The game itself doesn't have intrinsic chance, but as with everything in life, the players do.
I do agree with your last point though, winning doesn't mean you played well, it just means you played better than your opponent.
I also think there’s a larger element to reading your opponent in chess than many people give it credit for — what are they planning? …can you “tilt” them to make them play worse? Etc.
It’s only at the very highest level you should expect people to play nearly perfect games… and even those players discuss the psychology (eg, Hikaru Nakamura is top 50ish and discusses the role of psychology in high level chess).
:)
People have been saying "the players are nondeterministic not the game," but epistemically what is a game with no players?
I play chess seriously in a tournament setting. While it is true the board is revealed, the board is not the game. The board is the operating theater of a game which is entirely within both players minds. People have become overly dismissive with the idea that the game is deterministic because chess engines exist. But chess engines are not even necessarily deterministic because the result of the alpha beta search still vary based on depth and the evaluation heuristic.
Without an evaluation function you cannot even interpret a board position at all. This function is simply not deterministic (unless formalized and then it will be imperfect to situation), and any GM will tell you that some positions are impossible to evaluate.
Additionally there are many times where engines produce suboptimal results until the search space is collapsed by a player like Hikaru. It's not frequent but it definitely happens.
Chess is a game between two Turing machines sharing a tape. Sharing a tape does not allow you to see the state of the machine in each players head. And if you have no players you have no game. This makes chess highly probabilistic in so many senses that using the game theoretic construct of "prefect information game" causes game theorists to seemingly literally not understand it.
Chess is a deeply human game subject to human variance. This is nondeterministic. Poker is also human, in other ways. Anyone who sees chess as deterministic is probably a weak player (less than 2000 fide) and doesn't understand this fundamental aspect of the game. At the higher levels there is even forms of bluffing and swindling, which is fantastic simply because you CAN see the same board and you were still able to manipulate the other player with their own prejudices.
You could say the same about poker. A player looking to improve their game will review their hand histories, and plug hands into PIO or HRC.
That's really not what's meant by chance. Chess is no more a game of chance than tennis or golf.
In poker, there's an element of randomness that's an explicit core part of the game (the deck).
No such mechanic exists in chess.
An example that makes this element really obvious is turn-based fighting video game Toribash.