@@ Line 1: / Line 1: @@
 '''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
+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==
@@ Line 9: / Line 9: @@
 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 [[naki|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.
+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 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 [[pon]]'d.
 ===Taatsu===
@@ Line 15: / Line 15: @@
 {| class="wikitable" width=40%
-|-
+!Type !! align=center| Ryanmen !! align=center| Kanchan !! align=center| Penchan
-!Type
-| align=center| Ryanmen || align=center| Kanchan || align=center| Penchan
 |-
 !Incomplete
@@ Line 26: / Line 24: @@
 |}
-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).
+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|Toitsu}}
-'''Toitsu''' are pairs. Most hands need 1 pair to win. Pairs can be used to create [[triplet]]s, though, so having multiple pairs can increase efficiency.
+'''Toitsu''' are pairs - 2 copies of the same tile. Most hands need 1 pair to win. Pairs can be used to create [[triplet]]s, though, so having multiple pairs can increase efficiency.
+{| class="wikitable" width=15%
+! align=center| Pair
+|-
+| align=center| {{#mjt:11p}}
+|}
 ===Complex joints===
@@ Line 36: / Line 40: @@
 {| class="wikitable"
-|-
 !Type
-| align=center| Ryanmen + Pair || align=center| Kanchan + Pair || align=center| Ryankan
+! align=center| Ryanmen + Pair !! align=center| Kanchan + Pair !! align=center| Ryankan
 |-
 !Incomplete
@@ Line 51: / Line 54: @@
 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 of tiles ''that can be drawn'' to advance the hand.
+[[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 available to draw. 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.
+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==
+The general ideas of tile efficiency are:
+*Discard the tiles that contribute the least to tile acceptance / have the fewest amount of upgrades
+*Try to get a good wait at [[tenpai]]
+*Prefer ryanmen over other types of joints
-==Isolated tile utility==
+===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:
 {| class="wikitable"
-|-
 !Type !! Pair !! Ryanmen !! Kanchan !! Penchan !! Total
 |-
@@ Line 69: / Line 75: @@
 |-
 !1 & 9 ({{#mjt:1p}})
-|{{#mjt:1z}} (3 tiles) || 0 tiles || 0 tiles || {{#mjt:2p}} (4 tiles)) || 7 tiles
+|{{#mjt:1p}} (3 tiles) || 0 tiles || {{#mjt:3p}} (4 tiles) || {{#mjt:2p}} (4 tiles) || 11 tiles
 |-
 !2 & 8 ({{#mjt:2p}})
-|{{#mjt:2p}} (3 tiles) || {{#mjt:3p}} (4 tiles) || 0 tiles || {{#mjt:1p}} (4 tiles) || 11 tiles
+|{{#mjt:2p}} (3 tiles) || {{#mjt:3p}} (4 tiles) || {{#mjt:4p}} (4 tiles) || {{#mjt:1p}} (4 tiles) || 15 tiles
-|-
-!3 & 7 ({{#mjt:3p}})
-|{{#mjt:3p}} (3 tiles) || {{#mjt:2p}} / {{#mjt:4p}} (8 tiles) || {{#mjt:5p}} (4 tiles) || {{#mjt:1p}} (4 tiles) || 19 tiles
 |-
-!4 & 5 & 6 ({{#mjt:5p}})
+!3 thru 7 ({{#mjt:3p}})
-|{{#mjt:5p}} (3 tiles) || {{#mjt:4p}} / {{#mjt:6p}} (8 tiles) || {{#mjt:3p}} / {{#mjt:7p}} (8 tiles) || 0 tiles || 19 tiles
+|{{#mjt:3p}} (3 tiles) || {{#mjt:2p}} / {{#mjt:4p}} (8 tiles) || {{#mjt:1p}} / {{#mjt:5p}} (8 tiles) || 0 tiles || 19 tiles
 |}
-Therefore, for pure tile acceptance, a lone 4/5/6 >= lone 3/7 > lone 2/8 > lone 1/9 > lone guest winds. This is before considering mechanics like furiten and dora. With [[red fives]] in play, 4/5/6 become stronger than 3/7 due to being able to create ryanmen with a red five.
+Therefore, for pure tile acceptance, a lone 3/4/5/6/7 > lone 2/8 > lone 1/9 > lone guest winds. Therefore, 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 [[pon]]'d to instantly gain a yaku and a group, they are more valuable when both these conditions are met: 1. the hand would not have any yaku if opened, and 2. the hand does not have an obvious "4 groups + 1 pair" yet. In an average starting hand, they are more valuable than 1/9 but less important than 2/8.
+[[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).
+"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. Pairs are also considered a block, since they can be turned into a triplet. 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:
 * {{#mjt:12367m23p334s334z}} can be split into:
-* {{#mjt:123m}} (group) + {{#mjt:67m}} (joint) + {{#mjt:23m}} (joint) + {{#mjt:334s}} (complex joint) + {{#mjt:33z}} pair - 5 blocks
+* {{#mjt:123m}} (group) + {{#mjt:67m}} (joint) + {{#mjt:23m}} (joint) + {{#mjt:334s}} (complex joint) + {{#mjt:33z}} (pair) - 5 blocks
-* {{#mjt:4z}} is an isolated tile which does not add anything to the hand.
