Turnirji na izpadanje : delo diplomskega seminarja

Pust, Gašper (author), Dolžan, David (mentor)

V diplomski nalogi si bomo najprej ogledali dva modela turnirjev na izpadanje, in sicer turnir z rangiranjem igralcev ter naključni turnir. V vsakem od modelov si bomo pogledali verjetnosti za zmago najboljšega in drugega najboljšega igralca, kjer bo zmaga slednjega predstavljala presenečenje. Zanimala nas bo predvsem verjetnost tega presenečenja. V drugem delu naloge pa se bomo posvetili mejam za verjetnost zmage danega igralca na naključnem turnirju na izpadanje. Posebej si bomo pogledali verjetnost zmage najboljšega igralca na turnirju in preverili, če je njegova zmaga vedno najbolj verjetna.

• Language: Slovenian
• Keywords: turnir, presenečenje, verjetnost zmage, favorit
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-136305
• UDC: 519.2
• COBISS.SI-ID: 105854979
• Publication date in RUL: 23.04.2022

Secondary language

• Language: English
• Title: Knockout tournaments

Abstract

In this thesis, we will first look at two models of knockout tournaments, a playerranked tournament and a random tournament. In each model, we will look at the probabilities of the best player and the second best player winning, where the latter’s win will be called a surprise. We will be interested in the probability of this surprise. In the second part of the thesis, we will look at bounds on the probability of a given player winning a random knockout tournament. In particular, we will look at the probability of the best player in the tournament winning, and check if his victory is always the most probable.

• Keywords: tournament, surprise, probability of victory, favourite