  A rank-3 Maker-Breaker game is played on a hypergraph in which all hyperedges
are sets of at most 3 vertices. The two players of the game, called Maker and
Breaker, move alternately. On his turn, maker chooses a vertex to be withdrawn
from all hyperedges, while Breaker on her turn chooses a vertex and delete all
the hyperedges containing that vertex. Maker wins when by the end of his turn
some hyperedge is completely covered, i.e. the last remaining vertex of that
hyperedge is withdrawn. Breaker wins when by the end of her turn, all
hyperedges have been deleted.
  Solving a Maker-Breaker game is the computational problem of choosing an
optimal move, or equivalently, deciding which player has a winning strategy in
a configuration. The complexity of solving two degenerate cases of rank-3 games
has been proven before to be polynomial. In this paper, we show that the
general case of rank-3 Maker-Breaker games is also solvable in polynomial time.
