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As far as I know, nowadays the chess engines can judge that a move is the best or that it is brilliant (usually denoted by ! or !!). I was wondering what is the precise criterion for this classification.

I was reading some forums and stepped on this discussion. There, some people claim that a brilliant move is one that the engine does not find and, a posteriori, finds it to be brilliant. Some other people claim that a move is marked as brilliant only if the player continues the game responding with the absolute best moves, for some number of moves ahead. Finally, there is also the opinion that a brilliant move simply cannot be reached by the engine up to a certain depth, which is what I would instinctively think too. Thus, this would imply that if the engine performed a sufficiently large-depth analysis then there would not any be brilliant move markers. Is this correct?

Finally, my question: What is (if it even exists) the specific criterion, based on which a chess engine marks ones move as brilliant, rather than simply the best.

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    If you want to know why a chess engine marks a move a brilliant you will have to ask it. You might succeed with asking the developers, but they may not know either. In mathematical game theory there is no such thing as a brilliant move. Each position in chess is won, lost, or drawn with best play. A bad move is one that worsens the result of the position. No move improves the result of the position, because your opponent already assumes you play perfectly. There is no concept of a move that makes it harder or easier for your opponent to hold the draw. Jul 10, 2022 at 2:35
  • Most likely chesscom algs base it on positions with drastic eval changes and low search depths (not on a long depth!) to spice it up for users. It is probably just a good move in such situations (sometimes a non-losing one). This gimmick isn't tied to anything meaningful/useful in chess. It's not the same brilliant as in chess. Good/best moves are based on calculation to a certain depth and are also useless stats at excessive depth (always the case for amateurs). BTW, engines can't judge. They calculate just like calculators. +1 for a good question but I got no precise answer about their algs.
    – user32756
    Jul 10, 2022 at 3:52
  • @RossMillikan What is suggested by the OP's linked discussion is that the chess engine does not perfectly evaluate game theory but rather may find moves better after more search depth. I'm doubtful modern engines would significantly change their mind since they understand positions pretty well.
    – qwr
    Jul 11, 2022 at 4:46
  • @qwr: I see OP thinking there is a well defined criterion for a brilliant move. They give two rough definitions from the thread. It seems clear to me that poor follow-up does not render a move unbrilliant, though we might not recognize it as such if the later play is poor. I think there are different definitions in use depending on the writer/engine. Jul 11, 2022 at 4:54
  • @RossMillikan I agree with your main point but for most practical purposes, there is indeed a concept of "moves that make it harder for the opponent". It's just not the kind of thing you'd use an engine for.
    – David
    Jul 11, 2022 at 21:09

5 Answers 5

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At least for chess.com: (https://support.chess.com/article/2965-how-are-moves-classified-what-is-a-blunder-or-brilliant-and-etc)

Brilliant (!!) moves and Great Moves are always the best or nearly best move in the position, but are also special in some way. We replaced the old Brilliant algorithm with a simpler definition: a Brilliant move is when you find a good piece sacrifice. There are some other conditions, like you should not be in a bad position after a Brilliant move and you should not be completely winning even if you had not found the move. Also, we are more generous in defining a piece sacrifice for newer players, compared with those who are higher rated.

I'm of the opinion that only human players think like humans, so only human annotated brilliant moves actually are meaningful. Brilliant to me means unexpected and strong, so unlike chess.com's definition, even a quiet preparatory move can be brilliant if it sets up a non-obvious idea.

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  • "Brilliant move is when you find a good piece sacrifice" - this begs the question, not just for Chess.com but in general, what is a reasonable way to define (algorithmically) a good piece sacrifice? How do you draw the line between a simple recapture, winning back the material by force in a tactically calculable way, and the position being winning in general? Jul 11, 2022 at 22:02
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As far as I know, nowadays the chess engines can judge that a move is the best or that it is brilliant (usually denoted by ! or !!). I was wondering what is the precise criterion for this classification.

Chess engines do not / cannot annotate moves. They evaluate positions. The annotations in game reviews from chess.com / lichess are generated in the following way: The engine evaluation of the position resulting from the move played is compared to the engine eval of the best move (according to the engine). Depending on the evaluation change, inaccuracies,mistakes and blunders are marked, with different eval change thresholds for each category. Note, that these thresholds are relative to the current evaluation, i.e. a move that turns a position from +0.3 to -2 will be marked as a blunder, but a change from +10.3 to +8 will not be marked as a blunder, even though there is the same absolute difference in evaluation. Therefore, these annotations are objective (w.r.t the used engine) and are straight-forward to generate. The relativity of evaluation change is usually implemented using expected points instead of the raw engine evaluation, so that winning moves will not be marked as blunders. Each engine (centipawn) evaluation can be translated to expected points using the following formula:

winning chances = 50 + 50 * (2 / (1 + exp(-0.004 * centipawns)) - 1).

For example, an advantage of +1 (100 centipawns) translates to a 60% winning chance (or more precisely 0.6 expected points). The thresholds used at chess.com can be found here. Lichess also uses this model to annotate moves.

