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Topic: Shannon switching game

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	CLAUDE ELWOOD SHANNON FACTS AND INFORMATION (Site not responding. Last check: 2007-10-09)
		Shannon was born in Petoskey,_Michigan and was a distant relative of Thomas_Edison.
		Shannon developed information_entropy as a measure for the uncertainty in a message while essentially inventing what became known as the dominant form of "information theory." By introducing the concept of the thermodynamics of computation, Shannon became the first scientist to successfully address the conundrum of Maxwell's_Demon.
		Shannon gave a rough example of an evaluation function in which the value of the fl position was subtracted from that of the white position.
	www.19gmarketinggroup.com /Claude_Elwood_Shannon (1103 words)

	Shannon switching game - Wikipedia, the free encyclopedia
		The Shannon switching game is an abstract strategy game for two players, invented by "the father of information theory", Claude Shannon.
		The game is played on a finite graph with two special nodes, A and B.
		The definition of the game can be generalized to include any matroid and a solution has been explicitly found for any such game using matroid theory, unlike a similar game Hex, which is PSPACE hard.
	www.wikipedia.org /wiki/Shannon_switching_game (223 words)

	Hex (board game) - Wikipedia, the free encyclopedia
		Hex is a board game played on a hexagonal grid, usually in the shape of a 10 by 10 or a 11 by 11 rhombus.
		The game was invented by the Danish mathematician Piet Hein, who introduced the game in 1942 at the Niels Bohr Institute, and independently by the mathematician John Nash in the late 1940s.
		The game can never end in a tie, a fact found by Nash: the only way to prevent your opponent from forming a connecting path is to form a path yourself.
	en.wikipedia.org /wiki/Hex_(board_game) (1032 words)

	Strategy-stealing argument - Wikipedia, the free encyclopedia
		In combinatorial game theory, the Strategy-stealing argument is a general argument that shows, for many games, that the second player cannot have a winning strategy.
		The strategy-stealing argument applies to any symmetric game (one in which the two players have corresponding moves available to them, so that it makes sense to pretend to be the other player and steal their strategy) in which an extra move can never be a disadvantage.
		Examples of games to which the argument applies are the m,n,k-games such as gomoku, hex, and the Shannon switching game.
	www.wikipedia.org /wiki/Strategy_stealing (421 words)

	Paper and pencil game - Wikipedia, the free encyclopedia
		Paper and pencil games are games that can be played solely with pencil and paper.
		Gomoku) are abstract strategy games, which are equally well suited to playing as a board game - in this case the defining characteristic will be that once played a piece will not be moved on the board or removed from the board.
		Battleship was played as a pencil and paper game, long before Hasbro came out with a board game version.
	en.wikipedia.org /wiki/Pencil_and_paper_game (197 words)

	Encyclopedia: Y (game)
		It is a member of the connection game family inhabited by Hex, Havannah, TwixT, and others; it is also an early member in a long line of games that Ea Ea has developed, each game more complex but also more generalised.
		As in most games of this type, one player takes the part of Black and one takes the part of White; they place stones on the board one at a time, neither removing nor moving any previously-placed stones, and the pie rule can be used to mitigate any first-move advantage.
		As in most connection games, the size of the board changes the nature of the game; small boards lend towards pure tactical play, whereas larger boards tend to make the game more strategic.
	www.nationmaster.com /encyclopedia/Y-%28game%29 (753 words)

	Encyclopedia: Paper and pencil game
		Consequences is an old parlour game similar to the surrealist game exquisite corpse.
		A board game is any game played with a premarked surface, with counters or pieces that are moved across the board.
		A live action role-playing game, or LARP as it is commonly known, is a form of role-playing game where the participants perform some or all of the physical actions of the characters they play the role of.
	www.nationmaster.com /encyclopedia/Paper-and-pencil-game (807 words)

	Abstract Games magazine: game strategy articles, game reviews, news : MAGAZINE (Site not responding. Last check: 2007-10-09)
		A game can never end in a tie: if one player completes a connection between his edges, then the other player is prevented from doing so.
		David Parlett, in The Oxford History of Board Games, places it within the overall context of board games as a game of linear connection and describes Hex as a classic of its type.
		Estimating the strategic depth of a game is not as simple as describing the size of the complete game tree.
	www.abstractgamesmagazine.com /hex.html (1863 words)

	Hex
		Games with three or more players are very difficult to discuss mathematically because there is almost always an element of diplomacy and psychology which throws over any predictability.
		In a game with complete information, such as chess, both players can predict the effects of their own moves and the winner is often the one who is able to predict most moves.
		Suddenly in the half-light of dawn a game awoke, demanding to be born.
	maarup.net /thomas/hex (5616 words)

