4 ms·

I 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 inter

by dkbrk 10y ago

I 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.

Flow 10y ago
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?
- hellbanner 10y ago
  I'm having fun playing 3D tic tac toe and other games on a Shibumi set: https://boardgamegeek.com/boardgamefamily/13434/shibumi https://boardgamegeek.com/boardgamefamily/13434/shibumi
tedsanders 10y ago
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.
- DanWaterworth 10y ago
  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.
  - cousin_it 10y ago
    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.
    - DanWaterworth 10y ago
      Thanks, that's an interesting nuance.
kevinwang 10y ago
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.
- ybird 10y ago
  > we can't in reality solve chess and go with computers I don't think this is correct. Both could be solved by determining the perfect move for each board arrangement, leading to a very simple, but very data-heavy solution (see: https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number - number of chess positions somewhere below 2^155 - and also need to track for each position whether can empassant for each pawn like X-FEN does, and http://tromp.github.io/go/legal.html http://tromp.github.io/go/legal.html - number of Go positions for 19x19 board ~2.081681994 * 10^170, though other-sized boards would each need their own set of solutions). In addition, both Chess and Go engines have beaten masters: https://en.wikipedia.org/wiki/Human%E2%80%93computer_chess_matches https://en.wikipedia.org/wiki/Human%E2%80%93computer_chess_m... http://www.wired.com/2016/03/googles-ai-wins-fifth-final-game-go-genius-lee-sedol/ http://www.wired.com/2016/03/googles-ai-wins-fifth-final-gam... You could be correct about the human brain being incapable of storing all of the Chess or Go solutions. While the brain could perhaps memorize enough strategies and board positions to substitute, the theoretical maximum of 2.5 PB may not be enough to hold all board positions and metadata. http://www.scientificamerican.com/article/what-is-the-memory-capacity/ http://www.scientificamerican.com/article/what-is-the-memory...
  - omnigoat 10y ago
    "In reality" means that the working set of memory and time complexity on solving Chess (let alone Go) is vastly too large for computers now and in the future. I don't get why you tacked on computers beating grandmasters/9-dans, since that has nothing to do with solving the game. Oh you added something on the end. Well, augmenting a human brain doesn't change the search space of solving Chess and Go (especially Go). You may be underestimating how large those problems are.
Pamar 10y ago
Regarding your surprise about chess being played as a sort of wargame: actually when used as such, they did include "fog of war": https://en.m.wikipedia.org/wiki/Kriegsspiel_(wargame) https://en.m.wikipedia.org/wiki/Kriegsspiel_(wargame) See also: https://en.m.wikipedia.org/wiki/Kriegspiel_(chess) https://en.m.wikipedia.org/wiki/Kriegspiel_(chess)
- eric_h 10y ago
  Blind chess sounds like an extremely difficult game. I really want to play it. Seems as though it's most easily played as a computer game.
EvgeniyZh 10y ago
Yet we got poker solved (kind of - https://en.wikipedia.org/wiki/Cepheus_(poker_bot) https://en.wikipedia.org/wiki/Cepheus_(poker_bot) ) earlier than chess. If you asked me before I knew it, I'd say chess is easier to solve.
- kriro 10y ago
  That is only for HU limit poker though. Limit is played very little these days. There are some decent bots for no limit but I'm not aware of one that plays well with deep stacks (200bb+). There's http://www.computerpokercompetition.org/ http://www.computerpokercompetition.org/ and they usually provide a short writeup. However the best bots are likely not found in academia but at the table of online poker sites.
iosifakos 10y ago
You are absolutely right. Whoever has time for a long confirmation, can find it here: http://www.wsj.com/articles/bridgenot-chessis-the-ultimate-war-game-1431899680 http://www.wsj.com/articles/bridgenot-chessis-the-ultimate-w... For those who want something shorter I can say that based on your reasoning, bridge is much more interesting. This may be sound as a joke since in US bridge is mostly played by old people, but is true. The most important reason is that bridge will never be perfectly solved by computers. Someone said in this thread "for imperfect information (games), there is still a perfect, computable solution". This can be true, but the interesting point is that this perfect computable move may be the wrong move by far. In order to explain this I will say that in bridge there are many situations where you have to choose between two paths. Path one is a winner 65% of the time according to mathematical analysis. Path two is a winner 5% of the time according to the same analysis above. However path two is the winner, because the opponents have also incomplete information and even according to their BEST analysis (mathematical or psychological) they must follow up with a movement that will make you win 100%. Unfortunately as the author said, this cannot be appreciated if you are not very familiar with the game. Since you mentioned generals and the like, Eisenhower was a bridge fanatic. At present time it is enjoyed by the two richest men in Earth, Bill Gates and Warren Buffet.
gmluke 10y ago
Mathematics also has perfect information, but people find plenty of aesthetic appeal in that. (Though in many respects, competitive chess is not at all like mathematics. An uncooperative opponent and time constraints are important additions to the possibility of beautiful moves.)
pacala 10y ago
I don't mean to diminish the accomplishments or skill of backgammon players, but in my opinion being an imperfect information game makes backgammon, like poker, much less interesting. It means that, in principle, it is simply a matter of running Minimax over all possible distributions 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.
- citizen23 10y ago
  I think that backgammon is more similar to chess than poker in this respect. Despite the exogenous element of chance it can still be considered a perfect information game. Your statement does not hold for games truly characterised by imperfect information (e.g. poker), in theory or in practice.
pcmaffey 10y ago
This is why I play speed chess exclusively. It combines the potential strategic purity of chess with the human craftiness involved in games like poker. Limitation is the source of all creativity.
hellbanner 10y ago
Game designer Raph Koster suggests that "Learning is Fun". Human brains are wired to feel pleasure when they gain knowledge. So while in principle, the best chess program is, yes, a computer program, humans enjoy learning systems and that's part of why Go & Chess has survived thousand(s?) of years. www.amazon.com/Theory-Game-Design-Raph-Koster/dp/1449363210/ Additionally, humans seem to not learn by the "min-max" algorithm. Grandmaster Go & Chess players don't exhaustively search all options then compute the best. They use fundamentals (and perhaps intuition, maybe parallel processing?) to see a great move. We still know very little about how brains learn and strategy games are great opportunities to explore this.
nickpsecurity 10y ago
I agree. I tell people to play games like Poker and Starcraft instead. Poker because it teaches you how to spot and perform bluffs useful in real-world situations. Plus, keep your calm as money in pot grows. Starcraft because it combines board positions, fog of war, strategic thinking, real-time reactions, bluffs, and opponent bluffs. Nearly ideal type of strategy game except that it's so fast that hand-eye coordination becomes limit among pro's. Turn-based strategy with time limit per move could be best in theory but I know less great one's there outside Sid Meier's stuff. Just not knowledgeable.

