[caro_douglos]

The term I think is important to mention with your example is “forced mate” wherein the moves force the opponents next move with absolutely no choice except to play the rest of the game down a significant number of points.

The first time I saw grandmaster level play in person was a queen sacrifice which led to bishops mating the king in short order.

https://en.m.wikipedia.org/wiki/Queen_sacrifice

[casion]

A forced mate is _forced_. There are no options except to be mated.

If there was a way to not be mated it'd be referred to as "Tactics" or just "A Combination".

And further annoying pedantry: there's no points in chess outside of match or tournament score. Pieces have _possible_ pawn-equated values that someone can use for evaluation, but those are very loose. It's possible to have a naive material evaluation that is not in your favour and still be in a significantly winning position. Better players think in terms of a pieces ability to control squares, how soon it might control squares, the importance of those squares, the potential value of reducing another player's board control, the ability to create tactical threats etc... there's a couple dozen potential evaluative concepts that are often more important than piece value.

Funny enough, your example of a queen sacrifice demonstrates this ;)

[iCarrot]

Here's my understanding: a piece's value is dynamic, and it depends on the type of piece and its position on the board. Positioning leads to all other aspects you listed: controlled squares, to-be controlled squares, tactical threats, and so on... (hence the popularity of "positional" chess where there's no concrete threat or plan behind a move, only improving the position of your piece, which may create opportunities later). I believe this is also how Stockfish chess engine evaluates a position, and it has higher elo rating than any human player.

Having all those said, the type of piece is still the bigger factor in deciding the value of the piece. You don't often see a queen-knight trade for example. Queen sac is definitely something you don't see every game.

[casion]

You aren't wrong, but there's a nuance that I was trying to clarify on.

Regarding the idea that you rarely see trades of uneven values: that is largely because positions where such complications are likely tend to be avoided by most players. There are notable examples of players that make/made such trades disproportionately often. Morozevich, Tal, Shirov, Tate, Shabalov, Speelman, etc..

Playing in that manner is largely unusual because it is mentally fatiguing, risky and easily avoided with modern theory.