	Claude Shannon Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-09)
		Flush with this success, Vannevar Bush suggested that Shannon work on his dissertation at Cold Spring Harbor Laboratory, funded by the Carnegie Institution headed by Bush, to develop similar mathematical relationships for Mendelian genetics, which resulted in Shannon's 1940 PhD thesis at MIT, An Algebra for Theoretical Genetics.
		He also invented many devices, including a chess-playing machine (rather described how one could operate in a paper published in 1950), a rocket-powered pogo stick, a wearable computer to predict the result of playing roulette [1], and a flame-throwing trumpet for a science exhibition.
		Material was counted according to the usual relative chess piece point value (1 point for a pawn, 3 points for a knight or bishop, 5 points for a rook, and 9 points for a queen).
	www.variedtastes.com /encyclopedia/Claude_Shannon (1417 words)

	Hex (board game) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		Hex is a (A game played on a specially designed board) board game played on a (Click link for more info and facts about hexagonal) hexagonal grid, usually in the shape of a 10 by 10 or a 11 by 11 rhombus.
		The game was invented by the Danish mathematician (Click link for more info and facts about Piet Hein) Piet Hein, who introduced the game in 1942 at the Niels Bohr Institute, and independently by the mathematician (Click link for more info and facts about John Nash) John Nash in the late 1940s.
		Jhex is a game tree editor for hex with many features, written in Java.
	www.absoluteastronomy.com /encyclopedia/H/He/Hex_(board_game).htm (1202 words)

	Shannon switching game -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		Shannon switching game -- Facts, Info, and Encyclopedia article
		The Shannon switching game is an (Click link for more info and facts about abstract strategy game) abstract strategy game for two players, invented by "the father of information theory", (United States electrical engineer who pioneered mathematical communication theory (1916-2001)) Claude Shannon.
		The game is played on a finite (A drawing illustrating the relations between certain quantities plotted with reference to a set of axes) graph with two special nodes, A and B.
	www.absoluteastronomy.com /encyclopedia/s/sh/shannon_switching_game.htm (200 words)

	Jack van Rijswijck - hex: relatives (Site not responding. Last check: 2007-10-09)
		This game is a direct parent of Hex, meaning that Hex is a special case of it.
		As the name suggests, this game is the same as the previous one except that the players colour the edges of the graph, not the vertices.
		The game of Y was also discovered by several people independently from each other, in the early 1950s by Claude Shannon and by Craige Schensted with Charles Titus.
	www.cs.ualberta.ca /~javhar/hex/hex-relatives.html (676 words)

	Zillions of Games Discussion Forum
		If you like connection games such as Hex you should check out Jeff Roy's implementation of the Shannon Switching Game, which is tucked away in an update to his Hex zrf and can easily be missed.
		The game is called Snakes (by Jeff) and has been marketed since the 60s as Bridgit and Connections.
		It has been suggested that switching to a two-move per turn format (one move at the opening) might work.
	www.zillions-of-games.com /discus/messages/135/158.html (182 words)

	Computational Complexity of Games and Puzzles (Site not responding. Last check: 2007-10-09)
		Many of the games and puzzles people play are interesting because of their difficulty: it requires cleverness to solve them.
		If a game is in P, it becomes no fun once you learn "the trick" to perfect play, but hardness results imply that there is no such trick to learn: the game is inexhaustible.
		However some games are harder, EXPTIME-complete, which to me means that it may sometimes be necessary for a well-played game to go on for a tediously long sequence of moves.
	www.ics.uci.edu /~eppstein/cgt/hard.html (2681 words)

	Java(TM) Boutique Dynamic Puzzle Game Applets
		The Shannon Switching Game implementation is a two-player game.
		The classic MineSweeper game in memory of Princess Diana and the HALO trust.
		The object of the game is get the Rocks to pass through the gates to the bottom.
	javaboutique.internet.com /games/dynamic.html (774 words)

	Programming Project #2
		The second phase will be to create the simulation so that two humans may play the game - one acting as the gardener, one the woodchuck.
		It may be useful to create a method in your graph class that inputs a rather large graph that you can use to test your program along the way.
		You may have a special input when the user is asked for the number of vertices that triggers this large graph to be used for the game.
	max.cs.kzoo.edu /cs484/pp2.shtml (897 words)

	Combinatorial Game Theory (Site not responding. Last check: 2007-10-09)
		An important distinction between this subject and classical game theory (a branch of economics) is that game players are assumed to move in sequence rather than simultanously, so there is no point in randomization or other information-hiding strategies.
		Joust, a game in which two knights use up the squares of a chessboard until one is stuck.
		In this game, a position is represented by a number, and one moves by either adding or subtracting the largest prime number less than or equal to the position.
	www.ics.uci.edu /~eppstein/cgt (1499 words)

	Paper and pencil game - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-09)
		Games that can be played with only pencil and paper:
		Race Game Use one or more pens to race
		These are all games in which pieces stay put once you place them.
	encyclopedia.worldsearch.com /pencil_and_paper_game.htm (121 words)

