How to Count Shanten

Shanten is how many successful tile changes a hand still needs before tenpai. On this site, 0 means the hand is already tenpai: one more tile wins. 1 means one tile reaches tenpai. 2 means two. A finished win is −1. That integer is the first step of tile efficiency. The tiles that move it, and the copies still left of those tiles, are ukeire. This page is the ruler. It names the distance. It does not rank wait shapes, and it does not run an expected-value engine or a deal-in model.

The printed number is the minimum of three closed-hand paths: 4 melds + 1 pair, seven pairs, and kokushi (thirteen orphans). There is no ruleset switch on the analyzer. A hand the ordinary group-count calls farther away can print 0 because seven pairs is already tenpai, or print 1 because kokushi is one step away. Whether that minimum is a legal win is a separate sentence, and it is labeled 立直, 国标, or 川麻.

On 13 tiles the question is the number. On 14 tiles the analyzer asks which tile to cut, and every row is the shanten and the hand-only copy-count of the 13 that remain. The shanten drill deals 13 tiles only. Copies on this page are hand-only: four minus the copies already in the hand. Discards, calls, and indicators stay out. A wall you can see is a side calculation, and it lives on the ukeire page.

Every hand below is closed. The caption's integers are the analyzer's. The meld reading is something you do on the tiles. The analyzer returns a number, tile ids, and counts. It does not return a meld diagram, a han total, or a legal-win flag.

What the number means

The drill's buttons are 0 through 6. There is no −1 button and no 7 button. A 13-tile answer of 8 cannot occur while seven pairs is inside the minimum. The worst measured 13 on this page prints 6, and 6 is what the drill grades.

A second convention calls a different integer by a similar name. Li and Yan, in Let's Play Mahjong! (2019), define deficiency 0 as a complete 14-tile of 4 melds and one eye. Yan, Li and Li (2021) extend that definition to 13 tiles: deficiency 1 if some added tile completes the hand, and they call that 13 tenpai. They also write that deficiency is "shanten" in Japanese mahjong. On a hand whose ordinary path is the minimum this site prints, the two integers sit one apart. Their 0 is this site's −1. Their 1 is this site's 0. Their 2 is this site's 1. The tiles that move the hand one step are the same tiles. The integer on the drill is this site's.

A short way to hold the offset: shanten counts draws until tenpai, a replacement count draws until a win, and shanten equals that replacement count minus 1. Use the offset when you read a paper. Answer the drill with 0 for a tenpai 13.

The 2019 bounds are about that other integer. Any one-suit 14-tile in their Mahjong-0 has deficiency at most 3. Any 14-tile in their three-suit set has deficiency at most 6. Mahjong-0 there is 4 melds + 1 pair. Seven pairs, a two-suit restriction, and different scores for different wins are extensions in that paper, not the theorems. Those bounds are not the drill's buttons, and they are not seven-pair or kokushi bounds. This page does not claim any hand below is a worst case of their cost, and it did not run their search. The bound and the drill's 6 are different sentences.

立直 counts exactly these three winning shapes on a closed hand: 4 melds + 1 pair, seven pairs, and kokushi. For a 立直 reader the printed minimum is the structural distance. It is not a yaku check. An open hand with no yaku can sit at shanten 0 and still be unable to win. This page does not score han. A caption that says the number is structural has finished its job. See Riichi Mahjong when the question is han.

Tenpai is 0

Both hands below are tenpai. The first wait is two kinds. The second is the three fills of a five-tile run. The number is 0 in both. The width is Wait Types and Counting Effective Tiles. Width is not a second shanten.

234m is the meld and 67m is the ryanmen. There is no 5m in the hand, so 456m is not a meld yet. 5m completes 67m into 567. 8m completes 67m into 678. The hand holds neither wait, so each kind contributes 4. A reader who answers 1 on the drill is counting steps to the win. By the 2021 definition this 13 has deficiency 1, because adding 5m or 8m completes it. The analyzer prints 0. The drill grades 0.

45678p is two groups, not three. 456+78, or 678+45, each uses one meld and one taatsu. 6p completes 456 and it completes 678, and the list still has 6p once. Five-block theory is where that marking is the whole lesson. Here the marking only has to explain why the number is already 0. Eleven copies is wider than eight. Both hands are the same distance from a win.

