Tile efficiency
Tile efficiency refers to the speed of hand development. Having better tile efficiency means that the hand is more likely to complete, and is thus faster on average.
Only one person can win per round, and a hand of any value can win. Therefore, learning how to optimize tile efficiency is important to improving at riichi mahjong. Sometimes, it may not be best to go for the maximum efficiency play (e.g. slowing the hand to go for a yaku), but strong players should know how to reach maximum tile efficiency
Tile categories
Tiles can be grouped into a few basic categories:
Isolated
Isolated tiles, also known as "lone" or "floating" tiles, are those with no neighbors. A tile is isolated when there is no tiles numerically or categorically adjacent. Therefore, they may not be used for tile calls.
These tiles are not very useful, so they are often discarded first. However, an isolated tile may be used to "upgrade" the hand. For example, an isolated 5 can be used to improve the hand's shape. An isolated dora can be used to increase the value of the hand. An isolated yakuhai can be paired and then pon'd.
Taatsu
Taatsu 「塔子」, or "joints"/"shapes", are two tiles that can create a sequence. These resemble the basic wait patterns:
| Type | Ryanmen | Kanchan | Penchan |
|---|---|---|---|
| Incomplete |   |
 |
|
| Complete | /  |
|
|
All else equal, a ryanmen is twice as good as the other joints, because they accept twice as many tiles. Kanchans can be upgraded to ryanmens (e.g. 24-pin, after drawing 5, turns into 45-pin).
Toitsu
Toitsu are pairs. Most hands need 1 pair to win. Pairs can be used to create triplets, though, so having multiple pairs can increase efficiency.
Complex joints
Complex joints are a joint made up of 3 tiles. When the joint is completed, two tiles are used in the group, and the third tile becomes isolated.
| Type | Ryanmen + Pair | Kanchan + Pair | Ryankan |
|---|---|---|---|
| Incomplete | |
|
|
| Complete | / / |
/ |
/
|
Tile acceptance
A hand's shanten measures how far a hand is from tenpai. A hand that is 1-shanten is 1-away from tenpai, a hand in 2-shanten is 2-away from tenpai, and so on.
Ukeire, or tile acceptance, measures how many tiles can be used to reduce a hand's shanten. For example, a hand may have a tile acceptance of 40 tiles, meaning that there are 40 different tiles that can be drawn to advance the hand. The hand may have 10, 14, 16 distinct types of tiles that improve the hand, but "tile acceptance of 40" means there are 40 tiles that can physically be drawn.
Note: when measuring tile acceptance in actual games, it is important to note the amount of tiles actually available. Any tile discarded, used in your hand, used in an opponents call, or in the dora indicators can no longer be drawn, which affects the hand's tile acceptance. For example, a 67-pin ryanmen joint normally has an acceptance of 8 (four 5-pins; four 8-pins). However, if all four 5-pin and three of the 8-pin are discarded, the wait effectively has an acceptance of 1 tile.
Important concepts
Isolated tile utility
Some isolated tiles are better than others. By measuring the # of tiles that can turn an isolated tile into a joint/pair, we can measure how useful they are.
In order of least useful to most:
| Type | Pair | Ryanmen | Kanchan | Penchan | Total |
|---|---|---|---|---|---|
Wind ( )
|
(3 tiles) |
0 tiles | 3 tiles | ||
| 1 & 9 ( )
|
(3 tiles) |
0 tiles | (4 tiles) |
(4 tiles) |
11 tiles |
| 2 & 8 ( )
|
(3 tiles) |
(4 tiles) |
(4 tiles) |
(4 tiles) |
15 tiles |
| 3 thru 7 ( )
|
(3 tiles) |
/ (8 tiles) |
(4 tiles) / (4 tiles) |
0 tiles | 19 tiles |
Therefore, for pure tile acceptance, a lone 3/4/5/6/7 > lone 2/8 > lone 1/9 > lone guest winds. This is before considering mechanics like furiten and dora. With red fives in play, 4/6 become stronger than 3/7 due to being able to create ryanmen with a red five.
Yakuhai are a special case. Because they can be pon'd to instantly gain a yaku and a group, they are more valuable when these conditions are met: 1. the hand would not have any yaku if opened, 2. the hand does not have an obvious "4 groups + 1 pair" yet, and 3. creating a triplet is possible (less than 2 copies are visible). In an average starting hand, they are more valuable than 1/9 but less important than 2/8. Yakuhai are a bit stronger in tonpuusen due to its faster paced nature.
Dora can greatly boost the value of the hand - a dora pair turns a 2000 point hand into a 7700 point one. Keeping the dora might not be the best when going for pure tile efficiency, but they can be good to keep if you need the value.
Five-block theory
"Five-block theory" states that a standard winning hand has five "blocks" - four groups + one pair. Each joint and sequence in the hand is considered a block. Since pairs can turned into triplets, each pair is also a block. When a hand has 6 blocks, one of them will eventually need to be discarded. Thus, it is good to build hands with 5 blocks in mind (i.e., having 6+ blocks is redundant).
Example hand split into blocks:
can be split into:- (group) + (joint) + (joint) + (complex joint) + (pair) - 5 blocks
- is an isolated tile which does not add anything to the hand. If it were useful, it could be treated as a 6th block.
