An exclamation mark after a move indicates that, well, it is a surprisingly good move and that had you been present to watch the chess game the player who made the move probably would have done so rather violently and followed it up with several fist pumps. Like, we're not talking "best move in the situation" good here – we mean more like "woah holy shit can he DO that?" good. Two exclamation marks indicate that it was such an insanely and incomprehensibly amazing and wholly remarkable move that a mere single exclamation mark did not do it justice, and that the player making it may have caused significant collateral damage. Further exclamation marks (after !!!, it is simply notated n! partially for convenience but probably more to irritate those who spend a lot of time with combinatorics) are in fact calculated based on the Richter scale.
A question mark after a move indicates that the move was surprisingly weak. Essentially, it shows a betrayal of trust. If one is annotating a game at a chess tournament between two amateurs, they will not add in question marks after each and every blunder they make, rather only if/when they manage to pull something so incredibly and mind-bewilderingly stupid that the annotator is genuinely surprised by their ineptitude. When a grandmaster moves in such a manner that he or she leaves a pawn in a slightly vulnerable and weakened position, this too is bewildering and can deserve a question mark. Now, the double question mark indicates not just a betrayal in the annotator's trust in the player, but rather its complete and utter destruction. An amateur could perhaps achieve this, but only by means of the most extraneously hindsighted moves such as losing in two turns as per 1. f4 e6 2. g4 Qh4#. A grandmaster can generally earn the same level of shame by losing a pawn.
Now, combinations of exclamation and question marks can get complex. The general forms of their usage are beyond the scope of this brief introduction, so only the two most basic forms will be discussed. An exclamation mark followed by a question mark indicates that the annotator is fairly confident in his or her intuition that it was a good move, even though a wide array of general guidelines indicate that it was in fact a blunder. While modest annotators will only go against the more flexible guidelines such as "avoiding doubled pawns" and "controlling open aisles," when the exclamation mark-question mark is used by more arrogant annotators, the counter-intuitive guidelines being ignored often include things such as "not sacrificing one's bishop" and "avoiding checkmate." A question mark followed by an exclamation mark indicates that the move was clearly a blunder. However, it does also indicate that the player who made the blunder could potentially perhaps just possible you know maybe kinda actually still win, but clearly if he does it would be due not to his making a brilliant move but rather to to the move winning an advantage by pure chance that he could not possible have thought of when he made the move. A better way of phrasing this would be to say that the question mark-exclamation mark is to be used when you are annotating Tal's games and you just know he is going to somehow squeeze a checkmate out of that bishop sacrifice but have no idea how.
So enough theory. Here's the annotation system. Put into use.
1. ... Nf6
2. Nc3 d5
3. e5 d4
4. exf6 dxc3
1. ... Nf6
2. Nc3 d5
3. e5 d4
4. exf6 dxc3
An unorthodox version of the Alekhine opening, where both knights are slaughtered on their natural squares.
5. fxe7 cxd2+?
Note that a + here stands for check, not plus. Chemists shouldn't be confused as the cxd2+ ion does not exist (as the only stable ion cxd can form is the 3+ cation; the other oxidation states do not exist not because they are structurally unstable, but simply because they are impossible). The question mark, if you have paid attention earlier, should denote that this move is considered unexpectedly bad by the annotator. It is not being added to cxd2, as if you have paid attention earlier, you'd know that the plus sign denotes a check. At this point, we don't really know why this move is unexpectedly bad, but it's a check, and a move that has a check in it has a higher chance of being bad. So now if black loses, we'll have a move to blame it on.
6. Bxd2 Bxe7
7. Nf3 0-0!
6. Bxd2 Bxe7
7. Nf3 0-0!
Here, 0-0 refers to kingside castling. It is not an emoticon, nor does it refer to zero minus zero factorial (the solution of which is -1). Castling is generally good, though typically not good enough to warrant an exclamation mark. However, his expectations having lowered due to black's terrible fifth move, the annotator is genuinely surprised at black's ability to respond with a half-decent move. Black also ruthlessly breaks the pseudo-symmetry.
8. Bc4 Bf6
9. c3 Bg4
10. 0-0 Bxf3
11. Qxf3 Qxd2
12. ½-½ (Mirage endgame)
8. Bc4 Bf6
9. c3 Bg4
10. 0-0 Bxf3
11. Qxf3 Qxd2
12. ½-½ (Mirage endgame)
