How about some diagonal tiles in the game, running from corner to corner?
That, or some "picket fence" tiles that go either horizontally or vertically but running in a sort of 'cross-hatched' (herringbone) pattern?
In _two_ games now I've been given the exact same choice when offered two tiles. Thus, instead of two choices, I've had no choice whatsoever. This is kinda frustrating. Is this something you want the game to do? Couldn't you have the game compare the two tile choices before it presents them to the player, and if the choices are exactly the same, the game (randomly) regenerates one of the tiles (and compares again), repeating this until two unique tile-choices are determined? Then _those two choices_ are offered the player?