To see why 5 blocks is important, look at these example 2-shanten hands:
| # Blocks | Hand | Tile acceptance |
|---|---|---|
| Hand with 5 blocks |        
|
    (24 tiles total, not counting the tiles in the hand)
|
| Hand with 6 blocks |  
|
 (28 tiles total)
|
The hand with 6 blocks has a better tile acceptance right now, since it can accept 28 tiles total. (Note: the 5 block hand can accept the same # of types of tile, but since some of the tiles are used in the hand, the acceptance is lower. In this case, 2/4 of the 3-sou tiles are used in the hand, so they can't be drawn, so accepting 3-sou equates to only +2 tiles of acceptance.)
However, once a useful tile is drawn, the hand with 6 blocks has to discard one of the blocks, lowering the efficiency in the future.
Example 1-shanten hands:
| # Blocks | Hand | Draw | Discard | Tile acceptance |
|---|---|---|---|---|
| Hand with 5 blocks | |
|
|
(20 tiles total)
|
|
| ||||
| Hand with 6 blocks | |
|
|
(16 tiles total)
|
|
|
As the hand reduces in shanten, its tile acceptance is also reduced. So going from 1-shanten to tenpai is the slowest part of hand development. Therefore, it's better to improve tile efficiency at 1-shanten than 2-shanten - the returns are bigger. In this example, the 5-block hand is 15% worse (24/28 tiles) at 2-shanten, but 25% better (20/16 tiles) at 1-shanten.
For this reason, aiming for 5 blocks is generally better for tile efficiency.
- That being said, having 6 blocks is better than 5 blocks with 2 useless isolated tiles. A 6th block is redundant, but better than useless. When you have excess blocks, you can discard one when:
- You can upgrade one of your joints (e.g. turning a 45 ryanmen joint into a 445 complex joint).
- You enter 1-shanten.
- You have multiple kanchan/penchans and you get an isolated middle tile. (E.g. with 79 kanchan + 12 penchan, discard the penchan to accept a 5, hoping to get a ryanmen.)
- When discarding the 6th block, discard the weakest block you have (the one that improves tile acceptance the least). For example, if deciding between a penchan and ryanmen, discard the penchan. If you have two blocks of 23-man + 56-man, they have "duplicate acceptance" on the 4-man, so discarding one of those only leads to a loss of 4 tiles of acceptance.
- You may want to keep 6 blocks when aiming for a yaku, such as pinfu or sanshoku.
- Sometimes, there may be multiple different ways to interpret a hand's blocks (e.g. 5568 can be seen as 556 + isolated 8, or 55 + 68).
Duplicate acceptance
When two joints and/or isolated tiles accept the same type of tile, they become worse for tile efficiency.
- A
ryanmen accepts ( 
). A 
ryanmen accepts ( 
). Combined, they accept , which is 4 tiles worse than having 2 separate ryanmen joints. If you happen to draw a 6, you do you get the 3-sided 45678 sanmenchan, but these 2 ryanmen are overall weaker than 2 unrelated ryanmen.
- A
ryanmen accepts 
. A 
shape also accepts (and if you need a pair). Therefore, the isn't doing much when you have already have and a stable pair elsewhere. If you don't have a pair, the 568 is decent to keep.
- A lone accepts
. Having a lone 
accepts . Therefore, if you have in your hand, the is extra bad, since it only adds acceptance of 1-sou (just slightly better than a guest wind).
- A shape can be treated as two separate ryanmen. However, they both accept the same tiles (
), so doing this isn't as efficient. The shape can be decent, since it has a ryanmen wait once you reach tenpai, and you can make either 2-man or 3-man into a triplet. But fishing for the iipeikou will slow down the hand.
Two pairs theory
A hand needs 1 pair to win. If the hand's only pair turns into a triplet, you'll need to make a pair elsewhere, or break the triplet later. When you have 2 pairs, either pair can be turned into a triplet freely, thus increasing tile acceptance by 4. When you have 3 pairs, one extra pair can be turned into a triplet, increasing tile efficiency by only 2. Therefore, keeping 2 pairs (ideally 1 as part of a 'ryanmen + pair' complex joint) is strong. Refer to the following tables:
| # Pairs | Shape | Tile acceptance |
|---|---|---|
| 1 |  |
0 tiles |
| 2 | |
(4 tiles)
|
| 3 | |
(6 tiles)
|
| # Pairs | Shape | Tile acceptance |
|---|---|---|
| 1 | |
  (16 tiles)
|
| 2 | |
(20 tiles)
|
| 3 | |
(22 tiles)
|
When you are likely to pon one of the triplets (e.g. yakuhai pair), then keeping 3 pairs can be good, since you'll be at 2 pairs once you make the pon.
Also, when you have an open hand, keeping pairs is relatively stronger than normal. This is because you can pon with any player's discard, but chii can only be done to the player to the left. Triplets of tiles likely to be discarded, like guest winds or 1s/9s, are better.
If you have 4 pairs you might want to consider chiitoitsu, but if a sequence or triplet forms, you should probably discard a pair and go for a normal hand. At 5 pairs, you're at 1-shanten for chiitoitsu, so you should likely go for that.
Yaku
At least one yaku is required to win a hand. Therefore, yaku are a key factor for tile efficiency. Having a yaku means you don't need to riichi to gain a yaku, which means you can call tiles, which allows you to complete faster than a closed hand would. When you need to complete a fast hand, getting a yaku is very helpful. Of course, sometimes it's best to stay closed for the value.
In other cases, players may end up simply having tenpai in mind, especially as the hand nears the later discards. This is of particular concern for the current dealer, who may have an interest in retaining the position and repeat the hand.