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 maximize tile efficiency when needed.

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. An isolated 5 can be kept to try and improve the hand's shape. An isolated dora can be kept to increase the value of the hand. An isolated yakuhai can be paired and then ponned.

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), so they are better than penchan.

Toitsu

Main article: Toitsu

Toitsu are pairs - 2 copies of the same tile. Most hands need 1 pair to win. Pairs can be used to create triplets, though, so having multiple pairs can increase efficiency.

Pair

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	/ /	/	/

Mentsu

Main article: Mentsu

Mentsu, or "tile groups", are completed groups of three. They are formed after a joint, pair, or complex joint gains a suitable tile. Mentsu are the strongest group, and it's rarely good to break one.

Sequence	Triplet

Tile acceptance

Main article: Ukeire

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:

Accepts: to enter tenpai

Assuming no tiles have been discarded, this hand's tile acceptance is 16 tiles (4 types * 4 copies/type = 16). If two 1-pin have been discarded, the effective tile acceptance is reduced to 14 tiles.

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). If all four 5-pin and three of the 8-pin are discarded, the wait effectively has an acceptance of 1 tile.

Important concepts

The general ideas of tile efficiency are:

• Discard the tiles that contribute the least to tile acceptance / have the fewest amount of upgrades.
• All else equal, prefer having better acceptance at 1-shanten over any other time.
• Try to get a good wait at tenpai.
• Prefer ryanmen over other types of joints.

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)	/ (8 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. When discarding tiles that are unrelated to your hand, you should normally discard guest winds, then 1s/9s, then 2s/8s. When discarding tiles, you should also keep in mind 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 ponned to instantly gain a yaku and a group, they are more valuable when: 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. Sequences and triplets count as blocks. Joints and pairs count as blocks, too, as they can be turned into sequences/triplets, respectively. 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 worse than 5 stronger blocks).

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, say dora, 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 accepts the same # of types of tile, but some tiles are already in the hand, lowering acceptance.) But once a useful tile is drawn, the hand with 6 blocks has to discard one of the blocks, lowering the efficiency in the future.

# 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. This means that 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 & 6 blocks, discard the penchan to accept a 5, hoping to get a ryanmen.)
• 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).

In isolation, 5 block theory is the best. But, when considering opponents' actions, keeping 6 blocks can be more flexible. If somebody calls a kan on 4-pin while you have 23-pin, the 23-pin becomes much weaker, so you can discard it and be better off than if you just had 5 blocks.

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.

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, as , they accept . This 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 only accepts to complete sequence (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 can be turned into a joint/pair with . A lone can be turned into a joint/pair . Therefore, if you have in your hand, the is extra bad, since it only adds 1-sou to the joint acceptance (making the tile 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 still be decent, since it ends on a ryanmen wait once you reach tenpai, but fishing for the iipeikou will slow down the hand. This shape can also be considered as 2 pairs.

Two pairs

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		(14 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. When open, pairs of tiles likely to be discarded, like guest winds or 1s/9s, are stronger.

When you have too many pairs, it's often best to turn a 'ryanmen + pair' into a normal ryanmen (e.g. from 778, discard a 7 to get 78). Ryanmen are already good to wait on, so they do not need the "improvement" as much. Then, discard pairs that are harder to form triplets/joints. With 6 blocks, discarding a pair outright is good.

If you have 4 pairs you might want to consider chiitoitsu, but if a sequence or triplet forms, you should consider discarding a pair and go for a normal hand (this depends on the rest of the hand). At 5 pairs, you're at 1-shanten for chiitoitsu, so you should likely go for that.

4+ tile complex shapes

These shapes are made out of 4+ tiles.

Sequence + sequential tile

A nobetan is a "sequence of 4 tiles":

Nobetan

It may be tempting to see the 4 or 7 as just an isolated tile. Technically, it is, but it can also be seen as a (45) ryanmen + (67) ryanmen. This shape accepts:

• to create kanchan + a sequence ( + )
• to create ryanmen or better + a sequence ( / + )
• to create a pair. ()

In other words, it is an extremely strong floating tile. The ryanmen acceptance is about twice that of a normal 4 or 7! Therefore, keeping this shape is very powerful if your hand's joints are not entirely composed out of ryanmen-or-better. It's also great to keep if you need a pair (even if your hand has all ryanmens).

Note: When this shape contains a terminal tile (1 or 9), it becomes worse: it's equivalent to a regular 4/6 for ryanmen acceptance, though it's better at completing a pair, and you can chii to create a good shape.

Sequence + middle tile

Nakabukure

Like the nobetan, the nakabukure ("bulging") shape can be seen as a floating 5 or as (45) ryanmen + (56) ryanmen. It accepts:

• to create ryanmen + sequence ( + / )
• to create a pair. ( + )

There's no ability to create a kanchan, so the acceptance is slightly worse than a nobetan. However, the ryanmen acceptance is still about twice that of normal floating tiles. Because this shape nearly guarantees a ryanmen when accepting a tile, it's great if you're going for pinfu. The chance for iipeikou also helps. If your hand's joints are already ryanmen-or-better, there's not much need to keep the bulging shape intact (here, discard the middle tile).

Note: It's good to have a pair when you have a nakabukure. Also, like the nobetan, this shape becomes much worse if it contains a terminal tile.

Extended ryankan

An extended ryankan is basically a ryankan with a sequence in the middle.

Extended Ryankan 1	Extended Ryankan 2

• A can be split into ( + + ) or ( + + ). It combines 2 kanchan shapes, so it is essentially the same as ryankan.

It accepts or to complete the 2nd sequence. Drawing a or upgrades it to a ryanmen.

• A can be seen as ( + ) or ( + + ).

It accepts to complete a second sequence. Discarding 9p is a mistake as it removes acceptance of 8p.

Yaku

Main article: 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.

Sakigiri

Main article: Sakigiri

Sakigiri is the practice of discarding dangerous tiles before opponents reach tenpai. Often, the term "sakigiri" means sacrificing tile efficiency for the sake of better defense.

Even when going for maximum efficiency, it's good to know the idea behind sakagiri. Specifically, when two tiles are equally useless, you should discard the tile that is more dangerous first. Usually the more dangerous tile is the tile closer to the middle.

• Draw:

Assume the red 5-man is unavailable. In this case, the 24-man kanchan is no longer useful to the hand. The hand will discard both 2-man and 4-man once it reaches tenpai. As the 4-man is a middle tile, it is more dangerous, so it should be discarded first.

• Draw:

Here, the 4-man is useful. The hand has a non-ryanmen joint, so you want to keep the 4-man because it could be used to upgrade the hand (if you draw 5-man, you get a 45-man ryanmen, allowing you to get rid of the 68-pin kanchan). Here, the better move is to discard 2-man (or 8-pin).

External links

• Tile efficiency articles
• Mahjong NY article