What if you played it where the square selected is the direction you move to go to the next board. If the player selects the center square on a board, that boar

What if you played it where the square selected is the direction you move to go to the next board. If the player selects the center square on a board, that board must be played again. If the player selects the left square, the board to the left must be played next. If a corner square is picked, you play the board to that diagonal direction. If the corner is not attached to a board, you roll the board around as though the ends are connected (or as though it's an infinitely repeating tiling of the same game). For example, the bottom right square on the bottom right board makes the next board the top left. The center-right square on the center-right board would result in the next board being the center-left board, and so on. Would there be a gambit in this ruleset? edit: So, it looks like the same gambit applies, instead of selecting the center piece you just pick the one pointing toward the center every time.