Five-Block Theory

Five-block theory is a way to look at a hand that wins as 4 melds + 1 pair. Those five groups are the finished shape. Before the hand is finished, a block is a completed meld, a taatsu, or a pair. An isolated tile is not a block. You mark the groups on the tiles. The analyzer does not return a block label. It returns shanten, the accepting kinds, and the copies still left of those kinds.

The frame around the marking is tile efficiency. The distance is How to Count Shanten. The count is Counting Effective Tiles. On 14 tiles this site sorts a cut by lower shanten, then more ukeire copies, then more ukeire kinds. Copies are hand-only: four minus the copies already in the hand. Discards, calls, and indicators stay out of that subtraction. Every integer below is that hand-only printout.

Marking five blocks usually points at the same cut the sort keeps. It parts from the sort when a classroom rank would keep the block the sort cuts, when a lower shanten sits on a wait the plan dislikes, or when a ruleset forbids the tile the sort wants to hold. Those three partings are later on this page. The marking is a scaffold you draw. The caption's integers are the analyzer's.

A kong, where the ruleset has one, is still one meld. Every hand below is closed. Seven pairs, thirteen orphans, and the 国标 special patterns that are not 4 melds + 1 pair sit outside the scaffold. They are named where they appear.

What you mark

On 13 tiles, mark in this order.

1. Completed melds, sequences or triplets. Pull them out first.
2. One pair you are willing to call the head, if a pair exists. A second pair is a meld candidate. The finished hand has one head.
3. Taatsu for the meld slots that remain. Four meld slots is the cap. A ryanmen, a kanchan, or a penchan is one taatsu. A fifth taatsu is a candidate you will drop, not a sixth requirement.
4. Whatever is left, once those groups are chosen, is the leftover. On a 13, call it surplus only when it is also absent from the accepting list.

Tile count checks a bad marking. Four melds and a pair are 14 tiles. On 13 tiles the same five groups are tenpai: one tile completes the last meld, or pairs a single. A one-shanten 13 that really has five groups therefore has the fifth group unfinished and, usually, one tile in none of them. Or it has no pair yet, so the five groups are all on the meld side. Or a short complex is doing the work of two groups: a five-tile run is one meld plus one taatsu, and 455 is a pair joint with a ryanmen. If your boxes need six groups to use every tile, one of those groups is the one a later cut removes.

123m and 456p are melds. 12s is a penchan. 68s is a kanchan. 99s is the pair, and it is already the head. That is five groups, twelve tiles. West is the thirteenth, and it sits in none of the five. 3s fills the penchan. 7s fills the kanchan. A third 9s does not drop shanten, because the head exists. West does not drop it either. Present, and absent from the list: that is surplus on this hand.

The next 13 keeps the same two melds and the same 99s pair, and then fails the block test. 1s, 5s, 8s, East, and North make no ryanmen, kanchan, or penchan with each other.

37 is larger than 8, and the hand is two steps farther from tenpai. More copies at a worse shanten is not "more blocks." While real blocks are still missing, you compare the isolated tiles with each other. You do not break a taatsu you do have in order to tidy a tile inside it. The wider number belongs to the hand that still has to build the groups.

立直 early-hand teaching ranks an isolated suited tile by how many sequence accepts it can grow: tiles nearer the middle outrank 2 and 8, which outrank 1 and 9, which outrank a guest wind. A guest wind only pairs. Two suited tiles three apart share accepts, and 1–4 and 6–9 are the sharp cases. Two tiles four apart are not a reason to hold both. Those are sequence facts. They apply in any ruleset that builds sequences. The 立直 extra is value honors and defense: a valueless wind is the usual cut while junk remains, and a value honor is kept while other junk can go, because calling it is speed. 川麻 has no honors, so that wind sentence has nothing to attach to. A z tile in a drill is not a 川麻 tile.

