Sprouts is a Combinatorial Games Conference oriented towards undergraduate research, created as a joint collaboration between the University of New England and Florida Southern College. Sprouts is also a combinatorial game that is especially popular in the Netherlands.
Combinatorial Game Theory is the mathematical study of turn-base games ("rulesets") where:
Many nice properties emerge from this, especially when we add games together. This conference is all about playing games, analyzing games, and even creating new games.
For a good introduction to Combinatorial Game Theory, we recommend these books:
This conference includes talks oriented towards undergrads, sessions for looking at unsolved problems, and both a human and computer game tournament. Prior knowledge of Combinatorial Game Theory is not necessary. (The first talk will cover much of the basics.) Although we expect the topics to be mostly applicable for Math and Computing students, everyone who enjoys abstract games is welcome!
There is no registration fee for Sprouts.
There is no cost to register for this conference. Email Kyle () to officially register. (It's still free!) Please include "Sprouts 2023 Registration" in the subject line of your email and let me know what your name and institution/organization are.
We are now accepting talk proposals. Preference will be given to talks by undergraduates and high-school students. All talks should be accessible to an undergraduate-level audience. Talk slots are usually 15 minutes long, and speakers should plan to talk for about 10 minutes, then answer questions for the remainder of the time.
To propose a talk, email your talk title and abstract to Kyle (). Please include whether you're an undergrad/grad student/professor/something else.
Local events: There will be an in-person Flag Coloring tournament held at Florida Southern College starting about 3:05pm in the Weinstein Computer Science building, Room 108.
Planned Events: (Talks get scheduled as they are accepted)
Throughout this talk, we explore a deterministic model as an alternative approach to studying two player simultaneous games. We call this the Cheating Robot model. This model forces both players to move at the same time, but one player has extra information about where their opponent will move and can react accordingly (they cheat!). In this talk we will examine this model via a case study of Toppling Dominoes. We will then take a look at some general results. Lastly, we will conclude by exploring the Cheating Robot model in the context of a pursuit-evasion game. This is joint work with Richard J. Nowakowski.
In Domineering the two players Left and Right place dominoes on the board. Left plays with vertically oriented dominoes and Right uses dominoes which are horizontally oriented. Each domino covers two adjacent squares and dominoes cannot overlap or go over the edge of the board. The temperature of a Domineering position is a measure of the urgency of the next move. One of the reasons we are interested in temperature is because for some Domineering positions, the next move has a major impact on the final outcome of the game. Berlekamp conjectured that the maximum temperature in Domineering is 2. We developed code to search for Domineering positions of temperature close to 2 and found several positions which showed similar patterns embedded in them.
The localization game on a graph was first introduced in 2012 by Seager. Given a graph, G, the localization game is a 2-player game with players called Sensor and Robber. First, the invisible robber chooses a vertex to start at. The sensor then probes a vertex and the robber tells the sensor the distance the robber is from the probe. The robber may then either stay put or move to a neighboring vertex. The game ends if the sensor can determine the location of the robber. The parameter of interest is the capture time, which is how many rounds it would take to catch the robber when both players play optimally. Behague, Bonato, Huggan, Marbah, and Pettman presented a conjecture which claims that the capture time on a graph is at most n, where n is the number of nodes of the graph. We will explore this conjecture and present partial results.
Node Kayles is a two-player game played on a simple graph in which each player alternately selects a vertex that is not adjacent to previously selected vertices. We study the Grundy values of Node Kayles while playing on different graphs, including paths. The focus is on determining if there is any periodicity in the sequence of Grundy values we calculated.
We introduce a new impartial game called plinko nim. There are piles on each node of a directed tree, and the players can take stones from the leaves of the tree. When one pile is reduced to 0, the piles cascade to fill the empty node. We share values for directed paths, discuss more complicated trees, and talk about future work.
This research examines a two-player combinatorial game, Game of Thrones: Hand of the King, and applies several different techniques to develop an effective AI player for this game. We used several approaches including simple game state analysis, heuristic search, minimax tree search, and Monte Carlo tree search. A game framework that supports random board generation and multi-game tournaments was used to test different players against each other. Our results show that a hybrid player using both minimax tree search and Monte Carlo tree search is effective at winning against a variety of other AI players.
Symmetry and combinatorial game theory can be used to develop optimal strategies for simplified versions of poker games, such as video poker and Caribbean Stud Poker. Symmetry can reduce the size of the game tree and simplify the analysis, while tools such as the Sprague-Grundy function can be used to determine the optimal strategy. By exploiting symmetry and analyzing the game from a combinatorial perspective, players can gain an advantage over opponents and increase their chances of winning. However, these techniques have limitations, including the need to tailor the analysis to the specific rules and mechanics of each game and the challenges in applying them to more complex versions of poker. I intend to cover such topics through my talk.
Abstracts will continue to appear here as they are accepted.
This year we'll be playing Flag Coloring! There are many ways to participate:
The main part of Sprouts 2023 will be held virtually.
Thanks to Florida Southern College Computer Science and University of New England Mathematics departments for supporting Sprouts 2023.
Other Combinatorial Games Conferences
