Igra križci in krožci

magistrsko delo

Martin Fras (Author), Boštjan Brešar (Mentor)

Abstract

V magistrskem delu predstavljamo osnovne pojme kombinatoričnih iger na treh variacijah igre Križci in krožci: simetrične igre, igre tipa Izdelovalec-Lomilec in igre tipa berač. Obravnavamo igre Križci in krožci z različnimi dimenzijami igralnega polja in predstavimo različne strategije igralcev ter opazujemo odnose med spremembo dimenzije igralnega polja in rezultatom igre. Ugotavljamo, da v simetrični igri na polju velikosti ▫$n^d$▫ z uporabo ustrezne strategije zmaga Prvi igralec, če je z uporabo iste strategije zmagal na polju ▫$n^k,\ k

Keywords

magistrska dela;pozicijska igra;križci in krožci;strategija;močan remi;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Fras]
UDC:	37.091.3:519.1(043.2)
COBISS:	24940296
Views:	871
Downloads:	77
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Tic tac toe game
Secondary abstract:	In this thesis, we present basic terms of combinatorial games on three variants of Tic-Tac-Toe game: symmetric game, Maker-Breaker game and Misere. We use these variants on different dimensions of the playing field to present different player strategies, while observing changes of the game outcome depending on the change of the game's playing field. We concluded, that the symmetric game on the playing field size of ▫$n^d$▫ is a First player strategy win, if First player won by using the same strategy on a playing field size of ▫$n^k,\ k<d$▫. In Maker-Breaker games, increasing the dimension of the playing field can not harm Maker, but it can harm Breaker, which is the result of higher number of winning sets in higher dimensions. In Misere games, we establish that First player, if using mirroring strategy, can achieve at least a draw on the playing field size of ▫$(2n-1)^d,\ n\geq 4,\ d\geq 2$▫, while win is achieved if the playing field has no final drawing position. Similarly, it is possible for Second player to achieve at least a draw, using similar mirroring strategy, if the playing field is of size ▫$2n^d,\ n\geq1,\ d\geq 2$▫. At the end of the thesis we additionally present games of Unlimited ▫$n$▫-in-a-row, Hex, Bridge-it and Maker-Breaker domination games, which are similar to the Tic-Tac-Toe games.
Secondary keywords:	master theses;positional game;Tic-Tac-Toe;strategy;weak win;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	X, 47 f.
ID:	11239313