Six factor formula - Revision history

en>Monkbot: Task 5: Fix CS1 deprecated coauthor parameter errors

2014-07-24T10:59:22Z

Task 5: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 12:59, 24 July 2014
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	~~In [[combinatorial game theory]], '''Maker-Breaker games''' are a subclass of [[positional game]]s.~~<~~ref~~>~~J. Beck: '~~'~~Combinatorial Games~~: ~~Tic-Tac-Toe Theory'', Cambridge University Press, 2008.</ref>~~		Hello! <br>I'm Arabic male :). <br>I really like Computer programming!<br><br>Feel free to visit my web blog: [http://fungonline.com/profile/124586/jumaestas Info size bike mountain bike sizing.]

	~~It is a two-person [[perfect information\|game with complete information]] played on a [[hypergraph]] ''(V,H)'' where ''V'' is an arbitrary set (called the board of the game~~) ~~and ''H'' is a family of subsets of ''V'', called the ''winning sets''. The two players alternately occupy previously unoccupied elements of ''V''.~~

	The ﬁrst player, ''Maker'', has to occupy a winning set to win; and the second player, ''Breaker'', has to stop Maker from doing so; if Breaker successfully prevents maker from occupying a winning set to the end of the game, then Breaker wins. Thus, in a Maker–Breaker positional game, Maker wins if he occupies all elements of some winning set and Breaker wins if he prevents Maker from doing so. There can be no draw in a Maker-Breaker positional game: one player always wins.

	~~The definition of Maker-Breaker game has a subtlety when <math>\|V\|=\infty~~<~~/math~~> ~~and~~ <~~math~~>~~\|H\|=\infty~~<~~/math>. In this case we say that Breaker has a winning strategy if, for all ''j'' ~~>~~ 0, Breaker can prevent Maker from completely occupying a winning set by turn ''j''.~~

	~~When [[tictactoe]] is played as a Maker–Breaker positional game, Maker has a winning strategy (Maker does not need~~ to ~~block Breaker from obtaining a winning line)~~
	~~.<ref name="kruczek2010">{{cite journal\| last=Kruczek\| first=Klay\|coauthor=Eric Sundberg\|title=Potential-based strategies for tic-tac-toe on the integer latticed with numerous directions\| journal=~~[~~[The Electronic Journal of Combinatorics]]\| year=2010\| volume=17\| pages=R5}}<~~/~~ref>~~

	~~==Maker-Breaker games on graphs==~~
	~~There has been quite some research done on playing Maker-Breaker games when the board of the game is the edge-set of a [[Graph (mathematics)\|graph]] <math>G=(V,E)<~~/~~math> (usually taken as the complete graph) and the family of winning sets is <math>\mathcal{F}=\{F\subset E\vert G[F]\hbox{ has property }\mathcal{P}\}<~~/~~math>, where <math>\mathcal{P}<~~/math> is some [[graph property]] (usually taken to be monotone increasing) such as connectivity (see, e.g.,<ref name="ChvatalErdos1978">{{cite journal\|last=Chvatal\|coauthor=Erdos\|title=Biased positional games\| journal=[[Annals of discrete mathematics]]\| year=1978\| volume=2\| pages=221–229}}</~~ref>)~~.

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Combinatorial game theory]~~]

en>Bgwhite: Fix section heading per WP:MOSHEAD using AWB (9838)

2014-01-10T22:41:04Z

Fix section heading per WP:MOSHEAD using AWB (9838)

