Discard Strategy
A discard puzzle is a closed 14. One tile leaves. The rest is the hand you will actually play. On this site the answer is a best group: every discard that ties the first row of a three-key ladder. Lower shanten wins. At the same shanten, more ukeire copies win. At the same copies, more ukeire kinds win. The group can be one tile. It can be several. Value, wait shape, furiten, and the other seats come after that row. They do not rewrite it.
The ladder is tile efficiency. The integer is shanten: 0 is tenpai, 1 is one-shanten, and a finished hand prints as −1. The sum is ukeire. A kind counts once. The copies are four minus the copies already in the hand. A pond, a dead wall, a yaku, and a missing suit stay out of that subtraction. This site does not run an expected-value engine, and it does not print a deal-in rate.
A 13 prints one shanten and one list. A 14 prints the cut table. When shanten is above 0, a draw that keeps the shanten and raises the kind count is an improvement. That list is a second measurement. It is not a fourth key, and it is not ukeire. Tenpai leaves the improvement list empty, because the wait is the whole story.
The groups you might mark live on five-block theory. The cut while the hand is already at shanten 1 lives on one-shanten. Overlap, and the two-floater shape, live on sticky tiles. The name of a wait, once the cut is tenpai, lives on wait types. This page is the throw. Every hand below is closed.
| Neighbor | What stays there | What this page does with it |
|---|---|---|
| Efficiency | The ladder as a definition | Apply it to one 14, then show a reason to leave it |
| Shanten | The integer | Use the printed number |
| Ukeire | The sum, one kind once, and a wall | Quote the printed sum |
| Five-block | Four meld-holders and a pair | The reader may mark the hand. The cut table does not return blocks |
| One-shanten | Class names, and the cut at shanten 1 | A best row at shanten 1 can appear here as a comparison |
| Sticky tiles | Overlap and floater strength | Compare the cuts. The shape name stays on that page |
| Wait types | Ryanmen, kanchan, penchan, tanki, nobetan, fu | Name the wait when a tie is two different shapes |
What a discard puzzle is
The question is which tile to throw. Scoring and the table are sidebars. They do not change the best group the analyzer prints.
Best cut: 5m. Tenpai, 8 copies. Cutting 2m is also tenpai, with 4 copies. Cutting 3m is shanten 1 with 28 copies. The table has 13 rows. Only those two rows are tenpai, and the best group is 5m alone.
Man holds 235. Pin holds a sequence. Sou holds 345678 and a pair of 9s. Cutting 5m leaves 23m beside that body. The two follow-up hands below are the ryanmen and the kanchan. Eight copies at tenpai outrank four copies at tenpai, and they outrank 28 copies at one-shanten. The order is the ladder: shanten first.
Shanten, then copies
Lower shanten is the first key even when the slower hand accepts more tiles. The same 14 shows both comparisons.
Shanten 0. Two kinds, 8 copies: 1m×4, 4m×4. The man taatsu is 23m, a ryanmen. If 1m is already in your own discards, 立直 discard furiten forbids ron on both 1m and 4m. Tsumo on either tile remains. Deleting 1m from this 8 and leaving ron on 4m misreads the rule.
Shanten 0. One kind, 4 copies: 4m×4. The man taatsu is 35m, a kanchan. If 1m is in your discards and 4m is not, ron on 4m is still legal. The ladder on the 14 still prints 5m. A reader who needs a ron, and who cannot change the pond, may prefer this kanchan. The analyzer does not see the discards.
Shanten 1. Eight kinds, 28 copies: 1m×4, 2m×3, 3m×4, 4m×4, 5m×3, 6m×4, 7m×4, 9s×2. No improvement rows. Twenty-eight is the widest one-shanten on that 14, and it loses to the 8-copy tenpai.
| Cut from the 14 | Shanten | Copies | Kinds |
|---|---|---|---|
| 5m | 0 | 8 | 2, ryanmen 23m |
| 2m | 0 | 4 | 1, kanchan 35m |
| 3m | 1 | 28 | 8 |
Eight against four is the second key, copies, inside tenpai. Eight against 28 is the first key, shanten. The names ryanmen and kanchan belong to wait types. The count is the printout. The furiten sentence is Riichi Mahjong. Temporary furiten lasts until your next turn. Riichi furiten lasts the hand, because a declared riichi hand is frozen. Neither clock is a second ukeire number.
