Related papers: Does the first-serving team have a structural adva…
With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game,…
Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the…
We show that information on the first server influences the expected total number of games and margin in a tennis match under the standard assumption that each player's serve point win probability remains constant, and identify the exact…
Serves, especially first serves, are very important in professional tennis. Servers choose their serve directions strategically to maximize their winning chances while trying to be unpredictable. On the other hand, returners try to predict…
The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages,…
The progression of a single point in volleyball starts with a serve and then alternates between teams, each team allowed up to three contacts with the ball. Using charted data from the 2022 NCAA Division I women's volleyball season (4,147…
This paper considers the flight dynamics of the ball in the sport of pickleball. Various simplifications are introduced according to the features of the game. These simplifications and some approximations enable straightforward coding to…
We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…
Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidence…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…
We consider two-person sports where each rally is initiated by a \emph{server}, the other player (the \emph{receiver}) becoming the server when he/she wins a rally. Historically, these sports used a scoring based on the \emph{side-out…
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given…
The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective.…
In the Penney-Ante game, Player I chooses a head/tail string of a predetermined length $n\ge3$. Player II, upon seeing Player I's choice, chooses another head/tail string of the same length. A coin is then tossed repeatedly and the player…