The Game of Cycles (Su, 2020) is an impartial combinatorial game played on a connected planar graph. Each player takes turns marking an edge of an initially undirected graph with a direction subject to certain rules, with the goal of completing a cycle cell. Our research involves finding winning strategies for different classes of game boards. We begin by identifying either first or second player winning strategies for relatively simple boards. To study more complex boards, we implement a playable version of the game that can be run on a computer. We then use this to create a program that evaluates every possible game state of a given board and finally determines which player has a winning strategy. Currently, we have our playable computer game and can generate game trees for smaller boards. Going forward, we plan to implement more boards in our playable game and optimize our program to efficiently identify winning strategies in larger boards.
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Hi Nicholas, aside from computational limitations, are there any additional challenges you anticipate as your move toward your future work?
Hi Lisa, this is a great question! Assuming no computational limits, we could identify which player has a winning strategy for any board. The challenge would be to identify what that winning strategy is.
Looking far into the future of this project, a very useful tool would be one that visualizes the game tree and highlights the winning “paths” for the player. Then we could then analyze what the moves and responses were that led to the winning strategy and try to form general “rules” to win each board. Maybe we could then apply this knowledge to full classes of boards.