ReneDescartes wrote on 01/25/23 at 23:41:32:
I don't get it. A chess position with the side to move given is stateless except for (1) en passant, (2) castling rights because a piece has moved, (3) threefold repetition, and (4) the fifty-move rule.
Even those exceptions can be encoded as properties of the current position. The FEN string in a .pgn file does precisely this. For example, in Kerangali's position
[FEN "r3k3/P5P1/1P1P1P2/3PpK2/8/8/6B1/8 w - - 0 1"]
the additional fields have these meanings:
- w : white to move
- - : no castling rights
- - : no en passant captures available
- 0 : no half-moves have been made since the last pawn move
- 1 : next move is move number 1
ReneDescartes wrote on 01/25/23 at 23:41:32:
Other than that, it's stateless, mathematically a "time-homogeneous Markov chain" (if you substitute for probability some function that sums to 1 for all the possible moves). The rest is psychology. Am I missing something?
I don't think you are missing anything. But people can't play very much like engines, so the psychology is important.
ReneDescartes wrote on 01/25/23 at 23:41:32:
Rather than GeneM, I trust Botvinnik: "What is the essence of the chess master's art? Fundamentally it consists of the ability to analyse chess positions."
By relentlessly calling puzzles "shot puzzles", Milener reveals that he is overly focused on the "win" aspect of puzzles. I infer he thinks other people think the value of puzzles is learning "how to win" via: first, get the kind of position in the book; second, play the appropriate combination. Probably he was abetted in this misapprehension by de la Maza and the internet.
Botvinnik could certainly make deep and surprising combinations of the type found in puzzle books. He could also do the same deep and surprising game with openings, strategy, theoretical and practical endings, you name it. I remember a comment Botvinnik made about Reshevsky, saying Reshevsky excelled at two- or three-move mini-combinations and he (Botvinnik) needed to up his game in that department. This is the simple "I go here, they go there" aspect of calculation which is practiced by doing puzzles, along with the pattern learning which is also practiced.
Milener's complaint that "shot puzzles" account for only 4% of chess game positions overlooks that "I go here, they go there" accounts for 100%.
ReneDescartes wrote on 01/25/23 at 23:41:32:
Regarding future moves: aside from the aforementioned states and positions in which the game is over, the total set of very next moves, or rather very next positions, is a characteristic of the current position. In a way all future moves can be thought of as contained within the current position, and this is how we treat the situation when we say White has winning chances, etc. But to make a sensible mathematical model of the game, subsequent moves should be viewed as characteristics of the subsequent positions that immediately precede them.
The reason I brought up future moves is because of the logic. Just picture the current position as a sliding window on a sequence of moves. Logically if a previous move has an impact on the current move (kinetics), then the current move has an impact on the subsequent move. After all, where did the previous move come from in the first place? It came from you, back when it was a current move!?
Note I am not saying this is a correct way to play chess. I am just wondering why a chess philosopher didn't mention it.
This whole kinetics thing has an air of Emerson's foolish consistency. Or the Russian saying "Having said A, you must say B." (Maybe a Russian could chime in on whether this aphorism is sardonic, which is the only way I can make sense of it. And I note someone else has my question:
https://www.reddit.com/r/russian/comments/7pgceb/having_said_a_one_must_say_b/)
In fact, having said A, you are not at all required to say B. What you should do is consider everything that happened after you said A, and then say the most sensible thing that comes to mind.