Another idea would be some sort of "Dark Amazon" game - that is where you can not see the other players piece unless you in the same row/colum/diagnal - and there are not arrows between you and him.

You can see the whole board, and where current arrows are at (and last shot arrow), but only the other players piece is hidden (unless it is in view)

So you would add an extra step to the game. Step 1, move your piece and SUBMIT/COMMIT to having your piece there. At that point, you would be able to see what is in view so you will then know where to shot your arrow.