Up until now Master Tile has been available in a one-player version for iPhone. When introducing Master Tile HD for iPad the game is expanded to take advantage of the fact that the screen real estate of the iPad device is perfect for allowing dual players.
When competing against a fellow player you will not only need to plan for how to resolve the different patterns in the smartest way. You also need to consider that your opponent may ruin your plans if resolving the patterns before you do. This is forcing you to take rapid actions and to be prepared to re-plan and reroute.
Master Tile HD also contains an additional two-player possibility which allows you to just play along-side of you co-player if you do not dare to jeopardize your relationship...