+* {{#mjt:4z}} 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:
 {| class="wikitable"
-|-
 !# Blocks !! Hand !! Tile acceptance
 |-
@@ Line 118: / Line 120: @@
 {| class="wikitable"
-|-
 !# Blocks !! Hand !! Draw !! Discard !! Tile acceptance
 |-
@@ Line 140: / Line 141: @@
 **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.)
 *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 {{#mjt:45s}} ryanmen accepts ({{#mjt:36s}}). A {{#mjt:78s}} ryanmen accepts ({{#mjt:69s}}). Combined, they accept {{#mjt:369s}}, 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 {{#mjt:56p}} ryanmen accepts {{#mjt:47p}}. A {{#mjt:568p}} shape also accepts {{#mjt:47p}} (and {{#mjt:58p}} if you need a pair). Therefore, the {{#mjt:8p}} isn't doing much when you have already have {{#mjt:56p}} and a stable pair elsewhere. If you don't have a pair, the 568 is decent to keep.
+*A lone {{#mjt:4s}} can be turned into a joint/pair with {{#mjt:23456s}}. A lone {{#mjt:1s}} can be turned into a joint/pair {{#mjt:123s}}. Therefore, if you have {{#mjt:14s}} in your hand, the {{#mjt:1s}} is extra bad, since it only adds 1-sou to the joint acceptance (making the tile just slightly better than a guest wind).
+*A {{#mjt:2233m}} shape can be treated as two separate {{#mjt:23m}} ryanmen. However, they both accept the same tiles ({{#mjt:14m}}), so doing this isn't as efficient. The shape can be decent, since it has 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:
+{| class="wikitable"
+!# Pairs !! Shape !! Tile acceptance
+|-
+|1 || {{#mjt:22p00000000000z}} || 0 tiles
+|-
+|2 || {{#mjt:22p22m000000000z}} || {{#mjt:2p2m}} (4 tiles)
+|-
+|3 || {{#mjt:22p22m33s0000000z}} || {{#mjt:2p2m3s}} (6 tiles)
+|}
+{| class="wikitable"
+!# Pairs !! Shape !! Tile acceptance
+|-
+|1 || {{#mjt:23m22p78s0000000z}} || {{#mjt:14m69s}} (16 tiles)
+|-
+|2 || {{#mjt:23m22p778s000000z}} || {{#mjt:14m2p689s}} (20 tiles)
+|-
+|3 || {{#mjt:223m22p778s00000z}} || {{#mjt:124m2p689s}} (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. Pairs of tiles likely to be discarded, like guest winds or 1s/9s, are better.
+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
+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.
+==4+ tile complex shapes==
+These shapes are made out of 4+ tiles.
+===Sequence + sequential tile===
+A nobetan is a "sequence of 4 tiles":
+{| class="wikitable"
+! align=center| Nobetan
+|-
+| align=center| {{#mjt:4567p}}
+|}
+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:
+*{{#mjt:29p}} to create [[kanchan]] + a sequence ({{#mjt:24p}} + {{#mjt:567p}})
+*{{#mjt:3658p}} to create [[ryanmen]] or better + a sequence ({{#mjt:34567p}} / {{#mjt:456p}} + {{#mjt:67p}})
+*{{#mjt:47p}} to create a pair. ({{#mjt:44567p}})
+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 much worse. It's still good if you need a pair, but the ryanmen acceptance is halved, equal to a regular floating tile.
+===Sequence + middle tile===
+{| class="wikitable"
+! align=center| Bulging
+|-
+| align=center| {{#mjt:4556p}}
+|}
+Like the nobetan, the "bulging" shape can be seen as a floating 5 or as (45) ryanmen + (56) ryanmen. It accepts:
+*{{#mjt:3647p}} to create [[ryanmen]] + sequence ({{#mjt:345p}} + {{#mjt:56p}} / {{#mjt:44556p}})
+*{{#mjt:5p}} to create a pair. ({{#mjt:456p}} + {{#mjt:55p}})
+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 bulging shape. 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.
+{| class="wikitable"
+! align=center| Extended Ryankan 1 || Extended Ryankan 2
+|-
+| align=center| {{#mjt:245679p}} || {{#mjt:455679p}}
+|}
+* A {{#mjt:245679p}} can be split into ({{#mjt:24p}} + {{#mjt:567p}} + {{#mjt:9p}}) or ({{#mjt:2p}} + {{#mjt:456p}} + {{#mjt:79p}}). It combines 2 kanchan shapes, so it is essentially the same as ryankan.
+: It accepts {{#mjt:3p}} or {{#mjt:8p}} to complete the 2nd sequence. Drawing a {{#mjt:5p}} or {{#mjt:6p}} upgrades it to a ryanmen.
+* A {{#mjt:455679p}} can be seen as ({{#mjt:456p}} + {{#mjt:79p}}) or ({{#mjt:45p}} + {{#mjt:67p}} + {{#mjt:9p}}).
+: It accepts {{#mjt:368p}} to complete a second sequence.
 ==Yaku==
 {{main|Yaku}}
-'''At least one yaku is required to win a hand'''. Therefore, yaku are certainly a key factor for tile efficiency. Having a yaku means you don't need to [[riichi]] for a yaku, which means you can call tiles, which allows you to complete tiles faster than a closed hand would. When you need to complete a fast hand, confirming a yaku is important. Of course, sometimes it's best to stay closed for the value.
+'''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 [[Renchan|repeat the hand]].
+==Sakigiri==
+{{main|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.
+* {{#mjt:24m12345p5789s22z}} Draw: {{#mjt:4s}}
+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.
+* {{#mjt:24m12368p5789s22z}} Draw: {{#mjt:4s}}
+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 ==

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