by dkbrk 10y ago

Flow 10y ago

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?

hellbanner 10y ago
I'm having fun playing 3D tic tac toe and other games on a Shibumi set: https://boardgamegeek.com/boardgamefamily/13434/shibumi https://boardgamegeek.com/boardgamefamily/13434/shibumi

tedsanders 10y ago

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.

DanWaterworth 10y ago
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.
- cousin_it 10y ago
  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.
  - DanWaterworth 10y ago
    Thanks, that's an interesting nuance.

kevinwang 10y ago

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.

ybird 10y ago
> we can't in reality solve chess and go with computers I don't think this is correct. Both could be solved by determining the perfect move for each board arrangement, leading to a very simple, but very data-heavy solution (see: https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number - number of chess positions somewhere below 2^155 - and also need to track for each position whether can empassant for each pawn like X-FEN does, and http://tromp.github.io/go/legal.html http://tromp.github.io/go/legal.html - number of Go positions for 19x19 board ~2.081681994 * 10^170, though other-sized boards would each need their own set of solutions). In addition, both Chess and Go engines have beaten masters: https://en.wikipedia.org/wiki/Human%E2%80%93computer_chess_matches https://en.wikipedia.org/wiki/Human%E2%80%93computer_chess_m... http://www.wired.com/2016/03/googles-ai-wins-fifth-final-game-go-genius-lee-sedol/ http://www.wired.com/2016/03/googles-ai-wins-fifth-final-gam... You could be correct about the human brain being incapable of storing all of the Chess or Go solutions. While the brain could perhaps memorize enough strategies and board positions to substitute, the theoretical maximum of 2.5 PB may not be enough to hold all board positions and metadata. http://www.scientificamerican.com/article/what-is-the-memory-capacity/ http://www.scientificamerican.com/article/what-is-the-memory...
- omnigoat 10y ago
  "In reality" means that the working set of memory and time complexity on solving Chess (let alone Go) is vastly too large for computers now and in the future. I don't get why you tacked on computers beating grandmasters/9-dans, since that has nothing to do with solving the game. Oh you added something on the end. Well, augmenting a human brain doesn't change the search space of solving Chess and Go (especially Go). You may be underestimating how large those problems are.

