ABSTRACT

A number of mathematicians have attempted to devise an explicit winning strategy for Hex. To offset the advantage of playing first, Anatole Beck suggested this Hex variant: the second player is allowed to tell the first player where she must make her first move. When Gross says that Bridgit is not solved, he means that he does not know an efficient method — in particular, better than brute force — that solves arbitrary Bridgit positions that is finds a winning move if there is one. In Bridgit, each opening move wins, so the first player wins Beck’s Bridgit. In general, Alfred Lehman’s characterization has a different form for positions with Short to play. But for Bridgit, because the underlying graph is planar and the graph is self-dual, each player can contruct an equivalent Shannon switching game in which that player is Short, and so use the characterization.