Sprouts is a Combinatorial Games Conference oriented towards undergraduate research, created as a joint collaboration between the University of New England and Plymouth State University. 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 2022 Registration" in the subject line of your email.
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 ().
Kyle will run the computer Popping Balloons tournament.
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.
Abstracts will appear here.
Distance games are a subclass of combinatorial games played on graphs. They consist of the players colouring vertices/placing tokens without later moving or removing them and the placement of new pieces is dependent on the distance from previously played pieces. It was found that the independence polynomial of some graph, related to the game board, is a representation of the number of positions for that game on that board. Recent work enumerated the positions of three distances games (Snort, Col, and Cis) on paths by computing their generating functions. We extend this work to give bivariate polynomials enumerating the same games on new families of graphs. We also take a look at some new distance games on paths.
In 2016, a group of researchers at Google developed a computer program called AlphaGo that was capable of defeating the world’s best Go player. AlphaGo’s algorithm used a method called reinforcement learning to be able to accomplish this feat. Following the footsteps of AlphaGo, this research project aims to develop a Monte Carlo Tree Seach Algorithm for a set of board games called stacking games. These games are computationally interesting due to the “stacking” operation while maintaining the simplicity of the rules that these games are based on, and how this operation affects these algorithms’ ability to learn and play these games. In this presentation, we highlight the game Ultimate-Tic-Tac-Toe.
We will explore a modification to Nim where play is limited to 3 heaps at a time as the Kraken used has 3 tentacles. The middle tentacle is allowed to take as many as they want from the center heap, but must take the floor of half the two other heaps to each adjacent side, or the remainder of each flanking heap, whichever is larger. The game ends when no other moves can be played and the last player to have moved wins. In games with greater than 3 heaps, when one heap goes to zero then the zero is removed, the heaps to the left or right slide into place and the game continues as long as there are a consecutive 3 heaps for the Kraken to play on. We will look at 1n1 games, other 3 heap games, and we will begin to look at games with 4 heaps.
A partisan variation of traditional peg-solitaire consists of two players that make legal moves by orthogonally jumping pegs. Pegs that are jumped will be removed from the game. In this variation, player Left will make vertical jumps and player Right will move horizontally. Players move until there are no legal moves left, and the last player to make a legal move wins. We will examine the final values of 3x3 and 4x4 boards, as well as interesting values within the games. A 1xn and 2xn board will also be characterized.
The temperature of a combinatorial game measures the urgency of making a move and the boiling point of a class of games is the supremum of all temperatures occuring. We will show how to bound the boiling point from above by bounding the advantage of moving twice in a row. The game Domineering, in which the players place dominoes on a checkerboard, one vertically and the other horizontally, has been conjectured to have a boiling point of 2. Despite extensive work by many authors this conjecture remains open. As an example of our technique of bounding the boiling point we will discuss how to apply it to a particular class of Domineering boards.
In this talk, we give simple NP-hardness reductions for three popular video games. The first is Baba Is You, an award-winning 2D block puzzle game with the key premise being the ability to rewrite the rules of the game. The second is Fez, a puzzle platformer whose main draw is the ability to swap between four different 2-dimensional views of the player’s position. The final is Catherine, a 3-dimensional puzzle game where the player must climb a tower of rearrangable blocks.
We will learn about a partisan game similar to red-blue node kayles, except on a flower with red and blue petals. On a player's turn, the only legal move they can make is to remove two of their own petals and one of the opponent's in between theirs. For example, the legal move for red (right player) is removing a set of red-blue-red petals. We will look a variety of game values including integers, N values, P positions, fractions, and infinitesimals. We hypothesize that a significant number of games are in P, so it might be more advantageous to be the second player.
Loopy Games form a natural generalization of Conway's partizan games by allowing positions to repeat, allowing for pass moves and more complicated cycles. I'll explain different types of loopy games and some of the tools we have to compare them, approximate them, and find their canonical values.
This year we'll be playing Popping Balloons! We're going to have a tournament for computer players and we might have one for human players if we can find some nice way to do that over gather.town. We do have a site where you can play Popping Balloons as a human.
Sprouts 2022 will be held virtually, so there's no physical travel necessary.
Thanks to the Plymouth State Computer Science and Technology and University of New England Mathematics disciplines for supporting the Sprouts conference series.
Other Combinatorial Games Conferences
