What Is Tile Efficiency

Tile efficiency ranks the 13 tiles left after a cut. The order is fixed. Lower shanten wins. At the same shanten, more ukeire copies win. At the same copy count, more ukeire kinds win. The shared winning shape behind that distance is four melds and one pair. Seven pairs and kokushi enter only as alternate distances, and only the minimum is printed.

Han, fan, dora, and safety sit beside those three keys. They move with the ruleset. This site keeps a hand-only copy count: four minus the copies already in the hand. It has no expected-value engine and no deal-in model. A visible tile on the table is a recount you do yourself.

The ranking ladder

Every 14-tile row is one candidate cut. The sort reads the 13 that remain.

An improvement is a different list. It keeps the same shanten and raises the kind count. The default ranking never reads it. Two cuts that tie on all three keys stay tied. Wait shape, yaku, dora, and danger are how you choose inside that tie, or how you deliberately leave the ladder.

The shanten scale

Shanten is how many successful changes stand between the hand and tenpai. The counting method, including the minimum over four melds plus a pair, seven pairs, and kokushi, is in How to Count Shanten.

Tenpai is 0, and a win is −1

A finished 14-tile hand is −1. Li and Yan, in Let's Play Mahjong! (2019, arXiv:1903.03294), define deficiency 0 as that completed 14-tile of four melds and one pair. Yan, Li, and Li (2021, arXiv:2108.06832) then call a 13-tile that one added tile can finish a deficiency of 1, and they identify the word with Japanese shanten. On a hand whose ordinary path is the minimum this site prints, their 0 is this site's −1 and their 1 is tenpai. The tiles that move the hand one step are the same tiles. A replacement count that runs all the way to the win sits one above this site's shanten. Drills and the analyzer use the table above.

There is no ruleset switch on the number. Riichi can win on the same three closed paths the minimum already searches. Chinese Official adds patterns the trainer does not search, and a structural tenpai under the 8-fan floor still may not win. Sichuan play, after you name the missing suit, uses meld-and-pair distance in the suits you keep. The printed three-suit figure is the abstract count until that void is gone.

Shanten first

Read the distance before you admire a long list. Eight live copies at tenpai outrank thirty-six copies at one-shanten.

456789m is two sequences, and 345p is a third. The sou tiles 278 and the White pair are the part the cut changes. Dropping 2s leaves a two-sided 78s. Dropping 8s leaves 27s, which is not a taatsu, and the accept list explodes across the sou suit plus White. That explosion is still one-shanten. The ladder spends the short tenpai.

2s and 7s are held once, so those two kinds contribute three copies each. White is held twice, so it contributes two. None of that width changes the first key. The same comparison shows up again when a single cut reaches tenpai and a neighbor stays one-shanten with a fat list: the tenpai row is the result.

Only live copies count

Ukeire is every kind that reduces shanten. The copy total is in Counting Effective Tiles. At shanten 0 the same list is the wait. Names for those shapes are in Wait Types.

1. On 14 tiles, drop the candidate and measure the 13 that remain.
2. Read shanten.
3. Test each kind the hand holds fewer than four times. A kind that lowers shanten is ukeire.
4. For those kinds only, add four minus the copies already held.

A kind held four times is never tested. Copies already in the hand shrink their own kind. They do not shrink a different kind.

6789m is a nobetan. Drawing 6m makes pair 66m and sequence 789m. Drawing 9m makes sequence 678m and pair 99m. Each end is already held once, so the copies are three plus three, not the eight of an empty ryanmen. The Red triplet is a Riichi yakuhai on either wait, and a dragon pung is fan under Chinese Official. The caption is the width. It is not a han total or a fan total. Sichuan has no honors, so this 13 is not a Sichuan win.

The quad of 9m blocks that kind even if a story about the shape seems to want another 9m. West is ×3 because one West is held. 7s is ×2 because the pair is held. The 23 improvement kinds sit outside the 13 copies. They keep shanten at 1 and only change the next kind count.

