 I design board games and I'm a mathematician. I'm going to explain zeroth dimensional persistent homology, an essential tool in my work, through the popular board game, Carcassonne. Zeroth dimensional homology studies connected components, and a connected component translates exactly to a farming region in Carcassonne. As any Carcassonne player knows, farming can win or lose you the game. Even if you don't think you know what topology is, chances are you're using it whenever you play Carcassonne. So, in Carcassonne, a farming region is a set of points such that you can move your meeple within the set of tiles from any one point to any other point. In mathematics, a path connected component is a set of points such that between any pair of points, there exists a path between them. It's the same thing. One technique in farming is to try and add farmers to already claimed valuable farming land. In order to do this, one way is to add it to a disconnected component and then to connect them via another tile. Mathematically, what has happened when I've added this piece is that I have merged two different connected components. Understanding how these connected components evolve as you increase your space is a fundamental tool in applied algebraic topology.