In practice, Chess is not a game of perfect information, since you generally don't know which lines your opponent has prepared beforehand.
> In practice, Chess is not a game of perfect information, since you generally don't know which lines your opponent has prepared beforehand What do you mean when you say "game of perfect information"? What would be an example of one?
Chess, unlike war, is a game of perfect information
41–50 of 81 posts
Re: Chess, unlike war, is a game of perfect information
#42I 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…
There's a lot of games where the "State" is important the most obvious of which being poker.
In a game of poker you can devise a game theory optimal strategy for any given position which is objectively the best, but that's not what most players do. They try to mix in exploitative strategies which abuse the tendencies of their opponents. These tendencies are revealed after extensive experience with the players.
There is an aspect to this in chess as well, you can treat the best move as the one which is objectively best (Game theory optimal, as evaluated by chess engines usually), or you can treat the best move as the one people in general have a hard time responding well do or that your opponent doesn't play well against (Exploitative, as evaluated by opening database statistics or a players history). Yet once a tricky opening becomes popular, people wise up, and it starts becoming a bad opening again. Whereas old traps become forgotten and effective again. Whereas objectively good moves are always objectively good.
Another huge aspect to winning the game is just playing against bad players. In chess players your performance is rated based on the rating the other player, so you shouldn't fear playing games against a stronger player. In Poker your performance is measured in dollars, and you should absolutely fear playing games against a stronger player. So to be most effective in poker, you want to know the history of the people you're playing, which is why poker tools like sharkscope exist which tell people which tables are filled with historical winners.
You can play games in a stateless way and do pretty well, and the benefit to doing so is you learn skills that work against anything from the weakest to strongest opponents and allow you to play objectively good moves. But adopting a few stateful strategies can absolutely give you an edge against squishy humans. You can play the board, or you can play the player, at the end of the day all that matters is who won and who lost.
Re: Chess, unlike war, is a game of perfect information
#43Chess 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…
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Re: Chess, unlike war, is a game of perfect information
#44I 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…
There's a lot of games where the "State" is important the most obvious of which being poker. In a game of poker you can devise a game theory optimal strategy for any given position which is objectively the best, but that's not what most players do. They try to mix in exploitative strategies which abuse the tendencies of their opponents. These tendencies are revealed after extensive experience with the players. There…
> They try to mix in exploitative strategies which abuse the tendencies of their opponents.
without knowledge of other players, how do pros wins consistently at casinos?
Re: Chess, unlike war, is a game of perfect information
#45There's one match in which it was not a game of perfect information, as Garry Kasparov says in "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins": If you consider "perfect information" to include "knowledge of your opponent's previous games" (that's a big IF) then he did not have it against Deep Blue. IBM refused to give him any insight into what he was up against.
I don't think that's a very convincing argument, in game theory you are not supposed to be helping your opponent out, except in some very specific scenarios that usually involve zero and/or one probabilities or infinities, so they don't apply to real life. Using minimax in a non-infinite iterated game like chess, with the standard goal function, I don't think it ever happens. Winning is the optimal strategy every single time. You don't owe correct and useful information to your opponent, in fact it is against the goal function. All iterated games in the real world have a first game as well.
Re: Chess, unlike war, is a game of perfect information
#46Earlier quoted context omitted.
There's a lot of games where the "State" is important the most obvious of which being poker. In a game of poker you can devise a game theory optimal strategy for any given position which is objectively the best, but that's not what most players do. They try to mix in exploitative strategies which abuse the tendencies of their opponents. These tendencies are revealed after extensive experience with the players. There…
> They try to mix in exploitative strategies which abuse the tendencies of their opponents. without knowledge of other players, how do pros wins consistently at casinos?
The longer you're at a table with somebody, the more information you learn about them. If they're a weak player, if they're a strong player, if they're too aggressive, if they're too passive, if they play with crappy cards, if they only play with good cards, if they have a tell.
When you don't know much about the other players at a table, you tend to not use exploitative strategies as much and reply more on game theory optimal strategies and just play the cards you're dealt while you quietly gather information on your opponents tendencies so you can play the players. This might be enough to win on its own, or at least be good enough to just break even, presuming the other players are making enough mistakes.
Re: Chess, unlike war, is a game of perfect information
#47There's one match in which it was not a game of perfect information, as Garry Kasparov says in "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins": If you consider "perfect information" to include "knowledge of your opponent's previous games" (that's a big IF) then he did not have it against Deep Blue. IBM refused to give him any insight into what he was up against.
I don't think that's a very convincing argument, in game theory you are not supposed to be helping your opponent out, except in some very specific scenarios that usually involve zero and/or one probabilities or infinities, so they don't apply to real life. Using minimax in a non-infinite iterated game like chess, with the standard goal function, I don't think it ever happens. Winning is the optimal strategy every sin…
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Re: Chess, unlike war, is a game of perfect information
#48Earlier quoted context omitted.
You know the entire state of the chess board. You don’t know the entire state of your enemy forces. I’m both cases information could be said to be hidden by complexity, but in the case of war information is also just plain hidden. Edit: it would be similar to your example of war if you e.g. couldn’t see their pieces or something that would cause information asymmetry. This would make the game very different so clearl…
I suppose my problem is that the term 'perfect information' doesn't really communicate anything really interesting about chess. Whereas the equally valid term of art 'incomplete information' actually does, because it captures the fact that you lack knowledge of your opponent's strategy, but nobody ever uses that term. Chess is like navigating a maze or a minefield, it's like stumbling into an ambush. It's much more l…
> I suppose my problem is that the term 'perfect information' doesn't really communicate anything really interesting about chess.
Yes it _does_ communicate something interesting. It is a basic fact about the rules of play. If there were imperfect information, it would be a different game. Poker with perfect information means everyone plays with their cards up. It is a fundamentally different game.
The fact that chess has perfect information for all parties is fundamental to the game.
Re: Chess, unlike war, is a game of perfect information
#49There's one match in which it was not a game of perfect information, as Garry Kasparov says in "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins": If you consider "perfect information" to include "knowledge of your opponent's previous games" (that's a big IF) then he did not have it against Deep Blue. IBM refused to give him any insight into what he was up against.
I don't think that's a very convincing argument, in game theory you are not supposed to be helping your opponent out, except in some very specific scenarios that usually involve zero and/or one probabilities or infinities, so they don't apply to real life. Using minimax in a non-infinite iterated game like chess, with the standard goal function, I don't think it ever happens. Winning is the optimal strategy every sin…
> All iterated games in the real world have a first game as well
not really. Any opponent you face in a serious tournament has played before. If he's played in major matches, you have his games to study, so he's not "helping" you.
Experiment: A plays B, in two different scenarios, one where A knows all of B's prior games, and the other where he doesn't even know it's B. in which scenario would A do better?
Re: Chess, unlike war, is a game of perfect information
#50I 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…
Your intuition is actually proved mathematically for two-player games of perfect information (even for infinite games), in which chess is included, by Wolfgang Schmidt (Theorem 7 in https://www.jstor.org/stable/1994619). Roughly speaking, if a two-player games of perfect information has a winning strategy (which might need all previous moves of a play to make decisions), then it has a positional winning strategy, which only need the current state/position to make decisions. The `only` requirement needed for that theorem is the Axiom of Choice / Well-ordering Principle.