Count each accepting kind once

A tile that repairs two blocks is still one kind. Record it once, then multiply by the copies still left. Overlapping Taatsu is the block picture. The ladder never doubles a row because two readings mention it.

Two readings share the 13. Pair 77m plus ryanmen 67m waits on 5m and 8m, with the Green triplet as a meld. Triplet 777m plus a tanki waits on 6m. The union is three kinds. 6m belongs to the tanki reading, it is held once, and it occupies a single row at ×3. A count that added the tanki and then added 6m again would invent a copy.

Sequence 456m plus pair 55m, together with the West pair, is a shanpon on 5m and West. Triplet 555m plus kanchan 46m, with West as the pair, waits only on 5m. Both stories accept 5m. The hand already holds three 5m, so the shared kind contributes one copy. West contributes the other two, and only the shanpon uses it. The kind key sees two kinds, not three.

Kinds break a tie in copies

The third key runs only after shanten has tied and the copy count has tied. A one-copy gap never gets as far as the kind count. A zero-copy gap does.

6m, 3m, and South are the same distance and the same 19 copies. 6m has six accepting kinds and the other two have five. That single extra kind is the whole decision. Cuts that drop to 15 copies, or to 12, lose on the second key before anyone compares their kinds.

The leaders tie on every key, so the ladder will not pick 2m over 5m. One step down, 6p and 8p both offer 12 copies at one-shanten, and 6p's four kinds beat 8p's three. 4p's 58 copies are real and useless for the sort: they are two-shanten. The next section is that trap on its own.

A bigger count at a worse shanten loses

If you only remember one failure mode, remember this one. A two-shanten row can print a number that looks like "most of the wall." It still loses to a one-shanten row with a dozen copies.

Four cuts tie at one-shanten. Each leaves 12 copies of three kinds. 4p and 7p print 58 copies and 17 kinds at shanten 2. The first key ends the comparison. The biggest copy count on the chart is the row that loses.

Cutting 9p leaves 23467m as sequence 234 plus ryanmen 67, so the tenpai is 5m and 8m, eight copies, two kinds. Cutting 7m keeps a wide one-shanten of 35 copies. Eight copies is under a quarter of that list, and it still ranks first. Speed to shanten 0 is the product. Width is how you choose among ways to get there.

Tied cuts and all-tenpai hands

Once every candidate is tenpai, shanten has nothing left to say. Copies, then kinds, sort the waits. When those tie as well, wait quality is an overlay. For sequence hands the shared sense is that a ryanmen is a kinder locked wait than a kanchan, a penchan, or a tanki. Riichi pinfu pays han for a ryanmen. That han does not transfer to Chinese Official or Sichuan. The copy count does.

Either cut leaves 34567m untouched, plus a sou sequence, 456p, and the South pair. The wait is the sanmenchan 2m, 5m, and 8m. One 5m is already held, so the 11 copies are 4+3+4. The two discards match on shanten, copies, kinds, and the actual wait. Wait quality cannot split them. Suit danger can. The ladder will not.

The Red triplet, the pair of 5p, sequence 456s, and the six-tile man run give every discard a finishing tile. The sort still has a winner: 2m and 7m, each a three-kind wait of 11 copies. Narrower tenpai rows remain tenpai and rank lower. "Everything is ready" is a description of the first key. It is not a reason to ignore the second.

Cutting one South leaves a South triplet, sequences 789p and 456s, and 3456m. That four-in-a-row is a nobetan: 3m and 6m, each already held once, three copies plus three copies. Cutting 3m or 6m is still shanten 0, and the accept list is empty. The shape completes on another South, and all four South are already in the hand, so that kind is never tested. A tenpai with zero copies loses to a tenpai with six. After the keys have picked South, the overlay is the wait you actually locked: a two-kind nobetan.

Improvement tiles are not accepts

An accept lowers shanten. An improvement does not. On this site an improvement is a draw that keeps shanten and raises the number of ukeire kinds. A draw that only adds copies inside the same kinds is invisible. A draw that only sweetens a future wait, with no new kind, is invisible. The Chinese Official teaching term 改良进张 is wider than this list. The mechanism here is the kind count. It stays out of the copy sum and out of the default sort.