	References (Site not responding. Last check: 2007-10-09)
		Richard A. Brualdi, Networks and the Shannon switching game, Delta (Waukesha) 4 (1974), 1-23.
		John Bruno and Louis Weinberg, A constructive graph-theortic solution of the shannon switching game, IEEE Trans.
		Yahya Ould Hamidoune, The directed Shannon switching game and the one-way game, Graph theory with applications to algorithms and computer science (New York), Wiley, New York, 1984, pp.
	www.math.psu.edu /melvin/shannon/node1.html (181 words)

	Help For the Game Of Visavis
		Other commands are the same as for all pbmserv games.
		The next example shows a game won by X, who has completed a continuous chain of 'x' bridges from the top edge to the bottom edge.
		Visavis is a Shannon switching game on the edges and belongs to the same class of connection games as Bridg-It and TwixT (and to some extend Trellis).
	www.gamerz.net /pbmserv/visavis.html (692 words)

	Learn more about List of game topics in the online encyclopedia. (Site not responding. Last check: 2007-10-09)
		Abalone game - Acquire - Advanced Squad Leader - Adventure game - Alak (board game) - Algebraic chess notation - Alpha-beta pruning - Alquerque - Amazons (game) - Amiga games - Anagrams - Ancient game - Andantino (game) - Articulate
		Halma - Hangman - Hasbro's Game of Life - Havannah (game) - Hearts - Hex (game) - History of Board Games - History of the video game - Honinbo Shusaku - Horizon effect - Huff
		Icehouse (game) - Icehouse pieces - Impartial game - International Olympic Committee - Iterated prisoner's dilemma
	www.onlineencyclopedia.org /l/li/list_of_game_topics.html (616 words)

	The CDCer: Switching is a loser's game (Site not responding. Last check: 2007-10-09)
		But I believe the single most important factor is its lack of tenacity or discipline, and the recently announced switching from PowerPC to Intel x86 is a classic example.
		Unless Robert X. Cringely is correct with his profound analysis, this could be the greatest strategic blunder in the history of technology, for at least 4 reasons.
		In the short term, there are major benefits to Apple, as the growing portable computer market is extremely valuable and the switch to the Intel CPU architecture will bring their portables back in to a position where the slight price premium is once again justifiable.
	cdcer.blogspot.com /2005/06/switching-is-losers-game.html (3204 words)

	Jack van Rijswijck - hex history (Site not responding. Last check: 2007-10-09)
		Claude Shannon then realized that both Hex and Bridg-It are special cases of a more general game, the Shannon Switching game.
		This is a graph colouring game where one player tries to connect two fixed vertices while the other tries to cut them off from each other.
		Hex is a special case of Y, and Schensted went on to introduce several modifications and generalizations of it under the names "Mudcrack" and "Poly-Y", and a host of ever-expanding modifications.
	www.cs.ualberta.ca /~javhar/hex/hex-history.html (413 words)

	[No title]
		Games Sect., 1st version in Proc.10-th Advances in Computer Games (ACG-10 Conf.), H. van den Herik, H. Iida and E. Heinz eds., Graz, Austria, Nov.\ 2003, Kluwer, pp.
		Intelligencer\/} {\bf 13-}, column on mathematical games and gems.
		\emph{(Contributions to the Theory of Games, H. Kuhn and A. Tucker, eds.), Princeton}\/} {\bf 2}(28), 291--301.
	www.wisdom.weizmann.ac.il /~fraenkel/Papers/gb.bbl (16831 words)

	shannon
		In Celtic mythology, Shannon was the goddess of the river by the same name.
		Shannon is also the name of a city in Ireland, see Shannon, Ireland
		Claude E. Shannon was the most important founder of information theory.
	www.fact-library.com /shannon.html (103 words)

	Bridg-It - Classic Mathematical Strategy Game for Palm OS (Site not responding. Last check: 2007-10-09)
		Discovered in the 1950s by mathematician David Gale and independently by Craige Schensted with Charles Titus, Bridg-It was popularized as a Hasbro® board game introduced in 1960.
		Bridg-It belongs to a family of mathematical strategy games called Shannon Switching games.
		This type of game has been described as taking seconds to learn, but a lifetime to master.
	www.cyboursoft.com /games/bridgit (368 words)

	Paper and pencil game - Encyclopedia, History, Geography and Biography
		Paper and pencil game - Encyclopedia, History, Geography and Biography
		List of Paper and Pencil games usually played with a board
		Paper and pencil game, List of Paper and Pencil games, List of Paper & Pencil games usually played with a board and Other uses.
	www.arikah.net /encyclopedia/Pencil_and_paper_game (225 words)

	Strategies for the Shannon switching game
		We present a proof that the Shannon switching game on a graph with distinguished vertices A and B has a winning strategy for player Short iff the graph has a subgraph connecting A to B with two edge disjoint spanning trees.
		Our main theorem is the converse, that if he has a winning strategy from the second position, then there must be two such trees.
		Brualdi has written an excellent expository article about the switching game.
	www.math.psu.edu /melvin/shannon/shannon.html (1156 words)

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