Beginner tile efficiency: Beginning with the tile distribution

Source: http://blog.jpmahjong.net/read.php/504.htm

Tile efficiency is a skill that allows you to win in the fastest time. In Japanese mahjong, winning as fast as possible means quickly making [4 mentsu + 1 jantou + 1 yaku]. Therefore tile efficiency is about thinking in this direction, discarding the tile that gives you the smallest probability in making a mentsu, and increasing the probability of making a mentsu as much as possible.

In fact, tile efficiency is already useful at the start of the game.

Facing this typical hand, how should you deal with it?

Priorities in tile discarding
The tile efficiency here is simple, just discard the most useless tile. What do you mean by most useless tile?? Isolated guest wind tiles are the most useless, because you can't make shuntsu with them, you can only wait to make a pair with them, which has a low probability. What you need to note is, a single tile of your seat wind or round wind is a different story. As long as you can pon with it, you can clear the 1 yaku requirement. You can also chi others' tiles afterwards. Therefore it's value far surpasses the value of guest wind tiles.

After guest wind tiles, it's isolated 1 or 9 tiles. If you're using them, they will most likely turn into kanchan or penchan. However with the hand above, the value of 1 pin is lower than 9 pin, the reason is because of the 4 pin. Even if you discard 1 pin and draw 2 or 3 pin, they can form a mentsu with 4 pin without wastage. On the other hand, if you discard 9 pin and draw 7 and 8 pin, you'll have wasted a tile. In this example, the value of 1 pin is on the same level as isolated guest wind tiles due to 4 pin. 

In simple terms, the order of tile discarding is as below:
1. Isolated guest wind tiles, isolated 1 or 9 when there is 4 or 6
2. Isolated 1 or 9 tiles
3. Isolated yakuhai
4. Isolated 2 or 8 tiles
5. Isolated 3-7 tiles, penchan tiles
Note: The order of 3-5 may differ for different hands.

Here's some more examples

1 pin is the most useless here, discard it first. With this kind of bad shape, discarding chun is a bad move.

Discarding sha is the correct move. Despite the presence of 4 wan, 1 wan here will be viewed as an isolated 1 or 9 tiles as 456 is already a mentsu.

Translation:
4 mentsu + 1 jantou: mentsu refers to shuntsu or koutsu groups (Example 234, 555 etc)
Jantou is a Japanese mahjong term, equivalent to Cantonese mahjong's eyes.