Perfect Information Game: On Chess
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Perfect Information Game: On Chess
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Re: Perfect Information Game: On Chess
#2That story took an unexpected turn
Re: Perfect Information Game: On Chess
#3This was a fantastic read!
Re: Perfect Information Game: On Chess
#4I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting.
It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though this doesn't stop computers playing stronger than any human.
People find an abstract beauty in the purity of the game's structure, but I find that lack of information asymmetry makes the game less rich. One does not need to attempt to induce the other player's thoughts, their strategies or the location of the pieces, one merely has to look at the board. There are no feints, one cannot pretend to be following one strategy and actually be planning something else.
Some of these features do crop up, sort of: due to the size of the game's space and the imperfection of the players, players can be surprised by a particularly brilliant move. But this is an artifact of the players not being good enough, not a feature of the game itself.
I find it strange in this light that chess (and go) have historically been seen as a sort of wargame, a respectable pastime for generals and the like. Reasoning and planning in the presence of uncertain information (the "fog of war") is one of the most important aspects of military strategy and actually common to most human endeavours. The 'uncertainty' due to the combinatorial complexity of the game doesn't really capture that sort of probabilistic scenario very effectively. For example, many games lacking perfect information do not have a solution, rather the optimal 'solution' is a mixed strategy where a player randomly selects from a set of strategies weighted by probability. This also means that the other player can't simply know "my opponent is playing perfectly, therefore they will play strategy X", making the game in some sense much harder. This, of course, tends to generalise to imperfect players and real-world games as well as just the ideal.
Re: Perfect Information Game: On Chess
#5I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting. It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though thi…
You comment is excellent. Thank you! It made me realize that I've actually been regarding games like Sudoku and Reversi like this for decades already. Having written programs to play both I find the games "solved".
What games do you find interesting to either just think of or to play?
Re: Perfect Information Game: On Chess
#6I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting. It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though thi…
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And if the argument is that games of imperfect information allow exploitative strategies to succeed against non-equilibrium strategies, well the same is true of chess: the very idea of a trap is usually making a suboptimal move to hopefully exploit an imperfect opponent's likely mistake.
Re: Perfect Information Game: On Chess
#7Gonzo style reporting of the chess scene.
>> My own personal conception of existential dread is, like my inability to visualize, idiosyncratic. Many people, I think, are troubled by their own insignificance, preferring not to think about being a tiny part of a vanishing species in what couldn’t even be called a corner of the universe. Not me—I’m fine with that. ... That’s all infinity does, or rather doesn’t do. It doesn’t scare me.
>> What does scare me—what provokes real horror in me—is excess reality. I see mental horror—The Void—in the tumbling numbers of securities trading, or the heaps of barely decipherable ancient papyrus dug up in the near Middle East, or the global weather patterns which have evaded, to this date, capture by any mathematical model. I am troubled by the world’s great throngs of data—by thickets of facts I might comprehend individually, but that together make a chaos capable of receding before me as long as I live—the miles of definition leading nowhere.
>> That’s what I felt, staring at the board in front of me. I felt like I couldn’t put my pieces anywhere, because I felt like I could put them everywhere, for all eternity. I basically blacked out.
These parts are well written and convey his experience on entering the zone. These are negative images coming from the inability to perceive order. There is also the positive part with the state of flow in being absorbed in this alternate world.
I like Hikaru No Go, which conveys a sense of being a go player, with the attractions of a game, the competitions, the disappointment in the backdrop of a fantasy story.
Re: Perfect Information Game: On Chess
#8I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting. It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though thi…
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And if the argument is that games of imperfect information allow exploitative strategies to succeed against non-equilibrium strategies, well the same is true of chess: the very idea of a trap is usually making a suboptimal move to hopefully exploit an imperfect op…
When you have imperfect information, understanding the other player's strategy becomes part of the game. A perfect solution may be computable against any deterministic strategy, but its stops being a possibility when you don't know the other player's strategy.
Re: Perfect Information Game: On Chess
#9I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting. It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though thi…
I disagree with your premise. While it's true that in theory, we could run minimax on a sufficiently powerful computer to solve chess and go, we can't in reality solve chess and go with computers. And even if we could solve them with powerful computers, human brains still cannot.
You still have less than perfect information about the decision tree, and you have to pick what you think is the best move from all of the available moves. In that respect, games of perfect information are no different than games of imperfect information when the scale of the game is too large to be solved.
Re: Perfect Information Game: On Chess
#10Earlier quoted context omitted.
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And if the argument is that games of imperfect information allow exploitative strategies to succeed against non-equilibrium strategies, well the same is true of chess: the very idea of a trap is usually making a suboptimal move to hopefully exploit an imperfect op…
When you have imperfect information, understanding the other player's strategy becomes part of the game. A perfect solution may be computable against any deterministic strategy, but its stops being a possibility when you don't know the other player's strategy.
No, tedsanders is right. If the game has imperfect information but is zero-sum (i.e. the goals of players are perfectly opposed), you can always compute the subgame-perfect Nash equilibrium in mixed strategies, and it will be the best way to play against all possible opponents, both deterministic and random.
Mind games (bargaining, precommitment, etc.) only become important in non-zero-sum games, where the goals of players align in some ways and oppose in others. For example, if chess had an additional possible outcome where both players lose, that could make it impossible to find a single best strategy.