One-shanten is 1

One-shanten means one accepting draw reaches tenpai. The win is the step after that. Walk the three steps on this 13, then read the list the steps do not mention.

The head is already 99s. 234m, 567p, and 345s are three melds. The hand is one group short of 4 melds + 1 pair. That shortfall is 1. West and Green Dragon are not groups. They are still accepts, because pairing either of them finishes the fourth group as a pair and leaves the other honor beside it. A third 9s is an accept too, and it is ×2 because the pair is already held. 6s keeps the number at 1 and raises the kind count from 3 to 10. It is the improvement a later section draws. It is not one of the 8 copies. Adding an improvement into the ukeire total is the mistake the ukeire page already forbids. The two lists stay separate.

The shape of the tenpai you would reach, including a shanpon on the two honors, waits for Wait Types. This page stops at the distance.

Two-shanten is 2

Three finished sequences and no pair is two steps, even when four isolated honors look like material.

123m, 456p, and 789s are three melds. East, South, West, and North are floaters. They are also the entire accept list. Pairing any one of them drops the number, because the hand still needs a head, and a new pair is that head. A suited tile does not drop the number. 3p and 7p widen the next list and stay at 2. Counting the four honors as four blocks, and calling the hand close to tenpai, skips the number 2. Leaving the honors off the accept list, because they are not taatsu, skips the printed 12 copies. An isolated tile is not a group. It can still be the tile you need to draw.

The three steps

For a normal hand of 4 melds + 1 pair, read the tiles in this order. Five-block theory is the marking these steps are looking at.

1. Pick a pair candidate as the head, or decide you have none yet. If several pairs exist, keep the reading that leaves the smaller number. Freezing the first pair you see can overshoot.
2. Count groups that are still short of 4 melds + 1 pair. A finished sequence or triplet is a meld. A taatsu is one group toward a meld: a ryanmen (two adjacent tiles), a kanchan (one gap), or a penchan (12 or 89). An isolated tile is not a group. Tiles one number apart are a kanchan, not two floaters. Tiles two apart, such as 1 and 4, are not a taatsu.
3. Stop at four meld-slots. A fifth candidate does not subtract another full step. The shortfall that remains, after that budget, is the ordinary-path shanten.

With a head already chosen, an isolated tile fills a leftover slot only as a single, at the cost of one draw. That is why it is absent from the group count and can still appear on the accept list. Once the four meld-slots and the head are spoken for, the same isolated tile is surplus: it is in the hand, and it is absent from the list.

The three steps are the ordinary path said in words. They are the wrong finished caption in four situations.

• There is no head, and a tile inside a taatsu can become the head. "You still need a pair and a meld" counts two steps. The hand can be one step. The next section measures that.
• More than four block candidates are on the table. The fifth does not subtract a full step. The cap does.
• Two parses exist. Keep the minimum. The six-pair hand later on this page is the sharp case: the ordinary reading is one step, and seven pairs is already tenpai.
• Seven pairs or kokushi is smaller. The published number is that minimum, not step 3 alone.

Honors are not sequenced. Three of a kind is a meld. Two of a kind can be the head, or a pair-shaped block toward a triplet. One honor is isolated, and it connects by becoming a pair. Forgetting honor pairs and honor triplets is a common miss on the Normal drill, which deals honors. No Honor and Two Suit deals have no honors to forget, and they also cannot assemble kokushi, so that path is rarely the minimum there.

No pair, and the number is still 1

The headless shape's name stays on one-shanten. The distance is the lesson here.

123m is a sequence. 45678p and 34789s are each a meld plus a taatsu. No kind is duplicated, so there is no pair to nominate as the head. The sentence "no head, so you still need a pair and a meld, that is 2" overshoots. Pairing a tile inside a taatsu, or completing a taatsu in a way that uses the last slot, reaches tenpai in one tile. The eleven kinds are those fills. The 2021 extension would call this 13 deficiency 2, because one change reaches their tenpai. The analyzer prints 1. Both readings are the same distance to a win. The drill grades 1.

A floating tile that is not an accept

Surplus is a property of the list. "It looks idle" is not the test. Link the marking to five-block theory, and keep the integer here.

