25th Apr '16 12:09:31 PM

**advent_child** Is there an issue? Send a Message

**Added DiffLines:**

** ''GameBreaker/DynastyWarriors''

12th Apr '16 5:37:32 AM

**valozzy** Is there an issue? Send a Message

**Changed line(s) 44,45 (click to see context) from:**

*** The chessboard is not symmetrical, and there is a difference between moving the king's bishop's pawn one square and the queen's bishop's pawn one square. White has 8 distinct pawns that can move to one of two squares and two knights that also could move to two different squares each, for a total of 20 possible initial moves. Black has the same options, for another 20 distinct responses. That's four hundred possible states for the game after two turns. While the number of valid moves a player could make in chess is always in flux, they never are equivalent, so a computer trying to solve chess via a brute force search encounters a staggeringly large number of possible games. The lower bound of possible games is usually given as the Shannon Number (a number that estimates the lowest possible right answer for "How many games of chess are possible?") This number is 10^120 - a google followed by twenty more zeros. That's why no computer as of 2016 can solve chess via a brute force search. The numbers for go are even more staggering.

**to:**

*** The chessboard is not symmetrical, and there is a difference between moving the king's bishop's pawn one square and the queen's bishop's pawn one square. White has 8 distinct pawns that can move to one of two squares and two knights that also could move to two different squares each, for a total of 20 possible initial moves. Black has the same options, for another 20 distinct responses. That's four hundred possible states for the game after two turns. While the number of valid moves a player could make in chess is always in flux, they never are equivalent, so a computer trying to solve chess via a brute force search encounters a staggeringly large number of possible games. The lower bound of possible games is usually given as the Shannon Number (a number that estimates the lowest possible right answer for "How many games of chess are possible?") This number is 10^120 - a ~~google ~~googol followed by twenty more zeros. That's why no computer as of 2016 can solve chess via a brute force search. The numbers for go are even more staggering.

11th Apr '16 12:02:32 PM

**WiryEyas** Is there an issue? Send a Message

**Added DiffLines:**

*** ''GameBreaker/FireEmblemFates''

27th Mar '16 9:30:21 AM

**WearSystem** Is there an issue? Send a Message

**Changed line(s) 52 (click to see context) from:**

** GameBreaker/HearthstoneHeroesOfWarcraft

**to:**

** ~~GameBreaker/HearthstoneHeroesOfWarcraft~~''GameBreaker/HearthstoneHeroesOfWarcraft''

21st Mar '16 7:32:58 AM

**chc232323** Is there an issue? Send a Message

**Changed line(s) 41 (click to see context) from:**

**to:**

*** Additionally, as Go's metagame has evolved, the points given to player 2 has risen over time, as players have found going first to be more and more advantageous.

** Tic-Tac-Toe, Connect 4, and Chess also help introduce some ideas about why a game might be easier or harder to solve. Consider Tic-Tac-Toe. At first, it seems like the first player has 9 options for where to place their first mark, but that isn't the case. The play space is symmetrical. Each corner square is functionally identical, as is each side square. Thus, there are really only three options: side, corner, or center. Suppose first player chooses the center square. Now second player only has two options: corner or side. The number of meaningful choices in the game is surprisingly small, and it can be broken with a brute force search through those possibilities with a sheet of scrap paper.

*** Connect 4 has a symmetrical seven columns the first player can place their piece in, so really they have only four choices for first turn: center, one away from center, one away from the outside edge, and outer edge. If they drop into the center, the second player has the same number of choices (4), but if they drop into any of the other columns, then there is now a difference between all of the columns and second player has 7 choices, and so on. It takes a computer to use brute force to go through that many possible moves.

*** The chessboard is not symmetrical, and there is a difference between moving the king's bishop's pawn one square and the queen's bishop's pawn one square. White has 8 distinct pawns that can move to one of two squares and two knights that also could move to two different squares each, for a total of 20 possible initial moves. Black has the same options, for another 20 distinct responses. That's four hundred possible states for the game after two turns. While the number of valid moves a player could make in chess is always in flux, they never are equivalent, so a computer trying to solve chess via a brute force search encounters a staggeringly large number of possible games. The lower bound of possible games is usually given as the Shannon Number (a number that estimates the lowest possible right answer for "How many games of chess are possible?") This number is 10^120 - a google followed by twenty more zeros. That's why no computer as of 2016 can solve chess via a brute force search. The numbers for go are even more staggering.

