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.
Read more about this topic: Abstract Strategy Games
Famous quotes containing the word comparison:
“The comparison between Coleridge and Johnson is obvious in so far as each held sway chiefly by the power of his tongue. The difference between their methods is so marked that it is tempting, but also unnecessary, to judge one to be inferior to the other. Johnson was robust, combative, and concrete; Coleridge was the opposite. The contrast was perhaps in his mind when he said of Johnson: his bow-wow manner must have had a good deal to do with the effect produced.”
—Virginia Woolf (18821941)
“When we reflect on our past sentiments and affections, our thought is a faithful mirror, and copies its objects truly; but the colours which it employs are faint and dull, in comparison of those in which our original perceptions were clothed.”
—David Hume (17111776)
“He was a superior man. He did not value his bodily life in comparison with ideal things. He did not recognize unjust human laws, but resisted them as he was bid. For once we are lifted out of the trivialness and dust of politics into the region of truth and manhood.”
—Henry David Thoreau (18171862)