Pamar 10y ago

Regarding your surprise about chess being played as a sort of wargame: actually when used as such, they did include "fog of war": https://en.m.wikipedia.org/wiki/Kriegsspiel_(wargame) https://en.m.wikipedia.org/wiki/Kriegsspiel_(wargame) See also: https://en.m.wikipedia.org/wiki/Kriegspiel_(chess) https://en.m.wikipedia.org/wiki/Kriegspiel_(chess)

eric_h 10y ago
Blind chess sounds like an extremely difficult game. I really want to play it. Seems as though it's most easily played as a computer game.

EvgeniyZh 10y ago

Yet we got poker solved (kind of - https://en.wikipedia.org/wiki/Cepheus_(poker_bot) https://en.wikipedia.org/wiki/Cepheus_(poker_bot) ) earlier than chess. If you asked me before I knew it, I'd say chess is easier to solve.

kriro 10y ago
That is only for HU limit poker though. Limit is played very little these days. There are some decent bots for no limit but I'm not aware of one that plays well with deep stacks (200bb+). There's http://www.computerpokercompetition.org/ http://www.computerpokercompetition.org/ and they usually provide a short writeup. However the best bots are likely not found in academia but at the table of online poker sites.

iosifakos 10y ago

You are absolutely right. Whoever has time for a long confirmation, can find it here: http://www.wsj.com/articles/bridgenot-chessis-the-ultimate-war-game-1431899680 http://www.wsj.com/articles/bridgenot-chessis-the-ultimate-w... For those who want something shorter I can say that based on your reasoning, bridge is much more interesting. This may be sound as a joke since in US bridge is mostly played by old people, but is true. The most important reason is that bridge will never be perfectly solved by computers. Someone said in this thread "for imperfect information (games), there is still a perfect, computable solution". This can be true, but the interesting point is that this perfect computable move may be the wrong move by far. In order to explain this I will say that in bridge there are many situations where you have to choose between two paths. Path one is a winner 65% of the time according to mathematical analysis. Path two is a winner 5% of the time according to the same analysis above. However path two is the winner, because the opponents have also incomplete information and even according to their BEST analysis (mathematical or psychological) they must follow up with a movement that will make you win 100%. Unfortunately as the author said, this cannot be appreciated if you are not very familiar with the game. Since you mentioned generals and the like, Eisenhower was a bridge fanatic. At present time it is enjoyed by the two richest men in Earth, Bill Gates and Warren Buffet.

gmluke 10y ago

Mathematics also has perfect information, but people find plenty of aesthetic appeal in that. (Though in many respects, competitive chess is not at all like mathematics. An uncooperative opponent and time constraints are important additions to the possibility of beautiful moves.)

pacala 10y ago

I don't mean to diminish the accomplishments or skill of backgammon players, but in my opinion being an imperfect information game makes backgammon, like poker, much less interesting. It means that, in principle, it is simply a matter of running Minimax over all possible distributions 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.

citizen23 10y ago
I think that backgammon is more similar to chess than poker in this respect. Despite the exogenous element of chance it can still be considered a perfect information game. Your statement does not hold for games truly characterised by imperfect information (e.g. poker), in theory or in practice.

pcmaffey 10y ago

This is why I play speed chess exclusively. It combines the potential strategic purity of chess with the human craftiness involved in games like poker. Limitation is the source of all creativity.

hellbanner 10y ago

Game designer Raph Koster suggests that "Learning is Fun". Human brains are wired to feel pleasure when they gain knowledge. So while in principle, the best chess program is, yes, a computer program, humans enjoy learning systems and that's part of why Go & Chess has survived thousand(s?) of years. www.amazon.com/Theory-Game-Design-Raph-Koster/dp/1449363210/ Additionally, humans seem to not learn by the "min-max" algorithm. Grandmaster Go & Chess players don't exhaustively search all options then compute the best. They use fundamentals (and perhaps intuition, maybe parallel processing?) to see a great move. We still know very little about how brains learn and strategy games are great opportunities to explore this.

nickpsecurity 10y ago

I agree. I tell people to play games like Poker and Starcraft instead. Poker because it teaches you how to spot and perform bluffs useful in real-world situations. Plus, keep your calm as money in pot grows. Starcraft because it combines board positions, fog of war, strategic thinking, real-time reactions, bluffs, and opponent bluffs. Nearly ideal type of strategy game except that it's so fast that hand-eye coordination becomes limit among pro's. Turn-based strategy with time limit per move could be best in theory but I know less great one's there outside Sid Meier's stuff. Just not knowledgeable.