A finished marking is tenpai

Two 13s are already one tile from 4 melds + 1 pair. Each five-tile run is two blocks, a meld plus a taatsu, and the hand is already tenpai. A marking that calls the run three blocks has invented a group the tiles do not contain.

789m is a meld. The North triplet is a meld. 99s is the pair. 23456p is one meld plus one taatsu: 234+56, or 456+23. Both readings are two groups. The wait is the three-sided fill of that run. Wait Types is where the shape of a tenpai wait is named. This page stops at the cut that reaches tenpai.

789m, the West triplet, the 11p pair, and 34567s as meld plus taatsu. Same distance, same copy total, the shared kind counted once. The run is two blocks either way you split it.

Surplus, and the cut that breaks a taatsu

Draw to 14 and the question is which tile leaves. 123m and 456p are melds. 34s and 78s are ryanmen. 99s is the pair. 9m does not touch 123m. East touches nothing. Both sit outside those five groups.

The two winners tie on shanten, on copies, and on kinds. The sort keeps both. It does not prefer the honor over the terminal. A 立直 defense aside may still cut East first on that tie. Another 立直 aside keeps the wind for a later safe discard and throws a suited tile it judges even deader. Neither aside is in the table. The table is silent. The choice that remains, once the three keys match, is Discard Strategy.

The boxes on the 14 put East outside the five. After 9m goes, a different reading still uses East: pairing it drops shanten, which is why East×3 is on the list. The scaffold and the list answer different questions. Surplus, on a 13, is the stricter test from the first hand. West there is in the hand and absent from the list. East here is in the list. Call it an accept.

Cutting 9s is the quiet loss inside shanten 1. The pair is gone, 6s leaves the accepting list, and 17 falls to 14. Cutting 4s or 7s breaks a taatsu, raises shanten, and the larger copy total loses on the first key. The tiles to measure first are the ones outside the five.

Same shanten: keep the five-tile run

789m is a meld. 23456p is two blocks. 12s is a penchan. 99s and the North pair are a head and a triplet candidate. Four cuts on this 14 show 15 copies. They are not the same cut. Kinds break the tie. Counting Effective Tiles is the kind-count page. Two cuts still tie after kinds, and that remainder is Discard Strategy.

3p, 5p, and 6p are also 8 copies on the cut table. Kinds below are the 2p remainder only. 7m and 8m are shanten 2 with 23 copies. 4p is shanten 2 with 20. More copies, worse shanten, same rejection as the 45-copy cut above.

Cutting the penchan keeps the run. 1p, 4p, and 7p are the run. 9s and North are the two pair-upgrades. The penchan was the weak block. The two pairs were the head and a triplet candidate. That is the five-block reading that matches the sort.

The 9s remainder and the North remainder print the same four accepting kinds. Only the North remainder has an improvement list. Improvement means shanten stays and the kind count rises. Those rows are a second list. They are not added to the 15. The sort has already dropped both cuts, because 4 kinds loses to 5.

15 against 8 is the block choice, at the same shanten. 5 kinds against 4 is why "all the 15s" are not one cut. The best cuts are 1s and 2s only.

One kind, counted once

A tile that completes two readings is still one line. The copies are four minus the copies held, not four times the number of parses. Overlapping Taatsu is the shape page. This page only needs the count.

This is the 13 after cutting 2s from the run hand. It matches the 13 after cutting 1s, kind for kind. The sou tenpai above is the other run: 5s×3 fills 345s and 567s, and it is one row there too.

立直 teaching calls two taatsu that accept the same kind an overlap, and treats removing that overlap as the speed line when a cut can do it. The caption can say the two readings share a kind. It cannot add the copies. A four-tile run such as 4567 can be marked as two ryanmen, or as one meld plus a spare. Both markings are legal. The cut decides which one the 13 keeps. There is no single official parse to memorize.

