The game is set up on a finite graph with an integer number of dollars assigned to each vertex. A move consists of borrowing a dollar from all of a vertex's neighbors (performed by clicking the green region), or by lending a dollar to all neighbors of a vertex (the red region). The game ends when all vertices have nonnegative values.
Theorem: If the total number of dollars present is greater than or equal to the graph's cyclomatic number (number of edges - number of vertices + 1), the game can always be won. Otherwise, there is always an initial configuration of the graph that is unwinnable.