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Topic: Phutball

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	Phutball: Definition and Links by Encyclopedian.com - All about Phutball
		Phutball (also called Philosopher's Football) is a two-player board game described in Elwyn Berlekamp[?], John Conway, and Richard Guy[?]'s Winning Ways for your Mathematical Plays, a source of many other interesting games.
		Phutball is played on the intersections of a 19 by 15 grid using one white piece and as many fl pieces as necessary.
		Given that specialized phutball boards are hard to come by, the game is usually played on a 19 by 19 Go board, with a white stone representing the football and fl stones representing the men.
	www.encyclopedian.com /ph/Phutball.html (568 words)

	phutball (Site not responding. Last check: 2007-10-22)
		Phutball (short for philosopher's football) is a two-player board game described in Elwyn Berlekamp, John Conway, and Richard Guy's Winning Ways for your Mathematical Plays.
		Phutball is played on the intersections of a 19×15 grid using one white stone and as many fl stones as needed.
		Given that specialized phutball boards are hard to come by, the game is usually played on a 19×19 go board, with a white stone representing the football and fl stones representing the men.
	www.yourencyclopedia.net /phutball.html (570 words)

	Research Stuff?
		Phutball is an open question mark left in the second volume of this text.
		Grossman + Nowakowski: One-dimensional Phutball A paper doing the same thing I'm trying to do, in which two mathematicians explore one-dimensional phutball, talk about some of its quirks and difficulties of analyzation, and proves a special case they coined "Oddish phutball" which they give an explicit strategy.
		Demaine, Demaine + Eppstein: Phutball Endgames are Hard Proves that determining if a position has a winning move in regular (2D) phutball is NP-hard, contrary to many other games.
	www.tjhsst.edu /~yzhang/techlab/research.html (972 words)

	Phutball
		If a handicap is specified and positive, the initial position of the phutball is moved number spaces towards userid2's goal.
		Because phutball has a noticeable first-move advantage, handicaps of 0 and +0.5 will count towards ratings.
		Specify the phutball's location and the path of spaces it follows while moving.
	www.gamerz.net /pbmserv/phutball.html (523 words)

	My Project (Site not responding. Last check: 2007-10-22)
		Each turn, a player either places a stone on a board or jumps over a chain of stones with a "ball" that is shared by the two players.
		The analysis of a particular position in Phutball can be proven to be NP-complete; even the analysis of a general position in the reduced, one-dimensional game can be shown to be NP-complete.
		This combinatorial problem is not as a hot topic in combinatorial game theory as, say, Go, Chess, or Chomp, but it still seems to be an enlightening problem.
	www.tjhsst.edu /~yzhang/techlab/proj3/index_phut.html (225 words)

	John Conway - ArtPolitic Encyclopedia of Politics : Information Portal
		Among amateur mathematicians, he is perhaps most widely known for his mathematical games, in particular the creation of the Game of Life.
		He is also one of the inventors of the Sprouts game, as well as Phutball, and he developed detailed analyses of many other games and puzzles, such as the Soma cube.
		He invented a new number system, the surreal numbers, which are closely related to certain games and have been the subject of a mathematical novel by Donald Knuth.
	www.artpolitic.org /infopedia/jo/John_Conway.html (242 words)

	making and breaking games :: More on Rake (Site not responding. Last check: 2007-10-22)
		In ATITD it's played on a 15x9 board though I later learned that there is originally a more popular version called phutball (Philosopher's Football) that is played on a 19x13 board.
		Anyways, what I find remarkable about the game is that the rules are extremely simple, but the strategy is deep.
		Phutball is also extremely complex, but is also unique in it's gameplay.
	www.planetcerulean.com /candle?p=15&c=1 (435 words)

	Phutball Endgames are Hard - Demaine, Demaine, Eppst (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Phutball Endgames are Hard - Demaine, Demaine, Eppst (ResearchIndex)
		Abstract: We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game.
		In contrast, the similar problems of determining whether there is an immediately winning move in checkers, or a move that kings a man, are both solvable in polynomial time.
	citeseer.ist.psu.edu /demaine02phutball.html (371 words)

