Testiranje generatorjev izidov v igrah na srečo

delo diplomskega seminarja

Špela Petan (Author), Mihael Perman (Mentor)

Abstract

V algoritme za generiranje izidov v igrah na srečo so vgrajeni generatorji slučajnih števil. V diplomskem delu je predstavljenih šest empiričnih Knuthovih testov, ki preverjajo, ali se verjetnosti generiranih izidov ujemajo s teoretičnimi verjetnostmi. Vsak test lahko prevedemo na Pearsonov $\chi^2$ test, ki ima za velike slučajne vzorce $\chi^2$ porazdelitev. Tako lahko izračunamo $p$-vrednost, na podlagi katere ocenimo poštenost generatorjev. Pearsonov $\chi^2$ test pa je kljub široki uporabljenosti zahteven, saj za natančnost potrebuje velik slučajni vzorec. Zato je v delu predstavljen tudi pred kratkim objavljen alternativen $\chi^2$ test.

Keywords

matematika;igre na srečo;statistični testi;generatorji slučajnih števil;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[Š. Petan]
UDC:	519.2
COBISS:	78379779
Views:	985
Downloads:	74
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Testing outcome generators in games of chance
Secondary abstract:	Random number generators are used in algorithms for outcome generating in games of chance. We present the six Knuth's tests. They check whether probabilities of generated outcomes match the theoretical probabilities. Each one of them reduces to Pearson's $\chi^2$ test, which has the $\chi^2$ distribution for large random samples. That is how we calculate $p$-values based on which we evaluate the fairness of outcome generators. Despite Pearson's $\chi^2$ test being widely used, it is complex, since a big random sample is needed for its accuracy. Therefore the recently published alternative $\chi^2$ test is also presented in the thesis.
Secondary keywords:	mathematics;games of chance;statistical tests;random number generators;▫$\chi^2$▫ tests;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	31 str.
ID:	13505882