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You may have played cops and robbers on the playground, but have you ever played on a graph? What about playing leapfrog on a grid? In this talk, we will talk about some combinatorial games including Cops and Robbers on Graphs, Toads and Frogs, and Chomp. Many combinatorial games have been mathematically studied to the point of knowing who will win before the game even starts! We will discuss what it means for a game to be ''solved'' or ''determined,'' and introduce tools of computability theory as a way to compare the complexity of various games and strategies.