	Games of Soldiers - PHUTBALL (Site not responding. Last check: 2007-10-22)
		Philosopher's Football or Phutball was invented by John Conway and is described in 'Winning Ways for Your Mathematical Plays'.
		The game can be handicapped by initially placing the Black stone near the weaker player's goal line.
		You can also play Phutball with Zillions (implemented by Matthew Burke).
	www.di.fc.ul.pt /~jpn/gv/phutball.htm (220 words)

	More Games of No Chance (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Msri Publications Volume 42, 2002 One-Dimensional Phutball J. Grossman And...
		We solve the case of a restricted version called Oddish Phutball by presenting an explicit strategy in terms of a potential function.
		2 Phutball endgames are hard - Demaine, Demaine et al.
	citeseer.ist.psu.edu /616287.html (168 words)

	[No title]
		Other appearances of at least two names for the same game are the couple: Phutball and Philosopher's Football, as well as Atari-Go and Ponnuki-Go.
		Tristan Cazenave is a researcher who clearly belongs to the group of scientists that possess a powerful tool and are searching for an appropriate application domain.
		It has been used to prove that 11x11 Phutball is a win for the first player in 25 plies or fewer, and that 6x6 Atari-Go with a crosscut in the centre is a win for the first player in 15 plies or fewer.
	www.cs.unimaas.nl /ICGA/journal/contents/content25-1.htm (3338 words)

	Erik D. Demaine, Martin L. Demaine, and David Eppstein: Phutball Endgames are Hard (Site not responding. Last check: 2007-10-22)
		Erik D. Demaine, Martin L. Demaine, and David Eppstein: Phutball Endgames are Hard
		Erik D. Demaine, Martin L. Demaine, and David Eppstein, ``Phutball Endgames are Hard,'' in More Games of No Chance, edited by R. Nowakowski, 2002, pages 351-360, Cambridge University Press.
		We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game.
	theory.lcs.mit.edu /~edemaine/papers/Phutball (168 words)

	Sensei's Library: Philosopher's Football
		However, from your choice of words it appears that Right tries to get the ball into his/her own goal.
		Is this the common way to talk among Phutball players?
		Anonymous: I don't know what is standard for Phutball.
	senseis.xmp.net /?PhilosopherSFootball (788 words)

	Combinatorial Game Theory Combinatorics Math Science
		Elwyn Berlekamp - Combinatorial Game Theory - Elwyn's research in the field, including several papers.
		Erik Demaine's Combinatorial Games - Research on pushing blocks, Clickomania, Phutball, and sliding coins.
		Games that interest John Conway - Clever Games for Clever People, from the book On Numbers and Games.
	www.24up.org /Science/Math/Combinatorics/Combinatorial_Game_Theory (174 words)

	Enloe China Visit (Site not responding. Last check: 2007-10-22)
		Come to think of it, everyone asked us to sing the theme to Titanic.
		Later that day we played a game a PHUTball with our Chinese Counter Parts.
		And yes, they beasted us, but whatever we all had fun.
	enloehs.wcpss.net /chinavisit/page2.html (196 words)

	Combinatorial Game Theory
		Also a couple of papers on game theory, about Toads and Frogs and Sowing Games.
		Research on pushing blocks, Clickomania, Phutball, and sliding coins.
		Clever Games for Clever People, from the book On Numbers and Games.
	www.canadiancontent.net /dir/Top/Science/Math/Combinatorics/Combinatorial_Game_Theory (182 words)

	Bookpool: More Games of No Chance
		Phutball endgames are hard Erik D. Demaine, Martin L. Demaine and David Eppstein, 25.
		One-dimensional phutball J. Grossman and Richard J. Nowakowski; 26.
		A symmetric strategy in graph avoidance games Frank Harary, Wolfgang Slany and Oleg Verbitsky; 27.
	www.bookpool.com /.x/pbx84hrb8i/sm/0521808324 (627 words)

	: Class SquareReader (Site not responding. Last check: 2007-10-22)
		Amazons, Ataxx, Breakthrough, Epaminondas, Go, Gomoku, Gonnect, Gravity, LinesOfAction, Othello, Pente, Phutball, Renju, Reversi, Scramble, Tanbo
		This abstract class does not override any methods from the class SquareGrid, and provides methods for reading the text representation of any standard board played on a square board, such as Go and Othello.
		If a game format does not conform with the standard this method should be overridden.
	www.mi.uib.no /~taral/pbem/documentation/SquareReader.html (216 words)

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