345m and 678m are sequences. 23p is a ryanmen, waiting on 1p and 4p. 89s is a penchan, waiting on 7s, with an isolated 4s beside it. East is already the head. The two taatsu fills are the whole list. The isolated 4s is the surplus tile the three-step count refuses to call a group, and the accept list agrees. West, on the one-shanten hand above, is the opposite fact: a floater that is a kind. Floating does not decide. The list decides.

The same number, two widths

The drill accepts 1 for both of the 13s just measured. They are not equal hands.

Thirty-seven against twelve is the same distance. The analyzer's next question, which this page does not answer, is which 13 is wider and what the resulting wait will be. A caption that stops at "both are one-shanten" is complete for this page. A caption that calls them equal hands is not. Counting Effective Tiles builds the copy-count. One-Shanten Discard is what to cut once the number is already 1. Width is not a new shanten.

A finished win is −1

A finished 14 is not a 13 with shanten 0. The tiles already contain the win, so the distance to tenpai has gone past 0, and the site's name for that state is −1. Ask the analyzer about that 14 and it does not print −1. It prints a cut table. Each row is a discard, and the number on the row is the 13 that remains. From a real win, every discard leaves a tenpai 13, so the table is full of 0s. Reading the table's 0 as "this 14 is tenpai" collapses the win and the tenpai into one integer. The table exists so they stay apart.

The drill deals 13 tiles, grades buttons 0 through 6, and has no −1 button. Read −1 as the win you are already holding. Read a 14 as the cut table. An 8-tile or 11-tile fragment can also print −1, because the count is completed with honors that never appear on the screen. The drill does not deal those lengths, and that −1 is not a 13-tile answer.

Four melds and a pair, already complete

Sequences 234m and 567p, sequences 345s and 678s, and a pair of Green Dragon. Fourteen tiles, five groups, nothing left over.

Nothing on this table raises shanten. The sort's first key is already tied across every tile, so copies decide, and 3s and 8s lead at 11. The 13 after cutting 3s is measured below. The other rows are copy totals from the cut table. Their kind lists were not re-measured, so this page does not attach one.

45678s is the five-tile run again, now in sou, with the pair of Green Dragon still the head. The 14 contained two sou sequences. Discarding 3s left one sequence's worth of overlap, and the hand is tenpai. The 14 itself was the win those two sequences already finished.

Seven pairs, already complete

The same gap shows up on a seven-pair win. Seven pairs is a finished shape, so the 14 is −1. The cut table still refuses to say so.

The other six cuts tie this one on the table. They were not each re-measured as a 13, so their waits stay off this page. The pattern is the one this 13 shows: break one pair, wait on that kind, three copies because one tile of the pair is still held. Kokushi has the same 14-versus-0 gap, measured in the kokushi section.

Seven pairs, as its own path

Count this path on its own tiles. A kind with two or more copies is one pair. A triplet is one pair, not two. A quad is one pair, not two. A single fills a pair-slot only after you draw its mate. The ordinary three steps do not see this path, and on the hands below they overshoot.

立直 scores seven pairs. 国标 scores 七对 as a 特殊型, so this path counts there too. 川麻 scores 七对 only on tables that include it. The integers below include the path, because the analyzer always includes it. On a table that omits the pattern, do not publish these integers as if the minimum had been recomputed with the path turned off. This page did not turn it off. The yaku page is seven pairs.

The ordinary reading can still find work. Peel 456 twice, keep 88 as the head, and 11 and 22 are pair-shaped groups toward triplets, with 9m left over. That reading is one step from tenpai. The drill marks 1 wrong. Seven pairs is already tenpai on the 9m, three copies left, so the printed number is 0.

No sequence is available: 2m and 6m do not touch, and 4s does not touch 9s. Take one pair as the head and the other pairs as pair-shaped groups, then stop at four meld-slots. The ordinary shortfall is 3. The printed number is 0, because the sixth pair plus the single North is seven-pair tenpai. The same fact as the man-only hand, with an honor as the wait, so a Normal deal cannot skip it.

