Play to win: Mahjong Titans

1. The major constraint is that you can not see the lower tiles until you have peeled away the upper tiles. You can't move these 'covered' tiles.
2. There is an important secondary constraint: you can not move a tile when it is hemmed in on both sides by other tiles.  Think of these tiles as 'covered' from the side.

What should you do:
Of course, because of (1), you must try to get to the lowest level of tiles and eventually remove all the tiles. Dig vertically. 
Also, be strategic because of (2): when you see a long row of tiles with strong dependencies, focus on that row. Dig/Chisel/Peel horizontally too. 

Course of attack in Mahjong Titans

For example, in the Fortress layout, you will lose the game unless you focus almost absolutely on the two long rows of tiles.  If instead, you just pair tiles as they come, you will end up with several unpaired chunks/layers at the end of the game (i.e. loss of game).  Rule (2) is utterly important in Fortress.

I think it is also of the utmost importance in Spider, which has two super-long rows (focus on these), and then one other long row (the thin red arrow above the other two) where you should source for free tiles before considering other (largely freestanding) tiles.

(2) is also very important in Dragon, which is crowned with a super-long row of tiles.  You must focus on that row, and then also the two tricky bottom rows.  Secondarily, consider the two short half-rows.  Avoid the free-standing tiles as much as possible.

(2) is less important in the other layouts:

To solve Turtle: You can see why it's called a turtle: it has a hard shell on top - attack that, circled in red, very early or you may never win the game because the heart of the layout is buried layers deep.  It has a head and tail sticking out, cut those off early too.  First thing you should do in Mahjong Turtle, try to pair the top tile (circled), the and the three other tiles blocking progress (at the head and yansh).  There are also two long rows at top and bottom that you must peel back.  Turtle is a balancing act.  It was the first layout I played (previously I had a computer that had just this layout, back in the day).  I just matched tiles more-or-less randomly, although I noted the top two layers on the shell as well as the edge tiles.  I don't recall how much I won then. (Note: NEW Strategy for Turtle here, with very high win rate guaranteed) 

To solve Cat or Crab, it takes some Turtle skills (balance width with depth) and some rule (2) skills (don't leave long rows).  However, these are so easy that you could win without thinking about strategy.  Truly.

Anyhow,  in Crab, focus on two important long rows and the big belly, you should not focus on the small sections. Cat has a big region and a small region, so focus on the big region to some extent.  

I want to talk about other rules but they are less important and can wait till next time.  I am also dying to tell you why I think getting smarter at playing the "hard" layouts made me dumber at playing Turtle.
Footnote:  In a way, the gross strategy for playing a given game is to follow the rules of the game i.e. start pairing tiles in Mahjong. The finer strategy, then, is to discover what makes it nearly unsolvable (or nearly lost) and then combat that.  
For another example, I recently started playing chess: gross strategy - move in the allowed patterns, take hostages preferably big ones, take the king's head;  finer strategy (think what happens late in the game) : the queen is a vicious bitch so get your opponent's out, pawn promotion by your opponent is bad for you so frustrate the frisky pawns, etc.

Advertisement: Read my books.