Sprouts is a conference oriented towards undergraduate research in the analysis of games. The primary focus is Combinatorial Games, but Sprouts has a broad interest in all related fields. Although we focus on presentations by undergraduates, attendance is open to everyone! Sprouts is also a combinatorial game that is especially popular in the Netherlands. (The logo is a Sprouts position created from 15 points.)
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, friendly discussions, 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, anyone and 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 (paithanq@gmail.com) to officially register. (It's still free!) Please include "Sprouts 2025 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 high-school students, undergraduates, and recent graduates (especially for work done while an undergraduate). All talks should be accessible to an undergraduate-level audience. Talk slots are usually 15 minutes long, and speakers should plan to talk for up to about 10 minutes, then answer questions for the remainder of the time. (We are likely to cut you off after 11 minutes.)
To propose a talk, email your talk title and abstract to Kyle (paithanq@gmail.com). Please include whether you're an undergrad/grad student/professor/something else.
All times are listed in Eastern Time (ET). All events will take place on Zoom. The Zoom link will be made available to those who register.
Planned Events: (Talks get scheduled as they are accepted)
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. The OverLapping Area or ola is the sum of all individual areas. Every move must decrease the ola, 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. This is joint work with Urban Larsson.
In this talk we will present the result of our groups senior capstone project that we completed under the advisement of Dr. Kyle Burke. We will discuss the game Martian Chess and how we undertook to build a playable online JavaScript implementation of this game for Dr. Burke’s own website, along with our very own AI player that we built to play the game. We will focus on first explaining the game of Martian Chess and its rules, before discussing how we built the JavaScript implementation of the game along with building and training our very own AI players that we then integrated. This is joint work with Jake Roman.
In Combinatorics of JENGA (Carvalho, et. al., 2020), the authors propose a variant of Jenga that removes physical skill in order to study the game combinatorially. In this talk, we build on their work to propose a partisan variant of the game and analyze a few special positions.
Supernim is a slight generalization of nim. Instead of each pile being a nimber, now each pile is a position where left and rights options are both a collection of nimbers (possibly different nimbers). Considering nim is a rather simple game to learn how to play optimally, it might be surprising that this simple generalization is really difficult! In fact, it turns out that it is very difficult for even computers to play this game. We'll take a look at how these games become quickly become complicated and how we prove that it is difficult even for computers.
Snort is a two-player graph game where the players take turns colouring vertices, with the restriction that two adjacent vertices cannot have opposite colours. We will discuss a winning strategy on triangular grids with one or two rows of triangles, and many of their variants.
How can we protect a network from a threat? In this talk, we will explore how to model such a scenario using the damage number of a graph, a concept originating from graph theory and pursuit-evasion game theory. After a brief introduction to these areas, we will describe the damage variant of Cops and Robbers and show examples to illustrate its key ideas. We aim to provide an overview of the problem and highlight recent research directions. This talk is based on joint work with Dr. Melissa Huggan.
We consider a Subtraction Nim, where two players have exactly the same options, but is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. The example we consider is the following: Let a set of removable numbers S be a non-empty subset of positive integers greater than or equal to 2, which is applied for both players Left and Right. At the end of the game, Left wins if the number of remaining tokens is even, and Right wins if the number of remaining tokens is odd. We computed the outcomes for many S, and found surprising phenomena that in many examples of S (more than 81% of the samples), the outcomes are L-position for all large enough n. In comparison, R-positions appear occasionally. Our theorem explains why that phenomena occur. We prove that n±1 are L-positions when n is an R-position. Weaker restrictions apply for P-positions and N-positions. Only L-positions can last forever.
We will discuss a new ruleset of NIM, whose Grundy Number take transfinite values. There are 3 piles, say 1, 2, and 3, and the player takes at least 1 token from one pile, and she/he can add tokens to the piles with larger index. For example, One can play (2,3,4) to (1,5,100). The Grundy number of (x,y,z) is ω(2x)+z-y if y is less than or equal to z and ω(2x+1)+y-z-1 otherwise. If time permits, we will also discuss another rulesets with more transfinite Grundy Number.
Blippers and Flippers are two combinatorial games we made while studying about loopy games. Blippers involve taking out two pieces when the pair of pieces are orthogonal to each other, while flippers involve taking out the previous piece. If you have pieces connected diagonally or in case of placing a piece at the center leading to a 3 in a row, the pieces are not taken out. We find a series of generalizations and some loopy game values, especially in a 1*n Blippers. Also, some really perplexing game values can be found for some Flipper games too.
The game of Paintbucket is played in MS paint. The board consists of a square grid of pixels each coloured either black or white. The players, Black and White take turns applying the black (resp. white) paint bucket tools. So, a move consists of choosing a component of the "screen" of your opponent's colour and changing its colour to your own. The game ends once all the pixels on the screen are the same colour — Black wins if they are all black and White wins if they are all white. I will go over the definition of Paintbucket then state some results and open problems.
Simple projects have long existed to enable robots to play classic games such as Chess and Tic-Tac-Toe. These projects, however, have only been hard-programmed for one specific game and for one specific application. It would take great feats to re-use these projects to enable gameplay for all games. They also lack the combinatorial "solution" (strongly-solved metrics) and often do not play the game perfectly. In this project, we leverage the strongly-solved solution sets from GamesCrafters, a game theory research group at Berkeley, to enable perfect robot gameplay. We also introduce techniques to create a generalized robotic system to handle various games, boards and pieces. GamesmanROS will soon have the capabilities to play 20+ games, making all kinds of moves like re-arrangement, captures and adding pieces to the game board.
In this talk, I will show an implementation of the combinatorial game Gomoku and a NEAT AI-based player created for it.
This year we'll be playing Toppling Dominoes! There are many ways to participate:
Sprouts 2025 will be held virtually. There will be an in-person gathering on the Florida Southern Campus (WCS 135) with parking available off of Callahan Ct. (Don't park in the faculty spots.) The building will be locked, so please coordinate with Kyle well ahead of time in your registration email. (You'll want to make a lunch plan.)
paithanq@gmail.com)Thanks to Florida Southern College Computer Science and University of New England Mathematics departments for supporting Sprouts 2025.
Other Combinatorial Games Conferences
