Sprouts is a Combinatorial Games Conference oriented towards undergraduate research. Sprouts is also a combinatorial game that is especially popular in the Netherlands.
Locking Nim is a variant of the game of Nim. It is a two-player impartial strategy game that will be studied using Combinatorial Game Theory. Since it is impartial, we find positions with game values that correspond with nimbers.
Polar Bear Plunge combines games Chomp and Go with the Floe into a two player, impartial strategy game. It is a grid game, of which there are no known similar games; however, it can be compared to a variant of Hackenbush known as Node Hackenbush.
Crab and Gulls is a variation of the well-known game of Queens. Game values and patterns were analyzed, however, Crab and Gulls becomes more complex as the board size increases. Two simplified variations of Crab and Gulls, King and Gulls and Rock and Gulls, have therefore also been analyzed.
Determining the outcome class of some games is easy, but others seem to necessitate evaluating all or most of the game tree. We can measure this difficulty using computational complexity. This talks explains the notion of complexity with respect to games, then shows sample reductions to prove hardness.
Undecidability has been studied using Turing Machines and through the proof of the Halting Problem. Wang Tiles have been used to simulate Turing Machines. The partizan game of Infinitiles will adapt the idea that Wang Tiles can simulate a Turing Machine into a game that will follow the idea of undecidability when played on an infinite board. Analysis of small boards done both by hand and using CGSuite will lead into more abstract results on infinite boards, at which point undecidability comes into play.
Also Kanye is a grid variant of the strip game Drag Over. Here we use CGSuite and Combinatorial Game Theory concepts to analyze first and second player strategies, as well as patterns in starting positions. Many game values matching integers, switches, and infinitesimals were found, as well as a clear triangular pattern in fully saturated boards.
Computationally hard games resist deterministic solutions to recognize all winning positions. Borrowing heuristic strategies from Chess and Go is a powerful tool for finding how to play difficult combinatorial games.
Protect The King is a new variation on the placement chess game, Queens. This game is played on a grid, which does not have to be symmetrical. We introduce the game of Protect The King which adapts Queens and Angel and Demon to create an interesting blocking strategy that can be analyzed in the context of Combinatorial Game Theory. Positions with game values of all integers and switches, and some infinitesimals are found.
Grid games are very common-place in combinatorial game theory. Herein, we analyze the new all-small, impartial grid game Kanye, developed from clobber and drag over. Canonical forms of one stone on an n by m grid and symmetrical board patterns are analyzed. Atomic weights for these same board types are discussed and canonical form boundaries are examined.
The following organizations provided funds to hold the meeting. Many thanks to:
Math Professor Craig Tennenhouse organizes combinatorial game theory conference at UNE from UNE.