Standard Talks, Mornings (9:30-13:00)

Working Sessions, Afternoons (15:00-18:00)

Anjali Bhagat, Indian Institute of Technology Bombay, India

Title: Fork positions and 2-dimensional toppling dominoes

Abstract: Toppling Dominoes is known as a one-dimensional combinatorial game where the dominoes are arranged in a straight line. This project introduces fork positions where the dominoes are placed in a 2-dimensional plane. We define the rules for 2-dimensional fork positions in Toppling Dominoes. We explore how fork positions are different from 1-dimensional Toppling Dominoes. We prove that doubling a single domino to make the position two-dimensional favors the player whose domino was doubled. The game values become incomparable in the case of the neutral green domino. We also prove that when we make two 1-dimensional games into a fork position again, it favors the player whose domino was used to make the fork.

(Joint work with Urban Larsson)

Craig Tennenhouse, University of New England, USA

Title: Temperature of Partizan Arc Kayles

Abstract: Motivated by the longstanding conjecture that the temperature of Domineering is bounded by two we examine Partizan Arc Kayles as a generalization, and show that this game has unbounded temperature on trees.

(Joint work with Svenja Huntemann and Neil McKay)

Harman Agrawal, Indian Institute of Technology Bombay, India

Title: QuadroCount: A Combinatorial Game

Abstract: We define QuadroCount, a two-player grid-based partizan game. A given position is a configuration with n pieces for each player Left and Right. The individual area of each pair of pieces is computed by treating them as corner stones, as shown in the figures, which have areas 8 and 4, respectively.

The black squares represent Left's pieces and the yellow squares represent Right's pieces. The OverLapping Area or olá is the sum of all individual areas, computed as

where (x_i,y_i) denotes the coordinates of the i-th piece. Every move must decrease the olá, and a player who cannot do so loses (normal play). We propose sequences of terminal configurations that range over N and identify all Nash equilibrium-type local minima for n = 2. We also establish game values and conjecture that a player can have at most a one-move advantage over the other player.

(Joint work with Urban Larsson)

Helena Verrill, University Warwick, UK

Title: Grundy sequence of the cut game C(1,2)

Abstract: I will describe a formula for the values G(n) for the cut game C(1,2), which is a heap game, where players alternately divide heaps of counters into 2 or 3 piles. 

(Joint work with Alfie Davies) 

Martin Mueller, University of Alberta, Canada

Title: A search-based approach for solving sum games

Abstract: In combinatorial games, the most fundamental question is «who wins?». We study general purpose algorithms for efficiently answering this question for specific short game positions, especially for the case when the given position is a sum of independent subgames. The most popular existing software tools, such as Siegel's CGSuite, are built around the fundamental concept of canonical form. However, for solving sum games, computing canonical forms can very quickly become a major bottleneck - it is often a much more expensive procedure than «just» finding the winner. We report ongoing work on a new Minimax-based Combinatorial Game Solver (MCGS), a tool for finding the winner of a sum game by search. MCGS answers questions of the form «does player P win game G?». We develop specific algorithms for this purpose, which avoid computing canonical forms. Subgame decomposition and simplification techniques based on minimax search and on basic principles of combinatorial games greatly increase the efficiency of MCGS. After some motivational examples, we define our search framework and show first computational results for one-dimensional strips of combinatorial games such as Clobber and NoGo.

(Joint work with Henry Du, Taylor Folkersen, Zahra Bashir, and Fatemeh Tavakoli) 

Miloš Stojaković, University of Novi Sad, Serbia

Title: Generalized saturation game

Abstract: We study a game version of the generalized graph Turán problem. For two fixed graphs F and H, two players, Max and Mini, alternately claim unclaimed edges of the complete graph such that the graph with the claimed edges must remain F-free throughout the game. The game ends when no further edges can be claimed, i.e. when the graph becomes F-saturated. The H-score of the game is the number of copies of H. Max aims to maximize the H-score, while Mini wants to minimize it. We look for the H-score for several natural choices of F and H, when both players play optimally.

(Joint work with Balázs Patkós, Jelena Stratijev, and Máté Vizer)

Prem Kant, Indian Institute of Technology Bombay, India

Title: Numbers and Infinitesimals in bidding combinatorial games

Abstract: Discrete Richman Bidding Combinatorial Games that generalize alternating normal play were introduced by Kant, Larsson, Rai, and Upasany (2022). In this framework, the properties of integers, dyadic rationals, and defined zugzwang positions were explored in subsequent work by Kant, Larsson, Rai, and Upasany (2024). In the current study, we extend this work to investigate the structure of numbers and infinitesimals within the same bidding setup. 

(Joint work with Urban Larsson)

Vlado Uljarević, University of Novi Sad, Serbia

Title: A variation of Hats-in-a-line game

Abstract: Hat-guessing games gained the scientific community's attention at the end of the 20th century when, in 1998, Todd Ebert formulated the so-called n-prisoners puzzle. Despite being formulated in a way that brings it into recreational mathematics, Ebert's puzzle is closely related to certain problems and notions of coding and information theory. The different variations of this and similar games were developed and investigated in the years after. One of the most known hat-guessing games is the Hats-in-a-line game, in which a warden arranges n prisoners in a line, wearing hats colored in one of two colors (white and black for example), so that each of them can see all the hats of the prisoners before him, but can't see the hats of anybody behind. Then, each of them guesses (one by one, starting from the back of the line) whether the hat on his head is white or black. The goal is to maximize the total number of correct guesses. We introduce a new variant of this game in which the amount of information prisoners can transmit is significantly reduced, and we discuss the maximum number of correct guesses depending on the number of colors the hats are colored with. In the end, we briefly show how this problem can be translated into an instance of the SAT problem, allowing us to use modern SAT-solving algorithms as a last resort.

(Joint work with Bojan Bašić)