Kinds break a copy tie
Equal shanten and equal copies still have a third key. This 14 is man only, so discard training could deal it. The drill and the ladder agree that three cuts are tenpai. They disagree on which of those three to keep.
Best cut: 7m. Tenpai, 6 copies. Cutting 6m is tenpai with 6 copies. Cutting 9m is tenpai with 6 copies. The next row is 1m, shanten 1 with 23 copies. The table has 8 rows. Discard training accepts every tenpai cut at the maximum winning-tile count, so on this 14 it also accepts 6m and 9m. The analyzer's best group is 7m alone.
Shanten 0. Three kinds, 6 copies: 4m×2, 6m×2, 9m×2. The third key keeps this cut. The drill's wider grade still includes the two hands below, because each of those also has 6 winning-tile copies.
Shanten 0. Two kinds, 6 copies: 5m×4, 8m×2. Same shanten, same copies, fewer kinds. The ladder drops it. The drill keeps it.
Shanten 0. Two kinds, 6 copies: 5m×4, 8m×2. The winning tiles match the 6m cut. The kind count is 2, so the best group excludes 9m as well.
1m and 4m are both shanten 1 with 23 copies on the cut table. 2m and 3m are shanten 1 with 22. 8m is shanten 1 with 14. Those rows were not given a separate kind list here. The tenpai comparison is enough: 3 kinds beat 2 kinds when shanten and copies match. Both the ladder and the drill put those three tenpai cuts ahead of every one-shanten row. The drill stops before the kind key.
When the three keys tie
When shanten, copies, and kinds all match, the ladder stops. The tiles it keeps can still be different taatsu. Shape is a labeled reason to choose inside that tie. It is not a fourth key.
Best cuts: 1m and 4m. Each is tenpai with 4 copies. The next row is 2m, shanten 1 with 24 copies. The table has 13 rows. Only the two best rows are tenpai.
Shanten 0. One kind, 4 copies: 3m×4. The man taatsu left behind is 24m, a kanchan. The winning tile is 3m.
Shanten 0. One kind, 4 copies: 3m×4. The man taatsu left behind is 12m, a penchan. The winning tile is the same 3m.
Same shanten, same copies, same kinds, same winning tile. 立直 fu is +2 on a kanchan and +2 on a penchan, so fu does not pick either. The sheet is on fu and on wait types. 国标 边张 is the 1-point name for a win on exactly 12, and 坎张 is the 1-point name for a win on exactly the closed gap, here 24. The man taatsu is exactly those two tiles, so a longer run does not swallow the name. No fan is summed.
Before the hand is locked, a 立直 damaten reading and a 川麻 reading both prefer the kanchan, because a later draw can rebuild it more easily. After a riichi declaration the hand is frozen, and that upgrade does not arrive. The European Mahjong Association's rule is that a declared riichi hand cannot be changed. None of those readings enters the cut table.
Pinfu inside the tie
立直. The next 14 ties three tenpai cuts on every key. Pinfu keeps two of them. The ladder keeps all three.
Best cuts: 3m, 6m, and 9s. Each is tenpai with 6 copies. The next row is 8s, shanten 1 with 45 copies. The table has 13 rows. Only those three rows are tenpai. Throwing 9s costs 0 copies against the other two and leaves a nobetan. If 9s is genbutsu against one riichi player, safety and pinfu pull apart, and the copy count does not referee them. If 3m is the genbutsu tile, safety and pinfu agree.
Shanten 0. Two kinds, 6 copies: 6s×4, 9s×2. Sequences 456m, 234p, and 567p, ryanmen 78s, pair 99s. Both winning tiles finish that ryanmen. The pair is a number pair. The hand is closed. That is a pinfu shape. The hand holds 9s, and 9s is a winning tile, so tanyao fails.