** Tic-Tac-Toe, Connect 4, and Chess also help introduce some ideas about why a game might be easier or harder to solve. Consider Tic-Tac-Toe. At first, it seems like the first player has 9 options for where to place their first mark, but that isn't the case. The play space is symmetrical. Each corner square is functionally identical, as is each side square. Thus, there are really only three options: side, corner, or center. Suppose first player chooses the center square. Now second player only has two options: corner or side. The number of meaningful choices in the game is surprisingly small, and it can be broken with a brute force search through those possibilities with a sheet of scrap paper.

*** Connect 4 has a symmetrical seven columns the first player can place their piece in, so really they have only four choices for first turn: center, one away from center, one away from the outside edge, and outer edge. If they drop into the center, the second player has the same number of choices (4), but if they drop into any of the other columns, then there is now a difference between all of the columns and second player has 7 choices, and so on. It takes a computer to use brute force to go through that many possible moves.

*** The chessboard is not symmetrical, and there is a difference between moving the king's bishop's pawn one square and the queen's bishop's pawn one square. White has 8 distinct pawns that can move to one of two squares and two knights that also could move to two different squares each, for a total of 20 possible initial moves. Black has the same options, for another 20 distinct responses. That's four hundred possible states for the game after two turns. While the number of valid moves a player could make in chess is always in flux, they never are equivalent, so a computer trying to solve chess via a brute force search encounters a staggeringly large number of possible games. The lower bound of possible games is usually given as the Shannon Number (a number that estimates the lowest possible right answer for "How many games of chess are possible?") This number is 10^120 - a google followed by twenty more zeros. That's why no computer as of 2016 can solve chess via a brute force search. The numbers for go are even more staggering.

23rd Jan '16 6:05:17 PM

**BrendanRizzo** Is there an issue? Send a Message

23rd Jan '16 5:25:13 PM

**BrendanRizzo** Is there an issue? Send a Message

**Changed line(s) 39 (click to see context) from:**

** Chess and Go, [[SmartPeoplePlayChess the quintessential games for geniuses]], are both theoretically solvable for a sufficiently advanced computer, as both games have a finite board and no random elements -- though a computer powerful enough to perform the necessary calculations would be many orders of magnitude better than anything available with our current level of technology (the high branching factor in Go makes it intractable to analyze with the methods used for Chess, since you rapidly get too many options to explore via lookahead in any reasonable timeframe, with no obvious way of pruning 'bad' choices quickly). For a hypothetical intelligence far beyond our capacities, Chess and Go are as trivial as Tic-Tac-Toe, but no human creation as of 2013 - not even Deep Blue - is even close to having such a level of computational power. For some perspective, there are more [[http://www.chess.com/blog/Billy_Junior/number-of-possible-chess-games?_domain=old_blog_host&_parent=old_frontend_blog_view possible chess games]] than we estimate there are [[http://www.universetoday.com/36302/atoms-in-the-universe/ atoms in the observable universe]].

**to:**

** Chess and Go, [[SmartPeoplePlayChess the quintessential games for geniuses]], are both theoretically solvable for a sufficiently advanced computer, as both games have a finite board and no random elements -- though a computer powerful enough to perform the necessary calculations would be many orders of magnitude better than anything available with our current level of technology (the high branching factor in Go makes it intractable to analyze with the methods used for Chess, since you rapidly get too many options to explore via lookahead in any reasonable timeframe, with no obvious way of pruning 'bad' choices quickly). For a hypothetical intelligence far beyond our capacities, Chess and Go are as trivial as Tic-Tac-Toe, but no human creation as of ~~2013 ~~2016 - not even Deep Blue - is even close to having such a level of computational power. For some perspective, there are more [[http://www.chess.com/blog/Billy_Junior/number-of-possible-chess-games?_domain=old_blog_host&_parent=old_frontend_blog_view possible chess games]] than we estimate there are [[http://www.universetoday.com/36302/atoms-in-the-universe/ atoms in the observable universe]].

15th Jan '16 3:41:04 PM

**MeiwakunaBoku** Is there an issue? Send a Message

**Added DiffLines:**

** ''GameBreaker/DungeonFighterOnline''

18th Dec '15 9:27:07 PM

**VeryMelon** Is there an issue? Send a Message

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** ''GameBreaker/BatmanArkhamSeries''

7th Dec '15 10:48:51 AM

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** GameBreaker/HearthstoneHeroesOfWarcraft

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