Comparison
Analysis of “pure” abstract strategy games is the subject of combinatorial game theory. Abstract strategy games with hidden information, bluffing, or simultaneous move elements are better served by Von Neumann-Morgenstern game theory, while those with a component of luck may require probability theory incorporated into either of the above.
As for the qualitative aspects, ranking abstract strategy games according to their interest, complexity, or strategy levels is a daunting task and subject to extreme subjectivity. In terms of measuring how finite a mathematical field each of the three top contenders represents, it is estimated that checkers has a game-tree complexity of 1031 possible positions, whereas chess has approximately 10123. This suggests that computer programs, through brute force calculation alone, should often be able to surpass human players' abilities. As for Go, the possible legal game positions range in the magnitude of 10170. Computers have yet to come close to defeating a ranked professional Go player.
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Famous quotes containing the word comparison:
“What is man in nature? A nothing in comparison with the infinite, an all in comparison with the nothing—a mean between nothing and everything.”
—Blaise Pascal (1623–1662)
“Envy and jealousy are the private parts of the human soul. Perhaps the comparison can be extended.”
—Friedrich Nietzsche (1844–1900)
“Most parents aren’t even aware of how often they compare their children. . . . Comparisons carry the suggestion that specific conditions exist for parental love and acceptance. Thus, even when one child comes out on top in a comparison she is left feeling uneasy about the tenuousness of her position and the possibility of faring less well in the next comparison.”
—Marianne E. Neifert (20th century)