Many new players to Mahjongg find selecting a tile to discard to be one of the most challenging parts of the game. Here is some advice to help you select a good discard tile.
Note that this advice is designed to help you complete a winning hand quickly, it will not necessarily help you get a high score by exploiting the doubles table. Also, this advice does not take defensive considerations into account (much).
Honors tiles (Winds and Dragons) are the best choice for discarding because they are hardest to work with; you cannot make sequences out of them, only Pungs or Kongs ("sets").
#1) Worthless Winds: Any wind that is not your own and not prevailing can be junked. The only thing you might be wary of is discarding the wind that belongs to your neighbor who, on his turn, might pick it up.
#2) Already Discarded Honors: If you draw a Green Dragon and there are already one or two in the discard pile, you can safely discard yours, too.
#3) Singleton Honors: If you have only one of a given honor tile, you can probably discard it. The safest time to do so is early in the game. On the other hand, if you wait for awhile, you might be able to pick up a second to make a pair, and possibly claim the third out of turn for pung. Depends on how lucky you feel.
Naturally, if you are dealt two or more of the same honor tile, hold onto them and use them as the pair for your winning hand. By merry hap, someone may discard a third which you can claim for Pung.
Terminals (1's and 9's) are the second hardest type of tile to work with because you can only make sequences off of one end, making them less flexible than simples.
Note that I do not specify suit in any of these examples, I simply assume that the numbered tiles are all the same suit.
#4) Terminals with no neighboring tiles: If you are dealt the 1, 2, 5, and 9, The 9 should be discarded before the 1 because 1 has a neighbor (the 2) but the 9 does not.
#5) Terminals with neighboring tiles: If you have the 1,2, and 5, most beginners would discard the 5, believing they could easily make a sequence out of the 1-2 combo. If you look at my Winning Combinations page, you'll see that you have only 4 chances of completing the 1-2 sequence (4 3's). However, you have 8 chances of turning the 5 into a double-ended sequence (4 4's and 4 6's). Even after you draw one of those (say, the 4) you still have 8 chances of turning the combo into a chow (4 3's and 4 6's).
Simples (2 through 8) are the easiest tiles to work with because you can make sequences off of both ends. As such, they should be your last choice for discarding.
Again, I do not specify suit in any of these examples, I simply assume that the numbered tiles are all the same suit.
#6) Completely isolated simples: If you are holding the 3, 5, and 8, discard the 8 because there are no tiles even close to it. The 3 and 5 are "far neighbors" because there is a gap between them, but they could go somewhere. The 8 isn't going to do anything for you.
#7) Far-neighbor simples: If you are holding the 3, 4, and 6 discard the 6 because there are 8 chances of completing the 3-4 combo (4 2's and 4 5's) but only 4 chances of completing the 4..6 combo (4 5's). Likewise, if you are holding the 4,6 and draw the 7, keep the 7 and chuck the 4.
#8) Simples closest to a terminal: If you are holding the 4, 6 and 8, discard the 8 because it is closest to a terminal (the 9) which are hard to work with. Likewise, if you are holding the 2, 3 and 4 and draw the 5, keep the 5 and discard the 2 since it will be harder for anyone else to use it.
The bottom line here, is that tiles closer to the middle of a suit are easy to work with (and therefore desirable) and tiles closer to the ends of a suit are hard to work with (and therefore undesirable). Keep the middle numbers because you can probably do something with it. Conversely, don't discard a middle tile because someone else will be able to do something with it. Chuck a terminal or near-terminal tile because it will be hard for you to do anything with it, and hard for anyone else to do anything with it.
Let's see if I can come up with a good example here: Everything in your hand is either a) completed combinations, b) pairs, or c) two neighboring tiles in the same suit (neither of which is a terminal). Let's say that after you've drawn, you hand looks something like this:
|3 White Dragons||2,3,4,5,6 Bamboo||3,3,5,6 Circles||5,6 Characters|
The 3 White Dragons are obviously completed (and worth a double!) so you don't want to break them up. The pair of 3's looks like it might be going somewhere, too. The long run of Bamboo's seems like it could turn into two chows very easily. You have a 5,6 in several suits and it looks like any of them could be completed. Let's examine some of the quandries here...
So, what do you do?
Answer: Looking only at your hand does not give you enough information to make a decision. To help you decide, you'll need to look at the face-up tiles on the table, either the ones people have discarded or the exposed combinations that people have laid down from claiming tiles out of turn.
Looking across the table, you see the following tiles are exposed:
With this additional information, we can now make the following assessment:
With all that in mind, you might rearrange your hand as follows:
|Completed||Completed||Completed||Incomplete, best chance||Incomplete, lower chance||Discard||Next Discard|
|3 White Dragons||4,5,6 Bamboo||pair of 3 Circles||5,6 Characters||2,3 Bamboo||6 Circles||5 Circles|
Now you're two tiles away from winning with good chances.
Of course not. As we've learned skill can play a large part in Mahjongg (developing your hand, observing face-up tiles, looking for best chances), but luck still plays a large part. If you follow my advice in the previous example, you might discard the 6 Character and draw the 7 on the next turn (and grumble loudly as you toss it in the discard pile). One of the lessons Mahjongg teaches you is how not to live with regrets, but to just take the bitter with the sweet.