Juggler hinted at it, but what you’re describing is basically the crux of poker.
The information at hand is the bet size, the pot size, and your holdings.
You could make a decision based solely on that, but the rest of your information is what has happened previously on that hand, and what has happened on previous hands.
A person who knows the history of the hand, and a person who knows just the current state of the hand could make completely different decisions.
Sorry for the hijack, but after reading a bit about the game I’m interested in learning it. Can anyone suggest a free site to play Go on with a computer opponent?
For games with perfect information, all you need to know is the current situation in order to decide what your best move is. It does not matter how the situation was reached; it could be reached by many different combinations of moves. For games like chess, the current situation includes information like whether to castle (or capturing a pawn en passant) is still possible. For relatively simple games with perfect information (like tic-tac-toe), it is possible to calculate the final outcome of all the possible moves from any given situation and select the best one. The player that plays first and plays optimally in tic-tac-toe will never lose. A slightly more complicated game is Othello. In this case, it is not possible to calculate the outcome of every move to the end. Therefore, some heuristics are added that eliminate obviously bad moves. More of this is done for chess and even more for Go. But in the end, for perfect information games, there is always at least one optimal move.
I have only a passing acquaintance with Go, but the situations that Omi no Kami mentioned do not make it less than a perfect information game. Chess players also use their standard opening move sequences that do not give much of an advantage to either player. Because of the much larger number of possible moves at any point in the game, a player can take advantage of the other player’s style, but if it were possible to choose the best move in any situation, this would not be necessary. The situation with the Korean and Japanese players would be an example of imperfect information (since the two players had different interpretations of the rules) but that seems more of a misunderstanding than anything else.
For games with imperfect information, you also make you decisions based on the current state of the game. In the case of bridge, consider the bidding not as “moves” but as additional bits of information. So your starting point when the play of the cards begins may vary from game to game. Because of the imperfect information, instead of calculating the final outcome from all possible moves, you need to calculate the final outcome from all possible moves from all possible starting situations. Therefore, considerably more computation needs to be performed and the result for each move is not win/lose but a probability that the move will lead to a win or loss. You make the move with the highest probability of winning.
As the game progresses, the moves the opponents make add information (in bridge, a player that cannot follow suit must not have any more cards of that suit), but the different sequences of moves that lead to the same situation are not significant. The point that T_SQUARE made is interesting, but for calculating the best move from a given position (in a game like bridge), you don’t need to consider whether the other player(s) behaved rationally or not. In fact, such a strategy may backfire. Making an irrational move will put you into a bad position that can be exploited by a good opponent and you will lose. Every time.
Games like poker involve additional information that is only available from playing many games with the same player(s). Player A bluffs a lot, player B is an idiot, player C always blinks twice when he looks at a good hand, etc. As the games get more complicated (like economics), these sorts of things become even more important. You have to consider how others have acted in the past in similar situations. In that case, “others” don’t necessarily have to be the ones involved in the current “game”. These “games” also involve many players making moves at the same time (with or without your knowledge) which further adds to the complexity. In addition, the rules for games intended to model economics can change, even over the course of a single game.