Modeliranje igara na sreću pomoću Brownovog gibanja i primjene

master's thesis

• Author: Emil Miroslav Mesarić
• Mentor: Zoran Vondraček (mentor)
• Committee member: Zoran Vondraček (predsjednik povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kockarnice ponekad naprave promociju tipa povrat na gubitak što im može donijeti i gubitak. Najpoznatiji primjer je onaj u kojem je Don Johnson tijekom 6 mjeseci u 2011. godini igrajući blackjack osvojio preko 15 milijuna dolara u tri kockarnice u Atlantic City-ju. Cilj diplomskog rada je opisati i proučiti igre na sreću s uključenim povratom na gubitak, te pronći optimalna vremena zaustavljanja u slučaju dobitka, odnosno gubitka, kojima se maksimizira dugoročni profit. U matematičkim izračunima koristit će se Brownovo gibanje s driftom kao aproksimacija diskretnog slučajnog procesa.

Abstract (english)

Casinos can sometimes make such a promotion in which they return some percentage of a person's losses, but this may cause their own losses. The most famous example is when Don Johnson managed to win over 15 million dollars playing blackjack in three casinos over a six months period in 2011, in Atlantic City. The aim of this thesis is to describe and study the games of chance, which include the return on loss, as well as to determine the optimal exit time. This includes leaving the game while they are still at a gain level rather than losing money, in order to maximize the long-term prot. The Brownian motion with drift as an approximation of the discrete random process will be used in the mathematics calculations.

• Keywords: blackjack; igre na sreću; Brownovo gibanje
• Keywords (english): games of chance; casinos; Brownian motion
• Language: croatian
• URN:NBN: urn:nbn:hr:217:951012
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-11-26 12:14:32