Those 46 copies are kinds that drop the 13 from one-shanten toward tenpai. They are the second key. Calling them "improvements" mixes the two lists. The cut is South because that row wins the ladder, not because a side list got longer.

The accepts are 3m, 6m, 9m, 3p, 6p, and East. 4p and 5p are already in the hand as 45p. Another copy of either one keeps shanten at 1 and moves the kind count from 6 to 14. They are absent from the 20. A player who "counts 4p as ukeire because the shape likes it" has moved a tile from the improvement list onto the accept list.

The accepts are 2p, 5p, East, and South, twelve copies. The only improvement is 7m. Drawing it keeps the distance and adds a fifth kind. Everything else either drops shanten, does nothing the list records, or is one of those four accepts. Small improvement lists are normal. An empty one is normal too.

Recount against the live wall

Drills and the analyzer score the hand-only figure. Melds, discards, and dora indicators are a table recount. Subtract a visible copy from that kind's remaining four. A kind with nothing left drops out of the list. Unseen copies can still sit in other hands or the dead wall, so the recounted number is an upper bound on what you can still draw, not a new analyzer mode.

34567p is a five-tile run, so the wait is the sanmenchan 2p, 5p, and 8p. The only held wait is 5p, which is why that kind is ×3. The pair of 8s is a different suit, so the 8p wait stays at four. The recount spends two of the four 2p and three of the four 8p. The three kinds survive. Show all four 2p on the table and that kind leaves the list. Both the copy count and the kind count fall.

Same width on the hand-only count, different suit. 45678p is the sanmenchan. The second recount is the edge the first one did not show: a kind at zero remaining copies is gone, not "zero but still a kind." Do the subtraction at the table. Leave the printed 11 as the hand-only baseline.

Dora and yaku over width

The ladder does not price dora, and it does not price han. Riichi gives a closed hand a yaku by declaring riichi. A dama win, closed and undeclared, needs a yaku in the shape. Red fives and the dora indicator have no fixed exchange rate against copies. The trainer still marks the wider row when the three keys say so. You may keep the dora on purpose. You should know which key you gave up.

Green is a single tile beside 2345m, 45678p, and the split sou 1279. The best row throws it and stays two-shanten with 49 copies. Keeping it, because the indicator makes Green dora, means taking some lower row on purpose. That cost is real and unpriced. There is no formula here that converts one dora into a number of copies.

The best cuts keep both sou taatsu, 12s and 89s, and open the pin run. Those terminals block Riichi tanyao. Cutting them stays at one-shanten and gives up 7 copies and 2 kinds against the 20-copy row. All Simples is also a Chinese Official fan pattern. The ladder still will not pay for it. Take the thinner row only when that yaku or fan is the plan you are actually playing.

Each of those five leaves a two-kind tenpai of eight copies and keeps the Green triplet. They tie with one another. Cutting a Green is a worse tenpai, so the copy count already protects the triplet. Riichi yakuhai is the overlay you still need when a true tie includes one cut that breaks a scoring pair and another that keeps it. On this deal the keys and the yaku point the same way, and the five leaders remain tied. Choose among them by the wait you want to lock and by the tile you are willing to throw. Pinfu's han for a ryanmen is Riichi only. All five are two-sided, so pinfu does not split them either.

Defense over width

While another seat may be tenpai, the tile you throw matters. The sort ignores the other seats. It will rank a narrow tenpai above a wide one-shanten, and it will tie three honors that are not equally safe. See Discard Strategy. The printed copy count stays. Refusing it is a judgment, not a fourth key.

Cutting 8s leaves a shanpon on 2m and Green, two copies plus two copies. Green is a Riichi yakuhai. The 2m wait needs a yaku of its own, which a riichi declaration supplies and a dama hand may lack. Cutting 2m refuses that tenpai and keeps a 41-copy one-shanten. If 8s is the dangerous discard, defense takes the slower row and says so. The ladder's winner is still 8s.

