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master's thesis
Analiza strategija i pripadnih vjerojatnosti u igri "Rizik"
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:887318
Lančić, Alen
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lančić, A. (2022). Analiza strategija i pripadnih vjerojatnosti u igri "Rizik" (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:887318

Lančić, Alen. "Analiza strategija i pripadnih vjerojatnosti u igri "Rizik"." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:887318

Lančić, Alen. "Analiza strategija i pripadnih vjerojatnosti u igri "Rizik"." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:887318

Lančić, A. (2022). 'Analiza strategija i pripadnih vjerojatnosti u igri "Rizik"', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:887318

Lančić A. Analiza strategija i pripadnih vjerojatnosti u igri "Rizik" [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:887318

A. Lančić, "Analiza strategija i pripadnih vjerojatnosti u igri "Rizik"", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:887318

Metadata
TitleAnaliza strategija i pripadnih vjerojatnosti u igri "Rizik"
Title (english)Analysis of strategies and associated probabilities in the game "Risk"
AuthorAlen Lančić
MentorMiljenko Huzak (mentor)
Committee memberMiljenko Huzak (predsjednik povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu smo analizirali neke elemente igre ”Rizik”. Izračunali smo vjerojatnosti ishoda jedne iteracije napada i obrane. Zatim smo igru promatrali kao Markovljev lanac s diskretnim vremenom, našli optimalne strategije obrane za svako stanje i vidjeli kako se skup stanja s obzirom na optimalne strategije obrane particionira na šest particija. Na kraju smo izračunali apsorbirajuće vjerojatnosti lanca počevši iz svakog neapsorbirajućeg stanja te to iskoristili da izračunamo funkcije gustoće vjerojatnosti konačnog ishoda napada teritorija i vjerojatnost njegovog osvajanja počevši iz različitih stanja Markovljevog lanca.
Abstract (english)
In this work, some elements of the game ”Risk” were analyzed. Outcome probabilities of a single iteration of attack and defense were obtained. Then, the game was considered as a Markov chain with discrete time, the optimal defense strategies for each state were found and the way in which the state set partitions into six partitions with regard to the optimal defense strategies was determined. In the end, absorbing probabilities of the chain from each source state were obtained, which were used for obtaining the probability mass functions of the final outcome of an attack of a territory and the probability of its capture starting from various states of the Markov chain.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:887318
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-03-28 11:50:00