Shanten 0. Two kinds, 6 copies: 6s×4, 9s×2. The sou wait matches the 3m cut, with 345m in place of 456m. The same pinfu reading applies. Tanyao still fails, because 9s remains.
Shanten 0. Two kinds, 6 copies: 3m×3, 6m×3. 3456m waits by completing a pair on either end: 3m makes pair 33 plus sequence 456, and 6m makes sequence 345 plus pair 66. That is a nobetan. Pinfu wants the winning tile to finish a two-sided wait, so this shape fails pinfu. The ladder still keeps 9s, because the three keys match.
A 立直 reader who wants pinfu throws 3m or 6m. The analyzer prints all three. This page does not add a han total for the deal. The 1-han definition of the yaku stays on the pinfu page. Forty-five copies at shanten 1, the 8s cut, lose to every member of the tie.
Value beside the ladder
The ladder does not score tanyao, pinfu, yakuhai, or dora. A human still might. Sometimes that reading picks the same tile the ladder prints. Sometimes it picks a narrower tenpai. Sometimes a teacher drops a whole shanten for the score, or for a better wait after the next draw. The ladder will keep the tenpai. There is no fixed "give up two copies for a dora" amount on this page. No dora hand was measured here.
Tanyao can be the widest cut
立直. Tanyao wants every tile in the finished hand, including the winning tile, inside 2–8. Clearing the only terminal is sometimes the wide row.
Best cut: 9m. Tenpai, 9 copies. Also tenpai, each with 3 copies: 2s, 5s, and 8s. The next row is 1p, shanten 1 with 23 copies. The table has 14 rows. The 5s and 8s remainders were not re-measured, so they do not inherit a wait list. The verified pair is 9m against 2s.
Shanten 0. Three kinds, 9 copies: 2s×3, 5s×3, 8s×3. Every tile in the hand is 2–8, and every winning tile is 2–8. Tanyao tenpai, and it is the wide row.
Shanten 0. One kind, 3 copies: 9m×3. The terminal is still in the hand, and it is the only winning tile. Tanyao fails. Nine copies against three, both tenpai: the ladder and the all-simples plan agree.
3s and 7s are also shanten 1 with 23 copies on that cut table. Their kinds were not re-measured. "Clear the terminal" is a description of this hand. The next tanyao hand reverses it.
The triplet is the narrower tenpai
立直. A wind triplet feels expensive to break. On this 14 the break is the wide tenpai, and a much larger one-shanten still loses. South is not a 川麻 tile. This section is a 立直 hand.
Best cut: South. Tenpai, 11 copies. Cutting 3p or 7p is tenpai with 6 copies. Cutting 4p or 6p is tenpai with 3 copies. Cutting 3m or 8m is shanten 1 with 46 copies. The table has 12 rows. The 7p, 4p, and 6p remainders were not re-measured. Their copy counts are the cut table only.
Shanten 0. Three kinds, 11 copies: 2p×4, 5p×3, 8p×4. Sequences 345m and 678m, the five-run 34567p, and a pair of South. 2p, 5p, and 8p are the three fills of that run, and each can finish a ryanmen taatsu.
Shanten 0. Two kinds, 6 copies: 4p×3, 7p×3. The South triplet remains. 4567p is a nobetan: 4p pairs the low end, 7p pairs the high end. Eleven beats six, so keeping the triplet loses on the ladder.
Shanten 1. Fourteen kinds, 46 copies: 3m×4, 4m×3, 5m×3, 6m×3, 7m×3, 8m×3, 9m×4, 2p×4, 3p×3, 4p×3, 5p×3, 6p×3, 7p×3, 8p×4. No improvement rows. Forty-six loses to the 11-copy tenpai.