Five pairs (22m, 66m, 33p, 44s, 99s) and three singles (South, North, White Dragon). The accepts are "make the sixth pair." Three singles plus five pairs are one step away, because a single is not yet a pair. Six pairs and one single would be the tenpai shape of the previous hand. The three singles are the whole list.

Two paths, one number

When both the ordinary shape and seven pairs are already tenpai, the wait list is every tile that completes the minimum. There is still one number.

A seven-pair-only reading sees the tanki on 8m, which is 3 copies. The printout has 7. 2m and 5m are ×2 because those pairs are already held. Both paths are tenpai, and the list is the union. The shanten drill still scores 0 if the reader saw only one path. The tenpai drill, which asks for every winning tile, does not. Wait Types names the list. Counting Effective Tiles is where "do not add the two paths' copy-counts as if they were two shanten numbers" is the rule. One hand, one minimum, one list.

Kokushi, as its own path

立直 for the pattern. Kokushi wants the thirteen terminals and honors — 1 and 9 of each suit, and East, South, West, North, White Dragon, Green Dragon, and Red Dragon — with one of those kinds paired. A tile that is not one of those thirteen kinds does not count toward the shape. The product counts the path even when the ruleset does not score it. 国标 and 川麻 do not have this win. The sidebars below say that again next to the hands a reader might misread. A called kokushi was not measured. Every string here is closed.

Twelve of the thirteen orphan kinds are present, and 1m is the pair. Red Dragon is the kind that is missing. The wait is that one tile. It is not the thirteen-orphan wait that pairs any of the thirteen. That wider wait shows up as a cut from the 14 below, and this page does not paste a separate string for it.

The terminals and honors are the same set, except Red Dragon is missing and a 5m sits in the hand instead of a second copy of anything. There is no pair. The ordinary group-count on this junk-plus-terminals hand is 8. The printed number is 1, because kokushi is one step away. The 13 kinds are "pair any terminal or honor you already hold, or draw the missing Red Dragon." 5m does none of those. A reader who answers 8 has stayed on 4 melds + 1 pair. The drill grades 1.

Pair of 1m, 2s instead of 9s, Red Dragon still absent. Because a pair of terminals already exists, the path does not want another pair. It wants the two missing kinds. A reader who memorizes "kokushi one-shanten has 13 kinds" from the previous hand will answer the wrong width. The number 1 is the same. The list is not. Eight copies against forty, at the same shanten, is the kokushi version of the width table above.

The kokushi win, and the cut that keeps 39

Thirteen orphans plus a second 1m. That 14 is a finished kokushi, so it is −1. The analyzer prints cuts.

Cutting Red Dragon from this 14 leaves the tanki 13 measured above, 1 kind and 4 copies, waiting on Red Dragon. The other non-1m cuts match that row's 4 copies on the table. They were not each opened as their own 13, so this page does not paste twelve kind lists. Cutting 1m is the best row, at 39 copies. That discard leaves the thirteen-orphan tenpai. The kind list of that remainder is the familiar thirteen-way wait, and this page cites the copy total the cut table printed rather than a second string.

Six, and a hand that is closer

The drill can ask for 6. Six is a legal button. It is the three-path minimum on a 13 with no pair and no two tiles that can form a taatsu. It is not the 2019 deficiency bound. A count that ignores seven pairs reads this hand as farther than 6, and the drill does not grade that larger figure.

1m, 4m, 7m, then 2p, 5p, 8p, then 3s, 6s, 9s, and the four winds. No pair. No two tiles within one rank of each other. The 13 accepts are "make any pair," three copies each, which is the seven-pair step: the first pair you complete moves a hand that has seven single-or-pair slots. The ordinary group-count, with every tile isolated and no seven-pair step, reads this hand as farther than 6. The page's answer is the minimum. The drill grades 6. Kokushi does not pull this one down either: too many of the thirteen orphans are missing, and the suited tiles are not all terminals.

The same 13 is the knitted shape a 国标 reader associates with 全不靠. Under the product it is neither a win nor tenpai. The 国标 section uses this printout again for that sentence. The number 6 does not change.

Odds in man and sou, and 2468p. No honors, no pair. 1m and 3m are a kanchan, not two floaters. The same one-gap link runs through 3–5, 5–7, and 7–9, and through the other two suits. The ordinary path counts those components, so the minimum is 4. Seven pairs is the worse reading on this hand, which is why the minimum followed the groups. "No pairs and no adjacent tiles means 6" fails as soon as a one-gap pair of ranks exists.