The three honors match on every key. Each of those cuts is one-shanten, eight copies, three kinds, and the other two honors stay in the accept list along with 5s. Nothing in the sort names the safest throw. Genbutsu, suji, and the honors already discarded are table facts. Use them inside the tie. Dropping a suited tile to "play safer" gives up the first two keys and is no longer free.

Furiten removes the ron

Riichi furiten blocks every ron on the wait, including a kind you never discarded. Tsumo still wins. The hand-only list still prints every kind. Furiten is not a Chinese Official rule and it is not a Sichuan rule.

78m is a ryanmen. Neither wait is held, so each kind is four copies. The Red triplet scores a Riichi ron on either side. Discard 9m, and the ron on 6m dies with it. Self-draw remains legal, and a closed tsumo still has menzen tsumo available as a yaku. The eight copies on the page do not shrink to four just because half the ron paths are closed.

45667m waits on 5m and 8m. One 5m is held, so the copies are three plus four. The White triplet is the Riichi yakuhai. Throw either wait and both rons are furiten. The list keeps showing 5m and 8m, because the structural distance did not change. Read furiten off your own river, not off the kind count.

Seven pairs and kokushi set the floor

The printed shanten is the minimum of the ordinary group count, seven pairs, and kokushi. When the special path is closer, that path sets every row. Chiitoitsu is the Riichi yaku. Chinese Official scores seven pairs and scores a finished thirteen orphans as a high fan pattern. The trainer does not search All Types, Knitted Straight, or Seven Stars. Sichuan tables usually win on four melds and a pair only. A hand full of honors is not a Sichuan example.

Five suited pairs and four single honors. Cutting any one honor leaves three live pair-tiles, three copies each, nine copies, three kinds, at one-shanten. On that 13 the seven-pairs distance is 1 and the ordinary four-meld distance is 3. The printed figure is the pairs path.

Twelve orphans are present and Green is the missing one, so Green is ×4 and the others are ×3. 3s is not a kokushi tile. It is why the hand is one-shanten rather than tenpai: draw Green, throw 3s. Forty copies is the special-pattern width. It is not a claim that every one of those tiles is a useful draw on a Sichuan or a tanyao plan.

Six suited pairs plus East and Red. Cutting East leaves a tanki on Red, three copies, one kind. Cutting Red leaves a tanki on East. On that 13 the pairs distance is 0 and the ordinary four-meld distance is 3, so the tenpai exists only on the pairs path. Breaking a pair leaves one-shanten. The ladder follows the minimum.

Five-block is a proposal, the ranking decides

Five-block theory looks for about five blocks: four meld-holders plus a pair candidate. Whatever is left is a floater. The scaffold is standard Japanese teaching for a win of four melds and a pair. It proposes a cut. The three keys accept it, tie it, or reject it. A tile shared by two blocks is still one kind, as with 6m and 5m above.

A workable block picture is kanchan 13m, kanchan 24p, ryanmen 67p, sequence 456s, penchan 89s, and the White pair. 8m sits in none of them. The ranking's unique best cut is that floater, at two-shanten, 20 copies, 5 kinds. The edge tiles 1m and 3m are worse rows. Here the scaffold and the ladder name the same discard.

Drop the isolated 8m and the sou side gains a pair of 9s. Five-block still wants the weak 13m edge gone. The ladder agrees that 1m and 3m are best, and it also ties them with 2p, 4p, 7p, and 8s, all at 20 copies and 6 kinds. The proposal is no longer a unique answer. Cut any tile in that tie for shape reasons of your own. Cutting 9s, the pair, is a worse row, so "I have a pair of 9s to spare" is the wrong spare.