Shanten 1. Fourteen kinds, 46 copies: 2m×4, 3m×3, 4m×3, 5m×3, 6m×3, 7m×3, 8m×4, 2p×4, 3p×3, 4p×3, 5p×3, 6p×3, 7p×3, 8p×4. No improvement rows. The pin side matches the 3m cut. The man side is 2m through 8m.
| Cut | Shanten | Copies | Kinds, where measured |
|---|---|---|---|
| South | 0 | 11 | 3 |
| 3p | 0 | 6 | 2, nobetan, triplet kept |
| 7p | 0 | 6 | Not re-measured |
| 4p, 6p | 0 | 3 | Not re-measured |
| 3m, 8m | 1 | 46 | 14 |
On the same cut table, 5m and 6m are shanten 1 with 37 copies, 4m and 7m are shanten 1 with 36, and 5p is shanten 1 with 24. Those kind lists were not re-measured.
If South is the seat wind or the round wind, the triplet is yakuhai and the pair blocks pinfu. The pair itself does not score yakuhai. The nobetan wait fails pinfu as well. If South is a guest wind, the triplet is not yakuhai, and a ryanmen reading of 2p, 5p, or 8p can be pinfu on the 11-copy wait, because a guest-wind pair is allowed. This page does not print a han total. The man sequences are already in the hand, so this is not a toitoi plan.
Some 立直 teaching drops back a shanten for tanyao, for pinfu, or for the wait the hand will have after it improves. A thin paired wait can lose that argument to a wide one-shanten. Those are judgments about the rest of the deal. This ladder prints South. Eleven beats 46 because tenpai comes first.
Tanyao can be the narrow cut
立直. The wide tenpai on the next 14 still contains 1m. The only measured all-simples tenpai is a 3-copy cut.
Best cut: 8s. Tenpai, 9 copies. Also tenpai, each with 3 copies: 1m, 4m, and 7m. The next row is 2m, shanten 1 with 23 copies. The table has 14 rows. The unique best cut is 8s.
Shanten 0. Three kinds, 9 copies: 1m×3, 4m×3, 7m×3. 1m is in the hand and in the wait. Tanyao fails. This is the wide row.
Shanten 0. One kind, 3 copies: 8s×3. The hand and the wait sit inside 2–8. Tanyao, and it is the narrow row. A reader who wants all simples throws 1m and gives up six copies, 9 against 3, at the same shanten.
Shanten 0. One kind, 3 copies: 8s×3. 1m is still in the hand. Tanyao fails. Sharing the 3-copy count with the 1m cut does not make this an all-simples tenpai.
Shanten 0. One kind, 3 copies: 8s×3. 1m remains. Tanyao fails. Among the measured tenpai rows, only the 1m cut is all simples.
3p and 8p are also shanten 1 with 23 copies on that table. Their kinds were not re-measured. The ladder's unique best is 8s. Tanyao is the slower tenpai here, and it is one specific 3-copy tile, not every 3-copy tile.
Cutting the wrong floater
Three man sequences, a pair of 2p, and three floaters: 5s, 9s, and Green Dragon. Nothing on this 14 is tenpai. The comparison is which one-shanten is wider. Sticky tiles owns the floater rank and the two-floater class. This page only compares the cuts.
An isolated 3 through 7 touches more sequence kinds than a 1 or a 9, which touches more than a non-yakuhai honor. That rank is why a reader clings to 5s. The count runs the other way.
Best cut: Green Dragon. Shanten 1, 28 copies. Cutting 9s stays at shanten 1 with 24 copies. Cutting 5s stays at shanten 1 with 16 copies. Cutting one 2p is shanten 2 with 44 copies. The table has 13 rows. Treating 5s as genbutsu against one riichi player keeps shanten 1 and moves the count from 28 to 16. Treating 9s that way moves it from 28 to 24. If Green Dragon itself is the safe tile, safety and the ladder agree.
Shanten 1. Eight kinds, 28 copies: 2p×2, 3s×4, 4s×4, 5s×3, 6s×4, 7s×4, 8s×4, 9s×3. Sixteen improvement kinds. The first rows are 3m and 7m, each to 15 kinds, and 14 further kinds follow. 3m is absent from the ukeire list. Genbutsu against one riichi player does not change these 28 copies. The other seats are a separate judgment.