Seventy-nine copies at shanten 4 is a wider hand than 39 copies at shanten 6, and it is also a closer hand. The copy-count did not produce the 4. The structure did. Lower shanten still beats a larger count when you compare two different deals. Here you do not have to choose. The closer hand is also the wider one.

Counting after a cut

On 13 tiles the drill asks for the number. On 14 tiles each row is the 13 after that discard. The sort takes a lower number even when the copy-count goes down. Same shanten, then more copies, then more kinds. This page shows the shanten key and one copy gap, then hands the copy-count to ukeire. It does not re-teach ryanmen versus kanchan.

Cut the spare, and reject 27 copies

The first tenpai on this page, plus an isolated 9m.

The spare 9m is the tile that leaves the tenpai already measured. Cutting 6m is also tenpai, and it is half the copies, so it loses the second key. Cutting 7m stays at one-shanten with 27 copies. Twenty-seven is larger than eight, and it is one step farther. The first key ends the comparison. Kind counts were measured for the 9m remainder only. The 4-copy tenpai and the shanten-1 rows stay at the copy totals the cut table printed.

Lower shanten, then 20 against 17

Run 234567m, sequence 345p, 6789s, and an isolated South.

The 7m cut matches 2m at 20 copies on the table. It was not re-measured, so it does not inherit this kind list. The 4m and 5m cuts are the second gap: shanten 1, 17 copies. Their kinds were not re-measured either. The shanten page's job ends at "the numbers match, so the next key is the copy-count." Twenty beats seventeen. Counting Effective Tiles owns how that copy-count is built. One-Shanten Discard owns the discard once you are choosing inside shanten 1. When shanten, copies, and kinds all tie, the remainder is Discard Strategy. That full tie was not measured as its own point here.

An improvement keeps the number

A tile that lowers shanten is an accept. A tile that keeps shanten and raises the kind count is an improvement. The product's test is narrower than "the future wait got prettier." The kind count must rise. At shanten 0 the list is empty. The tenpai hands at the top of this page printed no improvement block. The wait list is the whole story there, and it belongs to Wait Types.

The one-shanten 13 with West and Green Dragon does not contain 6s. 6s is an improvement there, to 10 kinds, and it is not one of the three accepting kinds. Add it.

Cutting Green Dragon ties West at 16 copies on the cut table. It was not re-measured, so it does not inherit West's five kinds. Before the draw, the 13 was shanten 1 with 8 copies. After the draw, cutting West or Green Dragon is still shanten 1 and is 16 copies. Cutting the tile you just drew is shanten 2, and the 37 copies do not save it. That is the operational meaning of an improvement. It is not an accept of the old 13, and it is not the next discard. The 8-copy row from cutting 9s is a copy total only. It is not the old 13, and this page does not attach the old kind list to it.

国标: the special patterns the count does not see

国标. The structural minimum on this site is unlabeled. The sentence about whether 国标 scores that shape is labeled. Association teaching calls a win that is not 4 melds + 1 pair a 特殊型. 型听 is a structural tenpai under the minimum-fan rule. 一向听, in that vocabulary, means one tile from tenpai, the same distance-word as on this page, not a second formula. Fan was not computed here, and 起和番 was not applied to any structural 0. A structural 0 is not "enough fan."

The specials named in that teaching include 七对, which the seven-pair section already counted, and 全不靠, 七星不靠, and 组合龙, which the minimum does not contain. 七星不靠 is the seven honors plus seven knitted tiles from the 147 / 258 / 369 pattern, and no pair. Kokushi, measured above, is a 立直 pattern. It is not a 国标 caption. Do not read the Red Dragon tanki as 国标 tenpai.

The knitted 13 in the shanten-6 section is the shape a 全不靠 plan recognizes: 147m, 258p, 369s, and four winds. The analyzer prints shanten 6, 13 kinds, 39 copies. A 全不靠 plan is not "this hand is ready." The 6 is the seven-pair figure on a hand with no pair yet. It is not tenpai under the product, and this page does not restamp it as a 国标 win.