Two pair candidates

4455m is two pairs on adjacent tiles. 67889s is a meld-side complex. 123p is a meld. East-East is a pair. 立直 block teaching treats a pair that can grow into a wide wait as stronger than an isolated pair whose only accept is the two remaining copies. This hand measures that idea as a connected pair-complex against an honor pair. The sentence is 立直. The integers are the sort.

6s, 8s, and 9s are the next rows at shanten 1 with 14 copies. Only the 9s remainder was re-measured: five kinds, 3m×4, 4m×2, 5m×2, 6m×4, East×2, and one improvement, 8s to 6 kinds. Do not hang that kind list on 6s or 8s.

Cutting 5m leaves 445m and the same shape on the other side: 3m×4, 4m×2, 6m×4, 7s×3, East×2. Five kinds, 15 copies. The two best cuts tie on every key.

Thinning 4455 leaves the joint and keeps East as the other pair. Cutting East keeps both man pairs and narrows 15 to 7, a loss of 8 copies at the same shanten. The honor pair is the head you can spare only after the complex has been thinned. On this hand it is the expensive cut. A 川麻 opening estimate ranks a pair above a ryanmen, because a live pair can be punged and a kong scores. The printout does not multiply a pair by four. A pair already in hand contributes two copies on that kind, four minus two. The estimate is 川麻 pedagogy. It is not this ladder.

A floating honor

The test is the accepting list. A tile in none of the five, and absent from that list, is surplus. A tile the list still contains is an accept, even when it is an honor, even when a classroom habit says "cut the wind."

On the first 13, m123 p456 s126899 z3, the five groups are 123m, 456p, the 12s penchan, the 68s kanchan, and 99s. West is the floating honor. It is not one of the two kinds. There is no cut to make on a 13. The job is the mark.

On the 14, m1239 p456 s347899 z1, East ties 9m at shanten 1 and 17 copies. Both are floaters outside the five. The 立直 defense sentence, a dead suited tile can go before the wind so the wind stays safe, is one reading of that tie. The sort itself has no preference.

The contrast is the East pair from the previous section. Cutting that East costs 8 copies at shanten 1, 15 against 7. There the wind is a pair block. Here, on the 14 with one East and one 9m, the wind is a floater and a best cut. "Always cut the wind" fits neither row. 立直 guest-wind advice is a label on top of the list. It does not survive a tie, and it does not survive a list that still needs the wind.

No pair yet, and a pair already chosen

Once a cut leaves shanten 1, width and the resulting wait live on One-Shanten Discard. This page owns why the blocks were chosen before that step. The shape names used in 立直 classrooms stay on that page. The table below is these three hands, not a ranking the analyzer returns as a law.

A pair already chosen narrows the list. Completing a taatsu drops shanten. Pairing a tile inside that taatsu usually does not, because the head exists. The first hand is that shape: shanten 1, 2 kinds, 8 copies, only 3s and 7s. 1s and 2s are in the hand and are improvements, not accepts. Pairing inside the penchan does not drop shanten once 99s is the head. West is surplus.

No pair yet is wider. Completing a taatsu drops shanten, and pairing a tile inside a taatsu drops shanten too.

The triplet is 444p. 789m and 123s are melds. 34m and 67s are ryanmen. Five meld-side groups, no head. Same shanten as the pair-locked 8. The gap is the missing head, plus ryanmen instead of a penchan and a kanchan. It is not a constant to memorize. A concealed triplet is why a 立直 reading expects the resulting waits to be ryanmen more often than a single-tile wait. This page does not re-teach that wait.

A pair plus two floaters is the third width. The floaters are not taatsu yet. They are still not surplus when they appear in the accepting list.

Three man melds, pair 22p, floater 4s, floater Red Dragon. Red Dragon connects only as a pair, three copies because one is held. 4s connects toward 2s through 6s. The man draws keep shanten at 1 and raise the kind count. They are improvements. They stay off the 24.