Shanten 1. Seven kinds, 24 copies: 2p×2, 3s×4, 4s×4, 5s×3, 6s×4, 7s×4, Green Dragon×3. Twenty-one improvement kinds. The first rows are 3m and 7m, each to 15 kinds, and 19 further kinds follow. The honor is still in the hand. The terminal is gone. Twenty-four sits between 28 and 16.
Shanten 1. Five kinds, 16 copies: 2p×2, 7s×4, 8s×4, 9s×3, Green Dragon×3. Twenty-three improvement kinds. The first rows are 3m and 7m, each to 13 kinds, and 21 further kinds follow. Same shanten as the Green Dragon cut, 12 copies fewer. This is the expensive one-shanten mistake.
Shanten 2. Twelve kinds, 44 copies: 1p×4, 2p×3, 3p×4, 4p×4, 3s×4, 4s×4, 5s×3, 6s×4, 7s×4, 8s×4, 9s×3, Green Dragon×3. Sixteen improvement kinds. The first rows are 3m and 7m, each to 20 kinds, and 14 further kinds follow. Forty-four copies buy a worse shanten. The ladder refuses the pair.
At the same shanten the honor cut is widest, then the terminal, then the middle tile. That is the reverse of the isolated-tile rank. The rank explains the temptation. The table is the decision: 28, then 24, then 16. Cutting the pair to reach 44 is the trap under the one-shanten band. Count first.
The tile you just drew
An improvement keeps shanten and raises the kind count. Ukeire lowers shanten. After the draw, the new 14 has its own cut table. Throwing the tile that just widened the hand walks the count backward.
Shanten 1. Seven kinds, 24 copies: 2p×2, 1s×3, 2s×4, 3s×4, 7s×4, 8s×4, 9s×3. Seventeen improvement kinds. 3m and 7m each move the kind count to 13. 4m and 6m move it to 11. Thirteen further kinds follow. 3m is an improvement, and 3m is absent from the ukeire list.
Draw 3m. The hand is now 14, and 3m is the tile that was on the improvement list.
Best cuts: 1s and 9s. Each leaves shanten 1 with 39 copies. Cutting 3m, 6m, or 9m stays at shanten 1 with 24 copies. Cutting one 2p is shanten 2 with 63 copies. The table has 12 rows. The 6m and 9m remainders were not re-measured, so they do not inherit the before-hand's kind list. Cutting the 3m you just drew does return that before-hand.
Shanten 1. Thirteen kinds, 39 copies: 1m×3, 2m×3, 3m×2, 4m×3, 5m×3, 6m×3, 7m×3, 8m×3, 9m×3, 2p×2, 7s×4, 8s×4, 9s×3. Eleven improvement kinds: 5p, 6p, 7p, 3s, 4s, 5s, and 6s each to 15 kinds, and 3p, 4p, 8p, and 2s each to 14 kinds. The 3m stayed. Twenty-four copies and 7 kinds became 39 copies and 13 kinds.
Shanten 1. Thirteen kinds, 39 copies: 1m×3, 2m×3, 3m×2, 4m×3, 5m×3, 6m×3, 7m×3, 8m×3, 9m×3, 2p×2, 1s×3, 2s×4, 3s×4. Six improvement kinds: 5p, 6p, and 7p to 15 kinds, and 3p, 4p, and 8p to 14 kinds. The keys match the 1s cut. The accepting list and the improvement list do not. The ladder ties them anyway.
Shanten 2. Nineteen kinds, 63 copies: 1m×3, 2m×3, 3m×2, 4m×3, 5m×3, 6m×3, 7m×3, 8m×3, 9m×3, 1p×4, 2p×3, 3p×4, 4p×4, 1s×3, 2s×4, 3s×4, 7s×4, 8s×4, 9s×3. Five improvement kinds: 7p and 6s to 21 kinds, and 6p, 8p, and 5s to 20 kinds. Sixty-three copies sit under the tie, at a worse shanten.
Both best remainders still hold 1m and 9m, so this pair of cuts is not a tanyao choice. The two 39-copy lists are different lists. Improvement does not break the tie, because it is not a key. Throwing 3m puts the old 13 back on the table: 24 copies, 7 kinds, shanten 1.