A 组合龙 shape the cut table leaves at 4

147m, 258p, 369s, a pung of East, and a pair of South. Under the pattern 国标 calls a special win, this 14 is finished. The analyzer does not have that pattern.

The best row is still 4-shanten. The 13 holds two honor pairs and the nine knitted singles, and the accepts are those nine singles, three copies each: make another pair. That is a seven-pair reading of the tiles the analyzer can see. It is not "4 steps from 组合龙," because 组合龙 was never computed. Cutting South is a worse shanten with more copies, 5 against 4 and 30 against 27, which the sort also rejects. The 24-copy rows were not re-measured, so they do not inherit the nine-kind list. Do not stamp a fan total on either row. Do not call the 27 copies 实质进张. Chinese Official Mahjong is the rules page. The number here stays the structural minimum.

川麻: a structural 0 can be an illegal hu

川麻. House rules differ. This reading follows 血战到底-style play: 108 tiles, no honors, no chi, 定缺 before a win is legal, and 查叫 at an exhaustive draw. A z tile in a drill is not a 川麻 tile. Kokushi cannot be a 川麻 path. There is no chi, so do not double a sequence accept, and do not import a 国标 sequence weight. Sichuan Mahjong is the rules page.

定缺: while a tile of the missing suit remains, it is the discard, and the hand cannot win. A structural tenpai whose wait is that suit, with one of that suit still held, is not a legal hu.

The sort already cuts a man. Under 定缺 of man the table rule says the same thing, and the resulting tenpai waits on the man that is still in the hand.

The 9m cut ties 8m at 3 copies. It was not re-measured. The structural 0 is an ordinary tenpai, and it is not a legal hu. The 33-copy one-shanten does not overturn 定缺.

After 定缺 of man is already clear, two suits remain and the wait is not the missing suit.

Pair this 13 with the 8m tenpai. Both print shanten 0. One still holds the missing suit and waits on it. The other has cleared man, and the wait is inside the suits that remain. "Structural tenpai" and "legal hu" are different rows. No chi, so the sequence tiles stay at the printed copies.

Seven pairs is still inside the analyzer on both of these hands. On these two it was not the minimum. A 川麻 caption still has to say "tables that score 七对" before it uses the seven-pair integers from earlier. On a table that does not score 七对, those earlier integers are not a recomputed distance.

查叫 at an exhaustive draw pays a legal tenpai against a hand that is not tenpai. It does not pay "smaller shanten," and it does not pay "wider ukeire." A legal tenpai — shanten 0, missing suit already gone — beats an illegal 0 that only looks closer. During the hand, while tiles remain to be drawn, the sort still prefers lower shanten. 定缺 decides which of those tiles you are allowed to keep.

What to practice

The method is the three steps, then the other two paths, then the minimum. The hands above are the cases where one of those steps is the one people skip.

1. The distance, including 0 and −1, on this page. Tenpai is 0. A finished win is −1. Counting steps to the win marks a tenpai hand as 1, and the drill marks that wrong.
2. Kinds and hand-only copies, in Counting Effective Tiles, once you know which tiles drop the number. An improvement stays on its own list.
3. The cut at shanten 1, in One-Shanten Discard. The isolated tile, when the groups are already chosen, is in five-block theory.
4. A tie on shanten, copies, and kinds, in Discard Strategy.
5. The wait as a shape, in Wait Types, after the number is already 0. Tenpai training asks you to name every winning tile.
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.

Answer the shanten of a 13-tile hand in shanten training. The length stays 13. There is no 7-tile deal and no 10-tile deal. Timed mode is 15 seconds. The buttons are 0 through 6, or the same keys. Normal includes honors. No Honor is man, pin, and sou. Two Suit is man and pin. The deals are real suits, not a one-suit hand recolored into three. The answer is the minimum of 4 melds + 1 pair, seven pairs, and kokushi. No Honor and Two Suit cannot build kokushi, so that path is rarely the minimum there.

The misses this page is built to prevent are the ones the drill sees most: calling tenpai 1, counting steps to the win, forgetting honor pairs and honor triplets on Normal, and looking at only one of the three paths. At shanten 0, go name the waits. At shanten 1, go select the ukeire. The integer stays here.