5s and 8s are three apart. Both can use 6s, and both can use 7s. Each of those kinds is one line. 24 and 28 are both "a pair and two floaters." The honor floater is the narrower of these two. Do not add a private maximum for 5s to a private maximum for 8s.

Reaching one-shanten with the blocks already chosen is why the marking exists. Acceptance usually shrinks as shanten falls, so the step from one-shanten into tenpai is the narrow one on an average hand. Five-block is the early pass that tries to arrive there with four meld-holders and a head candidate, rather than with six weak groups or with three groups and a pile of floaters. It is not a second shanten number.

A floater beside a real taatsu

Fewer blocks than you want means you compare the floaters. You do not break a real taatsu to "clean" it. This 14 is that cut, measured at shanten 2.

12m is a penchan beside 567m. 23p is a ryanmen, and 6p is isolated. 34s is a ryanmen. 89s is a penchan. North is the only pair.

6p is not a taatsu. Cutting it keeps the penchan. Cutting 1m breaks the penchan and drops 24 to 20 at the same shanten. Kinds for the 20-copy row are the 1m remainder. 2m, 8s, and 9s were not re-measured. 立直 teaching, on a different shape, says that at two-shanten with one meld, one head, and four taatsu and no floater, the default is to drop the weakest taatsu. This hand has a real floater. Do not treat it as that diagram. The measured order is the floater, then the penchan, then the pair, and shanten outranks the larger number.

Penchan, kanchan, and the sort

立直 classrooms often rank a taatsu by accepts first, then by how easily it upgrades: ryanmen, then a ryanmen-kanchan compound, then kanchan, then penchan. When two kanchan share a count, they keep the one that upgrades more easily. 川麻 opening pedagogy ranks a pair above a ryanmen, then a kanchan, then a penchan, and when accepts tie it compares the upgrade. Kanchan above penchan, in both of those teachings, is an upgrade preference. This site does not own that key. Equal copy counts stay tied until the kind count differs. A draw that only improves a future wait, without a new kind, is invisible to the sort.

The next 14 is the measured miss. Melds 123m and 456p, penchan 12s, kanchan 68s, pair 99s, pair West. The sort breaks the kanchan.

"Drop the penchan, keep the kanchan" is the wrong instruction on this hand. 8s and 9s are also 8 copies on the cut table. They were not re-measured, so they do not inherit the 1s kind list. A separate 立直 sentence says that once you have committed to five blocks, you attend to the weak one: a strong shape needs no follow-up tile, and a weak taatsu does. That is advice about the next draw. It is not a discard mode here, and it does not replace the three keys. On this hand those keys cut 6s out of the kanchan.

The 13 below is the tie those classrooms argue about. The accept line itself does not break.

123m and 456p are melds. 12s is the penchan. 57s is the kanchan. 99s is the pair. East is isolated. The penchan and the kanchan contribute the same four copies. A 立直 or 川麻 aside may point at 5s, the kanchan's upgrade, ahead of 1s and 2s, the penchan's pair-ups, inside that improvement list. The aside is labeled. The accepting line is a tie. This site does not sort the hand by those improvement rows. The improvement list is a second list, and a row qualifies only when the kind count rises.

国标: the block the tenpai uses

国标. The structural table is the same ladder. Fan is not computed. The Canada MCR association's glossary, in its 2020-07-16 lecture, uses 实质进张 for a structural accept that advances the core fan, and 无关第四组 for the group that is neither that fan nor the head. Five-block still counts the unrelated group as a block. The fan plan can be the reason to drop it even when the sort keeps it. Chinese Official Mahjong is the rules page. This section does not score a hand against it.

Chi exists in 国标. An association equivalent that multiplies a pair by four and a sequence by two is their teaching weight. It is not the number the analyzer prints.

123p, 456p, and 789p are melds. White Dragon is the pair. 458s is a 58 kanchan with a 4 beside it. The sort takes 8s and reaches tenpai through sou.

