Testiranje generatorjev izidov v igrah na srečo : delo diplomskega seminarja

Petan, Špela (author), Perman, Mihael (mentor)

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.

• Language: Slovenian
• Keywords: igre na srečo, statistični testi, generatorji slučajnih števil, $\chi^2$ testi
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-131040
• UDC: 519.2
• COBISS.SI-ID: 78379779
• Publication date in RUL: 22.09.2021

Secondary language

• Language: English
• Title: Testing outcome generators in games of chance

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.

• Keywords: games of chance, statistical tests, random number generators, $\chi^2$ tests