There are many valid strategies that can be used to play Mah-Jongg. Some of these strategies apply only to Chinese Mah-Jongg, and some apply to other forms as well.
1. Many beginners think they are doing well if they're making lots of melds (Chows, Pungs, Kongs) - they don't realize that melding is an onerous duty, not a sign of success! If you watch experienced players, you will see that they do not necessarily grab the first Chow opportunity that comes along, for several reasons:
a. It shows the other players three tiles that you have collected; opponents can learn more about your hand by the melds AND discards than they could from the discards alone.
b. It narrows the opportunities for the hand you are building (having made one Chow, you would be wise to make the rest of your hand all Chows and/or all the same suit).
c. Chow hands are not necessarily the best - with Pung hands, you aren't limited to the suit, you can also use Winds and Dragons.
2. Experienced players even think twice about grabbing available tiles to make a Pung or Kong. In general, don't take somebody else's discard unless you have a clear plan for your hand and that discard advances the hand closer to a Win.
3. Keep a Pair. It's harder to make a pair if you have only one tile than it is to make a Pung if you have a pair. So if you have a pair, don't be too quick to claim a matching tile to form a Pung.
4. Have patience. When first learning to play, it's typical to grab every opportunity to meld a Pung or Chow. In the early stages of a game, you should instead keep in mind that there are a lot of good tiles available for drawing from the Wall. By not melding your tiles, you don't clue everyone in to what you're doing, and you stand a chance to get a concealed hand.
5. Be flexible. As you build your hand, be ready to abandon your earlier thinking about how to build it as you see what kind of tiles others are discarding. If you are playing Western Mah-Jongg with restrictions on winning hands, don't be too quick to form your only Chow; there will be other chances.
6. Don't let someone else win. As much as you want to go out yourself, sometimes it's wiser to keep anybody else from winning. Especially, you don't want to "feed" a high-scoring hand. If a player has melded three sets of all one suit, that's especially dangerous (you might feed a Pure or Clean hand, and have to pay a high price); thus the player announces the danger when making a third meld in one suit.
7. Watch the discards and watch the number of tiles in the Wall. As it approaches the end (the game will stop when there are fourteen tiles remaining), the tension increases and it's more important to be careful what you discard when there are fewer tiles remaining to be drawn. If the number of tiles in the Wall is getting low, don't discard any tiles which you do not see in the discard area.
8. The "1-4-7 rule" is a good playing strategy (for all forms of MJ except American in which there are no chows). If the player to your right discards a four, and you don't have another of those to discard, you /might/ be all right if you discard a one or a seven. Remember that these number sequences are key: 1-4-7, 2-5-8, 3-6-9. Between any two numbers in these sequences there can be an incomplete chow; if a player throws one number, then that player probably does not have a chow that would be completed by that number or the number at the other end. Discarding tiles IDENTICAL to what another player discards is always good, if you can.
9. Keep in mind the profound difference between terminals ("ends," ones and nines) and simples ("non-ends," twos through eights). By their very nature, terminals can be used in far fewer potential melds. Therefore, if it is too early to form a strategy, get rid of a few terminals, and your hand will usually take shape enough to form a strategy. Most good players often go for an "all simples" hand or a "many terminals" type hand. Keep an eye on your opponents' discards to try to discern which they're doing. This will help you late in the game where you have a choice between several potentially dangerous discards - remember that the terminals are usually in less demand. Most one-away hands are not waiting for terminals.
10. Learn the three stages of a MJ hand.
Opening: DEVELOP your hand by removing unrelated tiles. Keep your options open; much depends on what you draw.
Middle game: ATTACK by deciding on a goal (are you going for all Pungs or a Pure hand, for instance), and build your hand towards that goal.
Endgame: DEFEND your game by making sure no one else wins. Your great hand will be useless if someone else wins!
11. Be mindful of your wind and the prevailing wind. Hang onto those winds in the early part of a hand until you can see that they're hopeless or your hand is shaping another way. Your wind (when it's not the round wind) may well be safe to discard. If a pair of dragons has already been thrown, the third and fourth are probably safe to discard (it's rare, but not unheard of, for someone to go out waiting for a dragon pair). Keep it to use later when it's getting dangerous.
12. Go for the high-scoring combinations (pure, clean, and if applicable, special hands). You only need a few high-scoring hands to win the game.
13. Watch the discards and try to figure out what other players are holding. Remember that other players can do that too.
14. If you're using Flowers and playing for minimum fan scores, watch your Flowers. If you have the right Flowers, you can go out with an otherwise chicken hand if necessary. Be aware if it's possible for anyone to get a bouquet (all four Flowers, or all four Seasons). It might affect your plan.
15. Try to go out waiting for multiple tiles (not just one). Imagine that you have three complete sets and two pairs. One pair is dead (its fellows are already on the table) and the other pair is Two Bams, and you draw a Three Bam from the wall - which tile do you discard now? In this situation, many experienced players will discard one of the Two Bams, keeping a Two Bam and a Three Bam. A One or Four Bam will complete the chow, and the hand. A two-way call is better than a one-way call because it gives you more chances to win. As you improve your Mah-Jongg skills, you will learn numerous patterns that give you multiple chances to win, such as the following. In these examples, it is assumed that the rest of the hand is complete, and you need only one tile to complete the hand.
Tiles in hand - Win with:
2224 ---------- 3 or 4 (two chances)
2223 ---------- 1 or 3 or 4 (three chances)
22234 RR ------ 2 or 5 or R (three chances)
23456 --------- 1 or 4 or 7 (Note: "1-4-7")
2223344 ------- 2 or 3 or 4 or 5 (four chances)
2223334 ------- 2 or 3 or 4 or 5 (four chances)
2223444 ------- 1 or 2 or 3 or 4 or 5 (five chances)
2223456 ------- 1 or 4 or 7 ("1-4-7"), or 3 or 6 (five chances)
1112345678999 - Any number (nine chances) ("Heavenly Gates")
There are also more complicated calling patterns -- you can learn them and make them, increasing your chances for a win.