← Older revision		Revision as of 00:41, 11 January 2014
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	~~Your writing should be well presented and fulfills all academic requirements~~. ~~Use them at the beginning and end of your paragraphs~~. ~~The scholarship essay that you write~~ is ~~supposed to present you well and thus should be detailed and giving reasons as to why you should be awarded the scholarship. We strive to be~~ a ~~world essay writing company through providing quality services at~~ a ~~price which~~ is ~~equivalent with our services. Now the writing~~ an ~~essay has become~~ the ~~big issue because if the person is not writing an essay~~ of ~~his or her own or for any body then this does not mean only that he or she do not know how to write it down but~~ the ~~thing~~ is ~~that there are many circumstances because~~ of ~~which most~~ of the ~~people cannot write it down. <br><br>Definition essay- A definition essay defines a particular term~~. The ~~company knows the needs~~ of ~~high school students and ensures they get a high school essay that meets their requirements~~. ~~Custom essay writing services today can produce anything ranging from originally researched and written term papers~~, ~~theses and essays~~ to ~~articles~~ and ~~blogs for people~~, ~~organizations~~, ~~websites and individuals based on their needs and requirements. This will also give coherence~~ to a ~~comparison paragraph~~. ~~However she let him go and~~ he ~~runs back to the island~~ and ~~tells Jim all the details~~ he ~~found out~~. <br><br>~~The main target is within the language being an result of your context~~, ~~and hence the beginning level~~ for ~~that instructing and mastering of writing abilities will be the last product or service~~. ~~Most people think of an essay~~ as a ~~written document~~, ~~and it is certainly that. This makes writing argumentative essay~~ a ~~very difficult task. This is~~ to ~~ensure writers who provide you with services are qualified. The console's launch was~~ a ~~success with over 200,000 units sold the first day~~. <br>~~<br>Papers are evaluated and judged~~ based on ~~your organization and development of ideas, supporting evidences or examples that you quote in your essay, understanding~~ the ~~intended audience, incorporating audiences needs in your essay, attaining the goal~~ of ~~your assigned task, and off course skilful use of language, correctness in using grammar.~~ There ~~is customer care team that is available to~~ the ~~customers at any hour~~ of the ~~day. Likewise to~~ the ~~similarities~~, the ~~next part of writing a compare~~ and ~~contrast essay is to find out~~ the ~~differences among them. essay against online material and a database~~ of ~~previously submitted papers. This~~ is ~~important to ensure that you~~ [~~http:~~/~~/www.bestwargamesonline.com/profile/clczlt buy essay papers] that are right, appropriate~~, ~~and of high quality.~~ <br><br>~~If your teacher or professor gives you a list of sample questions or topics from which the question may~~ be ~~formulated~~, ~~make sure you know everything there is to know about those questions~~. ~~One thing you require to come up with good essay writing is spelling it right~~. ~~You may have problems in understanding the subjects. Essay writing is an art~~ of ~~expressing views in a more descriptive and efficient manner. You should conclude the essay by focusing on the main purpose of the essay~~.		In [[combinatorial game theory]], '''Maker-Breaker games''' are a subclass of [[positional game]]s.<ref>J. Beck: ''Combinatorial Games: Tic-Tac-Toe Theory'', Cambridge University Press, 2008.</ref>

			It is a two-person [[perfect information\|game with complete information]] played on a [[hypergraph]] ''(V,H)'' where ''V'' is an arbitrary set (called the board of the game) and ''H'' is a family of subsets of ''V'', called the ''winning sets''. The two players alternately occupy previously unoccupied elements of ''V''.

			The ﬁrst player, ''Maker'', has to occupy a winning set to win; and the second player, ''Breaker'', has to stop Maker from doing so; if Breaker successfully prevents maker from occupying a winning set to the end of the game, then Breaker wins. Thus, in a Maker–Breaker positional game, Maker wins if he occupies all elements of some winning set and Breaker wins if he prevents Maker from doing so. There can be no draw in a Maker-Breaker positional game: one player always wins.

			The definition of Maker-Breaker game has a subtlety when <math>\|V\|=\infty</math> and <math>\|H\|=\infty</math>. In this case we say that Breaker has a winning strategy if, for all ''j'' > 0, Breaker can prevent Maker from completely occupying a winning set by turn ''j''.

			When [[tictactoe]] is played as a Maker–Breaker positional game, Maker has a winning strategy (Maker does not need to block Breaker from obtaining a winning line)
			.<ref name="kruczek2010">{{cite journal\| last=Kruczek\| first=Klay\|coauthor=Eric Sundberg\|title=Potential-based strategies for tic-tac-toe on the integer latticed with numerous directions\| journal=[[The Electronic Journal of Combinatorics]]\| year=2010\| volume=17\| pages=R5}}</ref>

			==Maker-Breaker games on graphs==
			There has been quite some research done on playing Maker-Breaker games when the board of the game is the edge-set of a [[Graph (mathematics)\|graph]] <math>G=(V,E)</math> (usually taken as the complete graph) and the family of winning sets is <math>\mathcal{F}=\{F\subset E\vert G[F]\hbox{ has property }\mathcal{P}\}</math>, where <math>\mathcal{P}</math> is some [[graph property]] (usually taken to be monotone increasing) such as connectivity (see, e.g.,<ref name="ChvatalErdos1978">{{cite journal\|last=Chvatal\|coauthor=Erdos\|title=Biased positional games\| journal=[[Annals of discrete mathematics]]\| year=1978\| volume=2\| pages=221–229}}</ref>).

			==References==
			{{reflist}}

			[[Category:Combinatorial game theory]]

en>Twitchax at 19:40, 1 September 2011

2011-09-01T19:40:00Z

New page

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