Ne najmočnejši zmagovalci teniškega turnirja

SIVAK, OLEKSANDR (author), Fijavž, Gašper (mentor)

Zmagovalec tekmovanja je odvisen od začetnih pozicij igralcev. Omejimo se na primer, ko se v vsaki igri pomerita dva igralca. Naš cilj je ugotoviti, kateri igralci so lahko zmagovalci tekmovanja, če vnaprej poznamo vse možne rezul- tate dvobojev. Omejili se bomo na tekmovanja, kjer zmagovalec dvoboja napreduje v naslednji krog, poraženec pa je izločen iz tekmovanja. Osredotočili se bomo na teniške turnirje na podlagi realnih podatkov s spletne strani atpworldtour.com. Končni zmagovalec turnirja je odvisen od začetnih pozicij igralcev v prvem krogu — temu rečemo razpored. Določiti želimo vse možne zmagovalce tekmovanja in za vsakega zmagovalca π določiti ustrezen razpored. Poleg tega študiramo tudi, kako dobri so zadostni pogoji, ki jih opiše Williams v članku Fixing a Tournament (Williams, AAAI 2010). Kot primer, eden naših rezultatov pravi, da je lahko igralec, katerega relativna uvrstitev je med 1. in 36. mestom, z veliko verjetnostjo lahko zmagovalec teniškega tekmovanja s 64 udeleženci.

• Language: English
• Keywords: manipulacija turnirja, tenis, deterministični zmagovalec, slabi zmagovalec, slabi igralec
• Work type: Bachelor thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2016
• PID: 20.500.12556/RUL-81577
• Publication date in RUL: 15.04.2016

Secondary language

• Language: Slovenian
• Title: May a weak tennis player win?

Abstract

The winner of a competition depends on the choice of actual matches played. We assume that each match is played between two players. Our goal is to examine which players can be made winners of a competition if we know any match result in advance. We only consider competitions in which the winner of a single match progresses to the next round and the loser leaves the competition. We focus on tennis competitions and use real data downloaded from atpworldtour.com. The final winner of a competition depends on the choice of matches in the first round — we call it a bracket. We would like to determine possible competition winners and for every winner π construct an appropriate bracket in which π is the winner. Apart from that we also study how tight are the sufficient conditions for a player to become a winner, as described in the paper Fixing a Tournament (Williams, AAAI 2010). For instance, one of our results is that a player whose relative rank is between 1 and 36 can with high probability be made a winner in a competition of 64 players.

• Keywords: competition manipulation, fixing a tournament, tennis, fair deterministic winner, weak winners, weak players