One-shanten shape width

Riichi classrooms name one-shanten shapes and often rank their usual width as sticky, then headless, then perfect, then surplus. Perfect means a pair plus two flexible taatsu, every accept reaching tenpai. That form is measured on One-Shanten Discard. The order is a convention, not a theorem. The four hands below are a different set: a surplus float, a headless run, an honor-floater sticky, and a seven-tile stretch. Their counts do not line up as sticky ahead of headless.

123m, 456m, and 789p are finished. The pair is 2s. East and White are spare. The accepts are 2s×2, East×3, and White×3. Drawing East or White makes a second pair, and throwing the other honor leaves a shanpon. Drawing 2s makes a triplet, and throwing one honor leaves a tanki on the other. Nothing in the direct list builds a new two-sided taatsu. Eight copies is the narrow end. The spare honor is also the tile a safety plan wants to throw once the hand is 14 again.

No pair and no honor. 23456m and 45678p are each a sequence plus a taatsu, and 678s is a sequence. Completing a taatsu drops shanten. Pairing a tile inside a taatsu drops shanten too. The accepts run through man from 1 to 7 and pin from 3 to 9: fourteen kinds, forty-six copies. No listed draw keeps shanten at 1 while adding a kind. The width is real, and a Riichi reading still expects some of those pair-accepts to land a tanki later. This page does not grade each accept. The wait names are on the machi page.

This is the sticky skeleton: three sequences, a pair, two floaters. The pair is South. The floaters are White and Red. The direct accepts are South×2, White×3, and Red×3, the same eight copies as the surplus hand. Suited floaters are why the classroom calls sticky wide. Honor floaters do not attach to 123m, 456p, or 789s, so the accept list stays narrow. The 27 improvement kinds are the attachments: draws that keep shanten at 1 and raise the kind count. They are not ukeire. The raw count on this 13 is 8. The wide number the class name suggests is sitting off the ladder.

2345678m is seven connected tiles. The accepts cover every man kind, plus 6s×2 and East×3. Eleven kinds, thirty-four copies. The run is wide because several windows inside it can become the meld-plus-taatsu, not because one perfect ryanmen is sitting on the end. Seventeen further kinds keep shanten and raise the kind count. On the measured set, headless leads on accepts (46), the stretch is next (34), and the two honor-floater hands tie at 8. That is a count. It is not the classroom ranking, and it does not overturn the classroom ranking for the hands that ranking was meant to describe.

Honor, edge, and a complex tenpai

An isolated honor and a terminal taatsu are the usual early choice. At one-shanten the same comparison is already a number. At tenpai, a hand can be ready after many different cuts, and the keys still sort those waits.

89m is a penchan. Its fill, 7m, is missing, so that kind is four copies. The 3s pair contributes two. The White pair contributes two. The edge has twice the live copies of the dragon. A Riichi plan that prefers White because a triplet would be yakuhai is choosing the thinner kind on purpose. Chinese Official can prefer White for fan the same way. The accept list already contains all three. It does not rank them by score.

Several cuts are already tenpai. 9m leads. The 13 it leaves keeps 45678m, and the wait is the sanmenchan 3m, 6m, and 9m, eleven copies, three kinds. Thinner tenpai cuts remain on the table and lose on copies or on kinds. "The hand is ready either way" is true and incomplete. Ready-and-wide beats ready-and-narrow.

34567m is the five-tile run players sometimes group with nobetan. On this site the wait it produces, once the other groups and a pair are finished, is a sanmenchan: 2m, 5m, and 8m. Cutting White leaves that run alone and locks those three kinds, eleven copies. Cutting an end of the run, 3m or 7m, is tenpai at 6 copies and 2 kinds. Cutting a middle tile, 4m or 6m, is tenpai at 3 copies and 1 kind. The strong cut is the honor. The middle of the run is what you keep.

Ruleset sidebars

A sidebar changes the discard when the numbers tie, or it changes which distance you are allowed to play. Carry each sidebar only into the ruleset it names.

