We investigate a game played on a hypergraph H = (V,E) by two players, Balancer and Unbalancer. They select one element of the vertex set V alternately until all vertices are selected. Balancer wins if at the end of the game all edges e ∈ E are roughly equally distributed between the two players. We give a polynomial time ∗Research supported in part by a USA-Israel BSF grant, by the Israel Scie...