I'd like to know if infinitely repeating sequences of moves (i.e. cycles) are possible in the following game: > [Prodway][1] is a game for two players (Black and White) that is > played on an initially empty square board. The top and bottom edges of > the board are colored black; the left and right edges are colored > white. > > A *crosscut* is a 2x2 area containing two diagonally adjacent black > stones and two diagonally adjacent white stones. > > Black plays first, then turns alternate. On your turn, place a stone > of your color on an empty point or on a point occupied by an enemy > stone. In the latter case, move the enemy stone to an orthogonally > adjacent empty point before placing your stone. Your newly placed > stone must not be part of any crosscuts. If the moved enemy > stone is part of one or more crosscuts, remove the other enemy stones > in those crosscuts. > > You win if, after a full move by either player, there is a chain of > orthogonally connected stones of your color touching the two opposite > board edges of your color. Passing is not allowed, but, if you have no > legal moves available, your turn is skipped. Here's a mesmerizing near cycle. [![enter image description here][2]][2] Reneo, a related game, is [finite][3], but has different rules for swaps and removals. In Prodway, captures are more frequent, and you can capture up to two enemy stones on a single turn. In Reneo, you never capture more than one stone on a single turn. [1]: https://boardgamegeek.com/thread/3130103/new-orthogonal-connection-games-reneo-prodway-and [2]: https://i.sstatic.net/Juosv.gif [3]: https://boardgamegeek.com/thread/3135288/are-cycles-possible