Group Actions on Winning Games of Super Tic-Tac-Toe
Whitney George, Janine E. Janoski

TL;DR
This paper explores the symmetries of super tic-tac-toe games using group actions, revealing that the symmetry group forms a Dihedral group, which helps classify equivalent game states.
Contribution
It introduces a formal group-action framework for super tic-tac-toe, demonstrating that these symmetries form a Dihedral group structure.
Findings
Group actions induce Dihedral symmetry in super tic-tac-toe
Equivalent game states can be classified via group orbits
Symmetry analysis simplifies understanding of game strategies
Abstract
Consider a tic-tac-toe board. In each field of the board, draw a smaller tic-tac-toe board. Now let super tic-tac-toe (STTT) be a game where each player's move dictates which field on the larger board a player must make their next move. We will play an impartial game of STTT where each player uses X. We define a set of actions on a game board which gives rise to a group-action on the game that creates equivalent games. We will discuss how the structure of this group-action forms a Dihedral group.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, programming, and type systems · Artificial Intelligence in Games
