000			05361nam a2200397Ki 4500
001			ocn857769768
003			OCoLC
005			20240726105417.0
008			130909s2008 enka ob 000 0 eng d
040			_aNT _erda _epn _beng _cNT
020			_a9781461941460 _q((electronic)l(electronic)ctronic)l((electronic)l(electronic)ctronic)ctronic bk.
050	0	4	_aQA269 _b.C663 2008
049			_aNTA
100	1		_aBeck, József. _e1
245	1	0	_aCombinatorial games : _btic-tac-toe theory / _cJózsef Beck.
260			_aCambridge : _bCambridge University Press, _c(c)2008.
300			_a1 online resource (xiv, 732 pages) : _billustrations.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_adata file _2rda
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 114
505	0	0	_apart A. Weak win and strong draw -- _tchapter I. Win vs. weak win -- _tIllustration : every finite point set in the plane is a weak winner -- _tAnalyzing the proof of theorem 1.1 -- _tExamples : tic-tac-toe games -- _tMore examples : tic-tac-toe like games -- _tGames on hypergraphs, and the combinatorial chaos -- _tchapter II. The main result : exact solutions for infinite classes of games -- _tRamsey theory and clique games -- _tArithmetic progressions -- _tTwo-dimensional arithmetic progressions -- _tExplaining the exact solutions : a meta-conjecture -- _tPotentials and the Erdős-Selfridge theorem -- _tLocal vs. global -- _tRamsey theory and hypercube tic-tac-toe -- _tpart B. Basic potential technique : game-theoretic first and second moments -- _tchapter III. Simple applications -- _tEasy building via theorem 1.2 -- _tGames beyond Ramsey theory -- _tA generalization of Kaplansky's game -- _tchapter IV. Games and randomness -- _tDiscrepancy games and the variance -- _tBiased discrepancy games : when the extension from fair to biased works! -- _tA simple illustration of "randomness" (I) -- _tA simple illustration of "randomness" (II) -- _tAnother illustration of "randomness" in games.
505	0	0	_apart C. Advanced weak win : game-theoretic higher moment -- _tchapter V. Self-improving potentials -- _tMotivating the probabilistic approach -- _tGame-theoretic second moment : application to the picker-choose game -- _tWeak win in the lattice games -- _tGame-theoretic higher moments -- _tExact solution of the clique game (I) -- _tMore applications -- _tWho-scores-more games -- _tchapter VI. What is the biased meta-conjecture, and why is it so difficult? -- _tDiscrepancy games (I) -- _tDiscrepancy games (II) -- _tBiased games (I) : biased meta-conjecture -- _tBiased games (II) : sacrificing the probabilistic intuition to force negativity -- _tBiased games (III) : sporadic results -- _tBiased games (IV) : more sporadic results -- _tpart D. Advanced strong draw : game-theoretic independence -- _tchapter VII. BigGame-SmallGame decomposition -- _tThe Hales-Jewett conjecture -- _tReinforcing the Erdős-Selfridge technique (I) -- _tReinforcing the Erdős-Selfridge technique (II) -- _tAlmost disjoint hypergraphs -- _tExact solution of the clique game (II).
505	0	0	_achapter VIII. Advanced decomposition -- _tProof of the second ugly theorem -- _tBreaking the "square-root barrier" (I) -- _tBreaking the "square-root barrier" (II) -- _tVan der Waerden game and the RELARIN technique -- _tchapter IX. Game-theoretic lattice-numbers -- _tWinning planes : exact solution -- _tWinning lattices : exact solution -- _tI-can-you-can't games -- _tsecond player's moral victory -- _tchapter X. Conclusion -- _tMore exact solutions and more partial results -- _tMiscellany (I) -- _tMiscellany (II) -- _tConcluding remarks -- _tAppendix A : Ramsey numbers -- _tAppendix B : Hales-Jewett theorem : Shelah's proof -- _tAppendix C : A formal treatment of positional games -- _tAppendix D : An informal introduction to game theory.
504			_a1
520	1		_a"Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solitaire, and hex. This is the subject of combinatorial game theory. Most board games are a challenge for mathematics: to analyze a position one has to examine the available options, and then the further options available after selecting any option, and so on. This leads to combinatorial chaos, where brute force study is impractical." "In this comprehensive volume, Jozsef Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine the exact results about infinite classes of many games, leading to the discovery of some striking new duality principles."--BOOK JACKET.
530			_a2 _ub
650		0	_aGame theory.
650		0	_aCombinatorial analysis.
655		1	_aElectronic Books.
856	4	0	_uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=616988&site=eds-live&custid=s3260518 _zClick to access digital title | log in using your CIU ID number and my.ciu.edu password
942			_cOB _D _eEB _hQA _m2008 _QOL _R _x _8NFIC _2LOC
994			_a02 _bNT
999			_c99479 _d99479
902			_a1 _bCynthia Snell _c1 _dCynthia Snell