Strong and brilliant moves are much harder to define, and there are almost no chess sites except chess.com that implement this annotation. On lichess, it is a much-requested feature, and thibault (the founder and main programmer of the site) tiredly asks: "What is a brilliant move?" And he has a good point, as the ! and !! annotations denote human concepts of strong or unexpected moves. Engines do not know what type of moves are difficult to find for humans, and it is very difficult to conceptualize. These annotations are much more subjective choices of an annotator. It is very unlikely that automatic brilliant move annotations will ever come to lichess for that reason. Such automated annotations will miss many brilliant moves (e.g. unexpected silent moves). The criterion at chess.com has changed multiple times due to ambiguity. Currently, they use the following classification of moves:

Move descriptors: Each of your moves fall into one of these categories

  • Brilliant - This was a difficult to find sacrifice which put you in a great position!
  • Great Move - This an important move that swings the course of the game, or is the only good move where any other move would have been trouble. Great find!
  • Best Move - The best move, according to the engine!
  • Excellent - A great move, but not quite the best!
  • Good - This move is okay, but could be better!
  • Book - An established opening move
  • Inaccuracy - This is a weak move that could be much better
  • Mistake - A bad move that immediately worsens your position
  • Blunder - A very bad move that could lose material or lose the game
  • Missed win - A move was missed that would have won material, or won the game

So, chess.com chose to define a brilliant move (!!) as a (non-obvious) piece sacrifice that maintains the current evaluation of the position.

Brilliant (!!) moves and Great Moves are always the best or nearly best move in the position [...] A Brilliant move is when you find a good piece sacrifice. There are some other conditions, like you should not be in a bad position after a Brilliant move and you should not be completely winning even if you had not found the move.

Also, Chess.com defines a Great move (!) as a non-trivial move (i.e. not a simple recapture) that is the only move to maintain the current engine evaluation (i.e. is the best and the only good move). Many of these moves would not be marked with ! or !! by human annotators. Only one specific question remains: What exactly are "difficult" moves? This is a proprietary assessment by chess.com and very unlikely to be disclosed for the reasons I have already outlined in this answer, as the notion of "difficult move" is likely used by their proprietary anti-cheat system. Previously, chess.com had a more sophisticated algorithm for determining brilliant moves, but switched to this more comprehensible definition. The rumors regarding engine depth are not accurate.

Therefore, to finally answer the question:

What is the difference between a brilliant move and the best move?

A brilliant move is a special type of best move, that is a "good" piece sacrifice. (See above for conditions of "good")

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Just my opinion.

The best move is the one with the best evaluation, with the exception of the "computer moves" which only delay the real threat for a move.

A brilliant move is not only good but has a surprise value. A correct sacrifice easily qualifies, but a move with an unusual (and correct) plan do tend to be brilliant. There are two examples: a computer played Re1 in its match against Kramnik with the plan to get the rook to g3, and a game (I think) by Fischer where he played a4 followed by Ra1-a3-b3 just to make black slightly more passive by having to defend the b6 pawn. (Normally every contributor would try to find these examples, but right now, I don't have the energy.)

BTW, this question is really a matter of opinion and shouldn't be asked. When/If this question gets closed, try to learn from the experience.

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    Thanks a lot for your reply. I don't really think that the question is based on opinion. I am just asking if anybody knows what is the criterion for the engine to judge such situations. Such a criterion should exist and should not be subjective. It should depend on the way engines are programmed. I am not asking for people to give me their personal opinion on why they think the engine classifies moves the way they do :)
    – Cyclops
    Mar 2, 2021 at 10:06
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    Difficult. I think anyone would find Marshalls Qg3!! brilliant, but telling that an engine...Clearly "surprise value" can't be programmed. Neither can "subtle" be (what Qg3 argueably lacks). In that example, the queen can be taken, with White being +8 for one half-move. This is a condition that can be programmed easily. Another condition would be the +8 would last for longer. Mar 2, 2021 at 11:50
  • To clarify, the difference between a computer's "!" and "!!" (neither one that I've seen a computer output) would be based on some arbitrary value programmed. Since I opened this answer with "Just my opinion.", it should be obvious that I'm answering with a human POV, although this also means that I didn't try to anwer the OP.
    – Mike Jones
    Mar 2, 2021 at 18:11
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Chess Engines have two settings: Depth & Variation. A Brilliant move is something which is counter-intuitive to humans as well as hard to find for a chess engine in terms of depth & variation. I again categorize brilliant moves into tactical brilliancy & Long Term positional Brilliancy. Tactical Brilliancy is when you are sacrificing or doing some odd move which is counter-intuitive yet we can see its positive outcomes within a few moves. For Example, If the queen is guarding the checkmating square then deflecting the queen by sacrificing a piece or other tactical motifs. Positional Brilliancy on the other hand is when you play a move(sacrificing or some other odd move) which is counter-intuitive and we see its positive outcome very late in the game. For Example, Based on your position-Exchange your queen for your opponents Rook & Bishop. Now if we see here there is no clear positive outcome instantly but it builds up towards the end.

Best Moves on the other hand are relatively easier to find for humans(GMs) as well as for engines because these moves are most of the time intuitive and for engines(less depth & a low number of variations).

Brilliant Moves are the Aha Moments whereas Best Moves are the daily routine.

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    Welcome to Chess! The author explicitly asks how a chess engine marks ones move as brilliant, rather than simply the best - could you edit your answer to address that please?
    – Glorfindel
    Jul 14, 2022 at 16:52
  • This is not how chess.com does it. Also, the claim that brilliant moves are ones, that the engine needs a higher depth to find is very questionable. There is no direct relationship between engine depth and difficulty for humans. I do not know where this claim / idea comes from. Maybe from the chess.com forums. I have seen many times, that the engine didn't prefer the human (theory) moves until a certain depth. Likewise, there may be brilliant moves that the engine finds rather quickly.
    – Hauptideal
    Jul 16, 2022 at 9:59
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A 'best' move means that the move played was better than any normal move that could have been played. A 'brilliant' move means that the move played was unexpected but leads to more advantage in form of greater evaluation of position than what a 'best' move can lead to.

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