For a half-flush in pin plus honors, 3s and 6s are structural ukeire, and they are not 实质进张. The 45s taatsu is the unrelated fourth group on that reading, and it is also the group the sort keeps in order to reach tenpai. The association's name for structural tenpai under the minimum fan is 型听. This page does not stamp that name with a fan total.

32 is the trap for a reader who ignores shanten. Eight copies at tenpai outrank 32 copies at shanten 1. And the 32 is not a pile of 实质进张 for a pin plan. One kind in that list, White Dragon, stays inside the plan. The other eight are sou.

Terminals are a second 国标 fork. All-simples and all-groups-with-a-terminal are opposite instructions. A 立直 habit that throws 1 and 9 first is the wrong default on a terminal-groups plan. Name the plan by its fan. The association's own taatsu note, that a kanchan upgrades and a penchan takes two steps, is the same labeled preference as the previous section. Their rule of thumb about giving the upgrade up when another block has more effective tiles is theirs. It is not a constant in the sort.

国标: three triplets, and a sequence wait

国标, with all-pungs as the plan. The structural table is unlabeled. Fan is not computed.

111m, 222p, and 333s stay. Breaking a finished triplet is 6 copies or 5, not 13. Five-block and the sort agree on that part.

The structural best cut keeps the pung blocks. The wait at 13 copies is not a pung-only list. That is the whole claim. The fan plan sits beside it, unnamed by a total.

川麻: 定缺 discards a block

川麻, 血战到底-style. 108 tiles, no honors, no chi. A sequence completes by draw. Once the missing suit is declared, a tile of that suit is discarded before any other tile, and the hand cannot win while one remains. Sichuan Mahjong is the rules page. House rules differ. The hands below follow that missing-suit rule. They do not choose among 血流, tile exchange, or a must-win rule.

A ryanmen, a kanchan, a pair, or a finished meld in the missing suit is not a block you keep. Choosing the suit at the start is a different sentence: the shortest suit is the usual choice, and a connected 345 can be a reason to leave that suit off the declaration. After the suit is named, the tiles go.

The sort already cuts a man. Under 定缺万 the rule says the same thing for a different reason. 46m is a real kanchan, and it is still the missing suit. The 33-copy line is not a reason to cut a pin or a sou while a man remains.

The next 14 is where the sort and 定缺 disagree. 345m is a completed block.

The best structural cuts are 4s and 8s, and that tenpai still holds 345m. 定缺万 discards a man even though 345 is a finished meld, and even though the man cuts are shanten 1. One man cut does not finish the job. The 3m remainder still holds 4m and 5m. The missing suit keeps leaving until it is gone. The connected-345 reason belongs to the moment before the declaration. This hand is the moment after 定缺万 is already declared.

川麻: after the missing suit is gone

Two suits only. If 定缺 is man, it is already clear. No man, no honor. No chi, so a sequence accept is a draw. Do not double it. The 国标 sequence weight does not apply.

2345678p and 345678s are meld-holders inside the two kept suits. The 9 is the structural count. Set it next to the illegal tenpai above, m6 p234567 s234567, which waits on 6m×3 while a man is still held. Structural tenpai and a legal hu are different rows.

血战 continues after a player wins. At exhaustive draw, 查叫 pays a tenpai hand against a hand that is not tenpai. It does not pay "wider ukeire." Once the missing suit is gone, a two-suit tenpai is tenpai for that comparison. The nine copies are not a second score.

Seven pairs is not five blocks

There is no meld to mark, and there is no head-plus-four to draw. Do not put five boxes on this hand.

立直 includes seven pairs. 国标 lists seven pairs among the special patterns, the wins that are not 4 melds + 1 pair. 川麻 includes it only on tables that score it. Some 血战到底 tables score it. Others omit it. Chiitoitsu is the 立直 pattern. The integers below are the count this site prints, which includes the ordinary win of 4 melds and a pair as well as seven pairs. A ruleset with seven pairs turned off needs a different measurement. This page did not recompute one.

