what is the mathematical basis for the concept of strategy? a perfect strategy in a game with complete information is one that guarantees a win. but we as humans talk of good strategies and bad strategies all the time without any clue as to what the perfect strategy for the particular game looks like. for example, in the game of go, there are moves that are considered good and moves that are considered bad, but from a game theoretic standpoint, there are only perfect moves (those that preserve a game winning strategy for the player) and vulnerable moves (those that allow the second player to seize the winning strategy).
strategy, in essence, is a set of general guidelines that give the player a better chance of winning the game. the point of delving into the very basis of strategy is that computers have no intuition and thus, to program a computer well, it would seem helpful to define the concept of strategy in terms that computers can understand.
in the game of chess, deep blue's defeat of garry kasparov in 1997, to many, signaled the changing of the guard from man to machine. but in games such as poker and go, the inherent computational complexity of the game makes it difficult for computers to approach the level of top humans. in order to tackle games that are computationally complex, it seems to be necessary to give the computer tools to simplify the game, in essence, create human-like strategies that guide the computer rather than have the computer calculate possibilities in a great number of directions and then defining some metric of desirable positions. this is the problem we attempt to tackle.
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in game theory, the way to determine the perfect strategy is to calculate all possible moves by both players and then to choose the decision tree that results in a win. however, if this were the only way to approach games, we would have no insight into any game whose possibilities were too large to compute. obviously, this is not the way humans approach games. there are human experts in games such as go, poker, and chess -- games that have not been solved in a game theoretic sense -- and to guide themselves during play, these players rely on strategic principles they have developed through experience and thought. but from a game theoretic standpoint, what exactly is a strategic principle? if for example, there is only one perfect strategy that can be calculated through game theory, then what do we mean by a good strategy or a poor strategy? for any strategy that is not perfect must be poor in some sense.
in all strategic games, experts use intuition, experience, and thought to develop strategies that allow them to consistently beat poorer players. those players who play multiple games might be an expert in one game, but their lack of experience in another game may cause them to be less than skillful in that one. but shouldn't there be some general principles that the expert of one game can carry to another? or put differently, shouldn't the training and effort one put in a strategic game pay off indirectly as that player tries to learn another game?
perhaps the lack of literature on general strategy is due to its former lack of applicability. a player who wanted to learn poker would read a poker book; a player learning chess would read chess. there was no real need to generalize concepts such as strategy for if a player wanted to learn the strategy for a game, it would be much more practical to learn that specific strategy as opposed to relying on generalities.
however, the time has come where computers are very powerful and yet are utterly weak in certain domains. for example in poker, an expert would jump at the opportunity to play a computer for real money. this is because computers these days that play poker are relying heavily on the strategies that have proven successful in chess--that being calculating a huge tree of possibilities and choosing the best one. but in a game as computationally complex as poker, general strategic principles (in other words, thinking more or less like a human) would seem a logical way to handle the current problem of technological limits.
just as many business executives have been quite successful without learning any formal economics, many thinkplayers have been successful without any notion of what game theory really is. however, with the demands of artificial intelligence, the time has come to develop a theory of general strategies for games, so that instead of thinking up a billion random thoughts and pruning down these thoughts to one, a computer can think of a much smaller number of sensible thoughts, and from there, make a decision that is in some sense, intelligent.
