So it turns out one of you was playing soccer while the other one was playing hockey! Importantly, this is not just a cosmetic difference. The soccer player thinks that they can kick the ball three spaces to either side (but not four spaces). See the table of allowed moves below. By contrast, the hockey player thinks that they can hit the puck four spaces to either side (but not three spaces).

But how is that possible?!?

Feel free to play around with the game some more to figure out how this is possible. You can also play with the game parameters below if you like. The width, height, and duality number control the "shape" of the game so to speak. There is nothing too special about 11, 13, and 4. Moreover, you can click on the "moves" grid below to change how far forwards, backwards, and sideways each player can move the ball/puck above. As you play with this, notice how the moves which are allowed for the soccer and hockey players are intimately tied together.