In practice, Chess is not a game of perfect information, since you generally don't know which lines your opponent has prepared beforehand.
"Perfect information" is a term of art for games, it doesn't literally mean you are omnipotent.
Chess, unlike war, is a game of perfect information
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Re: Chess, unlike war, is a game of perfect information
#12Chess belongs to a class of games that are particularly interesting to study: it is a finite extensive form game which basically means the game can be modeled as a tree and requires only shared knowledge among participants, all the participants have complete shared knowledge, it’s sequential, has perfect recall (nothing prevents looking backwards at the game state), and a simple payoff function (you win if you checkmate the opponent, in which case the opponent also loses) that is zero-sum.
This makes it so chess has a one-shot sub game perfect equilibrium: https://en.m.wikipedia.org/wiki/Subgame_perfect_equilibrium. But, the dimensionality of the possible end states is very high, because there are many different configurations leading to a checkmate, so you can’t easily perform backward induction. But you can perform minimax (which is how Stockfish works): https://en.m.wikipedia.org/wiki/Minimax
From a game theory perspective chess is really not at all like an actual war, because the properties of the game are different in almost every conceivable way - not just because of perfect information. But, you can model more complex “games” like war in a way that makes them more similar to chess if you wish. Just be careful because ignoring very fundamental differences like the payoff model could greatly affect decision making - for war, you’d probably rather surrender or make minor concessions in most cases than win at the cost of 99% of your people and infrastructure getting destroyed.
Re: Chess, unlike war, is a game of perfect information
#13In interviews, (US) General Stanley McChrystal has said he prefers backgammon to chess because it involves both strategy and chance.
Re: Chess, unlike war, is a game of perfect information
#14I wonder what chess would be like if it incorporated a fog of war mechanic where you could only see some tiles around each piece, and perhaps rooks could see a straight line all the way down the board.
You might like Reconnaissance Blind Chess [0]. It incorporates imperfect information into Chess and was developed for AI research at the Applied Physics Lab. [0] https://rbc.jhuapl.edu/
Interesting, one who makes an account to post about reconnaissance blind chess. Are you involved in it a lot? I know some who are post here.
Re: Chess, unlike war, is a game of perfect information
#15I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively.
This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well?
But in both cases, there is perhaps still some state… At least if you’re playing a human. You might be able to get a feel for what’s on their mind. Where they’re going with the game. What overall strategy they’re working on. And that can inform what comes next.
But is that just a form of gambler’s fallacy? Would an AI have a natural advantage if it made optimal moves given current state rather than being attached to a “plan”? Is the “plan” just an abstraction so you don’t have to re-analyze the board every time? Or is the “plan” some sort of advantage?
Re: Chess, unlike war, is a game of perfect information
#16Chess belongs to a class of games that are particularly interesting to study: it is a finite extensive form game which basically means the game can be modeled as a tree and requires only shared knowledge among participants, all the participants have complete shared knowledge, it’s sequential, has perfect recall (nothing prevents looking backwards at the game state), and a simple payoff function (you win if you checkm…
>But you can perform minimax (which is how AlphaZero works)
AlphaZero uses Neural Networks, old engines used to use Alpha-Beta pruning if I am not mistaken but after 2017 (the year AlphaZero papers were released) they started using a combination of the two or just NN.
Chess Programming Wiki [1] is an awesome website if you want to learn how Chess engines work in detail (or write one).
Re: Chess, unlike war, is a game of perfect information
#17I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
If you take into account player behavior dynamics, then I think path to a state becomes more important. I.e. "what my opponent thinks I'm trying to do" becomes important information to keep track of. Maybe not the case with chess, but definitely in other games.
Re: Chess, unlike war, is a game of perfect information
#18I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
I don't believe stockfish cares about past moves at all besides castling/en passant. It's able to evaluate a board so effectivly that it doesn't need it.
Re: Chess, unlike war, is a game of perfect information
#19In practice, Chess is not a game of perfect information, since you generally don't know which lines your opponent has prepared beforehand.
"Perfect information" is a term of art for games, it doesn't literally mean you are omnipotent.
Is it a particularly useful term here? It seems to mean you could theoretically play perfectly but in almost every real situation you can't, which is true of every human activity (including war). Information is hidden by complexity, but it's still utterly inaccessible.
Re: Chess, unlike war, is a game of perfect information
#20I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
>At least if you’re playing a human. You might be able to get a feel for what’s on their mind. Where they’re going with the game. What overall strategy they’re working on. And that can inform what comes next.
Every decent chess player is able to take over any position, there is no need to communicate the plan being worked on, you look at the board, you evaluate your and your opponent's strengths and weaknesses, and a plan (or even plans) should show up, assuming the game is not a dead draw, the evaluation of course differs from one player to another, and consequently, the continuation.