Pairs 11, 22, 33, 44, 55, and 77, plus a single 6m. The count keeps both wins.

The widest tenpai breaks a pair. A seven-pairs habit that throws the singleton and keeps every pair takes that 3-copy tanki and loses the 8-copy wait. A five-block habit has nothing to mark, which is the point: the scaffold does not apply, and borrowing it would not have found the 7m cut either.

On a table without seven pairs, do not read these integers as if the count had been recomputed with that pattern removed.

Lower shanten beats a thicker run

The last pitfall is polishing a five-tile run because an edge looks ugly. 34567m is the run. 123p is a meld. 789s has a spare 9s. South is the pair.

7s, 8s, and 1p are shanten 1 with 19 copies on the cut table. 2p and 3p are shanten 1 with 15. They were not re-measured.

Five-block, read on the tiles, also cuts 9s. It is the tile that is not one of the five. The reader who breaks the run to fix its edge walks into shanten 1 with a larger number and loses. Lower shanten beats the thicker run. The same rejection showed up as 17 against 45, as 15 against 8, and as 24 against 54. The copy total is the second key. It does not buy back a step.

What the marking does not decide

The ladder does not score all-simples, pinfu, dora, a minimum fan, all-pungs, a half flush, or a missing suit. Those readings were labeled when they changed the cut. A dora indicator, a red five, or a riichi declaration can pull a 立直 hand off the widest line. This page has no fixed "give up two copies for a dora" amount, and it does not run an expected-value engine or a deal-in model.

The ladder does not see the pond. Four copies of a kind already visible delete that kind from a live count. The printout cannot see them. Unseen copies can still sit in other hands or the dead wall, so a pond subtraction, when you do it by hand, is an upper bound. None of the captions above applied one.

The ladder does not prefer kanchan to penchan when both are four copies. That preference is the upgrade teaching in the penchan section, 立直 and 川麻, labeled. The improvement list on this site is the narrower test: shanten stays, and the kind count rises.

The ladder includes seven pairs and thirteen orphans in its minimum. A 川麻 or 国标 caption must not treat a missing-suit tile, or a z tile, as a legal win just because it appears in the list. The illegal tenpai and the two-suit tenpai are the pair to keep.

Open melds and calls are outside these hands. Chi, pung, and a 国标 call-weight are labeled sentences. They are not measured accepts on this page.

What to practice

The marking tells you which tiles are groups and which tile is outside them. The sort tells you whether cutting that outside tile actually wins on shanten, then copies, then kinds. Name the ruleset before you play past the numbers.

1. The distance, including 0 and −1, in How to Count Shanten. Fewer real blocks often means more steps. The integer is the shanten of the hand, not the number of empty boxes.
2. Kinds and hand-only copies, in Counting Effective Tiles. One kind once, including a tile that fills two readings. The overlap shape is Overlapping Taatsu.
3. The cut at shanten 1, in One-Shanten Discard. Wide and narrow shapes at that distance live there. This page is how the hand became wide or narrow.
4. A tie on shanten, copies, and kinds, in Discard Strategy. 9m against East, and 1s against 2s, stop there.
5. The wait as a shape, in Wait Types, after the cut has reached tenpai.
6. The table. Riichi Mahjong, Chinese Official Mahjong, or Sichuan Mahjong. A 立直, 国标, or 川麻 sentence travels only into the ruleset it names.

Enter a 13 or a 14 in the analyzer and mark the melds, the taatsu, the pair, and the leftover yourself. The printout will confirm shanten and the accepting tiles. It will not draw the boxes.

Discard training is the cut. The deals are man flush. The counted answer is the discard that leaves the most winning tiles, and a copy tie keeps every cut at that count. The drill does not draw the five boxes, and it does not grade a block label. When 15 copies splits into 5 kinds and 4 kinds, the kind key on this page is the one that separates them. Use the analyzer for that third key.