What qualifies as a "brilliant" move?

xd4 is brilliant, doesn't look like it

Does it follow then that you are less likely to have "brilliant" moves if you raise the depth setting before doing the analysis?

I just had a game where the evaluation didn't change at all but my move counted as brilliant... https://www.chess.com/analysis/game/live/13590068147?tab=analysis

I don't exactly know how the system works but I guess there are some specific moves that engine had already calculated and it says it as Brilliant Move

The whole idea of "brilliant" moves, as determined by a computer algorithm, is simply ridiculous. Moves are good or bad, strong or weak. That's all that matters. Trying to guess what some piece of computer code is going to call "brilliant" is--at best--a waste of time. 

fun fact, a "brilliant move" can never be possible against an engine that literally analyzes every single position in a chess game because it won't overlook anything because it doesn't skip anything

I dunno why people get so worked up over the "Brilliant" move. A brilliant move must be taken in the context of an idea. And computers don't have ideas, they just do math well. So an engine doesn't formulate a plan in the way that a person would. If a chess master flagged a move as brilliant, it would mean a lot more, IMHO

This is consistent with my experience, and seems more likely than the other theory that it's something that the engine has to analyze to some high depth before it's clear that it's a good move.

I just got my second "brilliant" move ever; it was a routine looking move in a K+4P v K+4P end game that drew the opponent's king further from the center of the board, giving me a chance of winning the queening race, and it was probably the only move that did that..  Unlike my previous "brilliant" move, it was not just the only move that took advantage of an opponent's blunder, as the opponent did not blunder before the "brilliant" move was played.  The opponent did blunder after the "brilliant" move was played, but I think the "brilliant" move turned the game from a loss to a draw for me, and the subsequent blunder then turned it into a win.

I think for a move to be evaluated as "brilliant", it also has to make your evaluation notably better than it was one full move before.  That requires either the opponent making a mistake in the interim, or the additional two ply of search depth resulting in a significant evaluation change.

I think there are several criteria that determine whether or not a move is brilliant. My guess is that the categories are as follows.

1) It has to be the only move that wins/draws

2) The move is not found by the engine until it reaches a certain depth

But, then again, why is this move not marked as brilliant?

Who is getting "worked up"? Brilliant moves are part of the feature. We use the feature. We want to know what it means. We would ask about any of the other categories if we didn't know what they meant. But those are obvious. This one isn't.

I'm pretty sure I've seen "brilliant" moves that don't meet your first criterion.

Sorry, I didn't present my point very well.

Every day you see on this forum posts that contain something like "I got a brilliant move in this game". Sometimes, that move is the most logical response OR even the ONLY response that doesn't lose. Even sometimes, the brilliant move is the natural response (recapturing a piece, for instance). 

What I was trying to convey is that brilliant moves can rarely be defined by an algorithm, because, by nature, chess is a game of ideas. An algorithm can easily tell you that a move was "Best", but the term Brilliant, as it relates to chess, is not purely mathematical. A brilliant move should be defined within the context of an idea. 

I concluded, therefore, that a brilliant move is more likely to be identified by a person, who has the capacity to understand the battle of ideas that are happening at the time, and to identify that the Best move was in some way contrary to "normal" chess philosophy.

The chess.com algorithm tries to guess at the brilliance of a move based on a formula that we don't know. Since I believe that a brilliant move can't be accurately determined my an algorithm, then I believe the "Brilliant move" flag in the analysis engine holds no value to the person analyzing their game. As a matter of fact, I think, perhaps, that the value of the brilliant move (by the CC Analysis engine) exists only within the forums.

Thanks for the explanation. Based on your reasoning, "best" and "not best" should be the only two categories.

Ultimately, we can't really evaluate the utility of the brilliant move category one way or the other without knowing the criteria . Unless and until those are revealed these questions are going to be asked (well, they'll be asked anyway, but I'm sure you know what I mean).

Surely enough, Stockfish failed to find the brilliant move 11...Qh4! when white is practically lost.

Online engines are weak, and this is no secret.

Haha, no that's not true. Blunder, Mistake, Inaccuracy: Those are all very well defined and measured with the same ruler as "Best" is: They are measured in centipawns. So of course, all of those flags relate to each other: Best means no other move has higher value in centipawns. Excellent and Good are higher values than Inaccuracy, but lower value than Best. 

All of the flags are based on cp EXCEPT brilliant. Brilliant doesn't use the same scale as the other flags

Qq

Which in no way contributes to answering the OP's question.

It was very fortunate for me to find the very first brilliant move in chess.com ever.

I was analysing this game this morning, and suddenly found out that Bf4 was the only brilliant move, shown on the diagram. Let me explain this briefly.

During that game, the opponent played Qh4, threatening the weak h2-pawn, as well as the castled king on g1. I was thinking of this critically how to defend this threat. Then I played Bf4, the brilliant defense and the only good move by protecting h2-pawn from the attacking queen. How lucky I was!

I realised this was the very first brilliant move I've ever played online, but it's hard to believe that not every player is likely to find the brilliant chess move in every situation. Who else agrees?

I once had an opponent play a "Brilliant" move. I was crushing him in material (I think like 7 points above) and he found a way to perpetually attack my queen. My only available moves were to sac the queen, or repeatedly defend it and draw by repetition. 

I sort of just assumed that it was Brilliant because it turned a near-hopeless position into a forced draw (or significant win). 

How about this?