomness in chess - when and how a player makes a mistake (suboptimal move) is random. By suboptimal move I mean anything different from best move. Of course there is no way to know for sure what is the best move (except when you are in tablebase position) but let's say if I let Stockfish analyse the position for 15 min it will come quite close to finding 1st best move, 2nd best move etc. One thing is sure - as we get stronger we make less mistakes and play closer to ideal play.

If player A is first to makes a mistake and player B sees it and punishes it  - it's not only question of skill but also of luck.

I would categorize luck as an opportunity that happened without conscious intent from either player. The board has so many possibilites and no one can compute them all beforehand. Perhaps a blunder wasnt really a blunder until your opponent thinks of an inventive way to defend, and in doing so opens himself up to an attack that was unforseeable to him. Neither players had the intent of making the moves, but one recognizes a way to profit from the circumstance.

Suboptimal move is above mistake in the hierarchy.  It goes something like this:

Optimal move: Improves position in the best possible way.  May be more than one (e.g., 1.d4 1.Nf3 1.c4 and 1.e4 are all considered optimal)

Suboptimal: Not best, but only worsens the position in a very minor way.  Suboptimal first moves are 1.b3 and 1.Nc3 for example)

Dubious: Worsens the position, but not enough to enter a losing position unless you were in a pretty bad spot to begin with (e.g., a drawn position that requires great accuracy and technique for the inferior side).  Annotated with ?!

Mistake: Here is where we see drastic evaluation changes.  Goes from a winning position to a slight or clear advantage.  These are the ? moves. 

Blunder: goes from winning to drawn or worse.  Represented with ??

Sure, that'a a well defined hierarchy. I was just trying to find some common term for a move that is not optimal. Shall we can it non-optimal? So my point was that the better player's skills mean his moves are closer to optimal, but when is he going to play non-optimal moves and how "bad" they will be is random - hence luck comes into play.

If the move is bad enough it'll be dubious.  Suboptimal may be a move that worsens the position by .10 pawns or carry out the best plan but not in the best and/or most forcing way.  Non-optimal is good and yes higher skill means fewer suboptimal and below moves.  Though even in world champion chess trying to find the optimal move all the time seems impractical, so people look for the best plan, which drives the analysis (candidates that support said plan, rejecting poor candidates through falsification via calculation and evaluation, etc.)

An example may be looking that everything is in position for a kingside attack, but calculating all the candidates deeply enough to find that optimal defense leaves the opponent better off in the endgame, so you instead go with another plan.  A lesser player would go for the attack and either have it be successful (optimal defense requires hard to find exact moves in this hypothetical) or his opponent would achieve better chances in the endgame after a tough defense. 

What are the chances of someone winning by luck rather than skill?

I once started a topic "Does winning involve any luck ?" Check it out on my profile, some interesting comments - Bottom line, the answer is YES.

I read many years ago that a well known Grand master said "the person that wins the game is the one that made the next to the last mistake". We're not rolling dice. We make moves that have a finite number of possible responses. If you want to call it luck when your opponent make the wrong move, then so be it. In my opinion luck has nothing to do with it.

Chance favors the prepared mind.

It's always a mix of both. In my last OTB game my opponent (with rating close to mine) have blundered a bishop on move 8 - that was luck. Then I had to play quite precisely for another 20+ moves until he resigned - that was skill. I feel that this win was more by luck but that's quite subjective.

So what do you call it when you opponent makes the wrong move before you do it? To me it looks like it is luck. There is no way to predict when the mistake will be made - just like when rolling dice.

Sometimes luck is involved. Not the dice rolling kind, but simply sometimes a player choosing a variation you know well (or don't), finding a great move when forced to (in other words, when you originally started a forced sequence, you overlooked another variation, but then found a move afterwards that busted his choice.

-When your opponent plays a bad move/misses the best move, is this not lucky for you?

-When your opponent feels ill/sick that day...and blunders because of this, is this not your luck?

-If your opponent cannot proceed to the next round in a tournament, and decides to resign all his games, is this not fortunate for you?

There are a host of events which may lead to you winning over your opponent...other than your skill...all of these I would consider luck.