Riichi

A win needs a yaku. Declaring riichi supplies one for a closed hand and freezes the tiles, so the locked wait is the wait you will actually have. Dama needs a yaku in the shape. Dora and red fives stay unpriced. Furiten blocks every ron the list still prints, and tsumo still wins. Seven pairs and kokushi stay inside the shanten figure. Wait names, and the han pinfu adds for a ryanmen, are in Wait Types and Riichi Mahjong. The shape-width convention above is Riichi teaching. The three keys under it are shared.

Chinese Official

A fan table scores the hand. This site documents an 8-fan minimum. Structural tenpai under that floor does not win. Name the edition when the floor differs. See Chinese Official Mahjong.

The Canada Chinese Mahjong Association's 2020-07-16 lecture separates two draws the ladder flattens. 实质进张 is a draw that cuts the distance on the scoring plan, not merely on the group count. 改良进张 keeps the distance and improves the wait or the future ukeire. This site's improvement list is the second idea narrowed to one test: same shanten, more kinds. It will not mark a draw that only makes a ryanmen out of a kanchan without adding a kind.

The trainer still reports the regular minimum: four melds and a pair, seven pairs, and kokushi. It does not search All Types Unmatched, Knitted Straight, Seven Stars Unmatched, or the rest of the 81-fan list. Play those distances yourself. Riichi and furiten do not transfer. A chi or a pung can buy a fan pattern the closed ladder never sees. A closed hand can be the high-fan plan. Either choice is allowed to lose the copy count.

Sichuan: the void suit comes first

Chengdu-style blood battle, and tables like it. House rules differ on whether play continues after the first win and on whether a late win is compulsory. Name the table. See Sichuan Mahjong. The usual set is 108 tiles and no honors. You void the thinnest suit unless a flush says otherwise. A win is illegal while that suit remains. After the void is chosen, ukeire lives in the two kept suits. Two-sided accepts stay wider than edge and closed accepts. Many tables do not allow chi. Blood-battle continuation, and the exhaustive-draw payment from non-tenpai seats to tenpai seats, sit outside the ranking. This site does not choose the missing suit. A three-suit hand is still an abstract four-meld count.

Man and pin are the hands you can win with. Sou is two tiles, 1s and 3s, a kanchan that the abstract count loves: throwing either one is two-shanten with 70-plus copies. Under Sichuan suit elimination those are the tiles that have to go. The legal chart then starts from the one-shanten rows, where 2m, 3p, and 6p lead at 15 copies and 4 kinds, and 5m and 8m trail at 8 copies and 2 kinds. Treat the 79-copy row as a description of a hand you are not allowed to keep.

A spare Green against a one-kind tenpai

The last cut is the same ladder with a score tile sitting on it. Reaching tenpai now, on a penchan, beats staying one-shanten with a spare dragon.

345678m is a stretch, 234p is a sequence, 89s is a penchan, and White is the pair. One Green is spare. Cutting it leaves a tenpai whose only kind is 7s, four copies. Cutting 9s keeps Green and stays one-shanten at 20 copies and 6 kinds. Cutting 8s is the same distance and a shorter list. If Green is dora, the slower row is how you keep it, at a cost of one full step of shanten. The ladder pays the step and throws the dragon. Riichi may refuse, and should say that the refusal is dora, not efficiency.

Learning roadmap

1. Shanten. The scale, including −1 and 0, is in How to Count Shanten. Drill it in shanten training.
2. Ukeire. Kinds and hand-only copies are in Counting Effective Tiles. Name every kind in one-shanten training, and cut by the count in one-shanten discard.
3. Discards. The ladder on a full cut is Discard Strategy. Repetitions are discard training.
4. One-shanten. The last cut before tenpai, including the perfect form this page left on that article, is One-Shanten Discard.
5. Waits. The shanten-0 list as a shape is Wait Types.
6. Five blocks, then overlap. Floaters are in Five-Block Theory. The shared tile is in Overlapping Taatsu.
7. The table you play. Open Riichi Mahjong, Chinese Official Mahjong, or Sichuan Mahjong. Carry a sidebar only into the ruleset it names.

Name the overlay and the ruleset when you leave the four-meld frame.