Danger
立直. Danger is about the tile you throw, against a particular player. Genbutsu is a tile already in that player's discards, or a tile that passed after their riichi. It is safe against that player, because they would be furiten. It says nothing about the other seats. Suji only rules out some ryanmen. Suji is not genbutsu, and it does not change a copy count. No deal-in percentage was measured. The word belongs on Riichi Mahjong. It is not a 国标 word and it is not a 川麻 word.
On the floater 14, Green Dragon is the unique best cut: shanten 1, 28 copies. A genbutsu 5s stays at shanten 1 and drops the count to 16. A genbutsu 9s drops it to 24. Green Dragon remains strictly ahead on the printed keys unless Green Dragon is the safe tile, in which case safety and the ladder pick the same discard. The other two players are still live.
On the three-way tenpai tie, 3m, 6m, and 9s each leave 6 copies and 2 kinds. Throwing 9s costs nothing on the ladder and loses the pinfu shape. Throwing 3m or 6m keeps that shape. When the safe tile is 3m, the defense read and pinfu agree. When the only safe tile in the group is 9s, they pull apart. Copies cannot settle it, because the copies match.
The copies above are four minus the copies in the closed hand. A kind that is already exhausted in the pond contributes nothing. That subtraction is the wall on the ukeire page. This caption does not build a pond, and it does not print a second integer.
Furiten blocks the whole wait
立直. Discard furiten looks at the whole wait. On the opening ryanmen, the winning tiles are 1m and 4m, four copies each. If 1m is already among your own discards, you cannot ron 1m, and you cannot ron 4m either. Tsumo on either tile remains. The repair that deletes 1m from the list and leaves ron on 4m is the mistake.
The kanchan from cutting 2m waits only on 4m. Ron on 4m is still legal when 1m is the dead kind and 4m is not. The ladder still prints 5m, the 8-copy ryanmen. A player who needs a ron, and whose discards will not change, may take the 4-copy kanchan for that reason. The caption says the analyzer did not look at the pond.
Temporary furiten and riichi furiten are the other two clocks on furiten. Passing a winning discard is temporary and lasts until your next turn. After riichi, missing a winning discard lasts the hand. They are rules about when ron is legal. They are not a second ukeire.
国标: the wide structural wait is the wrong suit
国标. The structural table is the same ladder. Fan is not computed. Teaching in this ruleset separates 实质进张, the structural accepts that advance the chosen fan, from 改良进张, the tiles that improve the shape without taking that step. The analyzer prints one list. The caption splits it in prose. See Chinese Official Mahjong.
Best cuts: 2p and 3p. Each is tenpai with 3 copies. Cutting one 3s, or cutting one 8s, is shanten 1 with 35 copies. The table has 8 rows. Six sou pairs plus 23p. The structural best wait is a pin tanki.
Shanten 0. One kind, 3 copies: 3p×3. Six sou pairs and a single 3p. The wait is off a sou-flush plan. For that plan this tanki is not 实质进张. The wait is simply off the named plan.
Shanten 0. One kind, 3 copies: 2p×3. The same shape, waiting on the other pin. Six pairs plus a tanki is how seven pairs reaches tenpai. The tiles do not make a pung-only hand.
Shanten 1. Twelve kinds, 35 copies: 1p×4, 2p×3, 3p×3, 4p×4, 2s×4, 3s×3, 4s×2, 5s×2, 6s×2, 7s×2, 8s×2, 9s×4. No improvement rows. Thirty-five loses to the 3-copy tenpai because shanten comes first.
The sou tiles mix terminals and simples, so 断幺 and 全带幺 are not the lesson on this hand. Those two plans give opposite instructions about terminals. A single terminal policy is not the ruleset. 国标 平和 is its own pattern. The pinfu sentences earlier on this page are 立直 only. Chi exists here. A teaching weight that counts a pair as four and a sequence as two is not the printed 3. That weight stays on the ukeire page. Seven pairs is the 立直 name of the pair pattern. The 国标 point value is not computed here.
川麻: 定缺, and the tenpai is still illegal
川麻, in the 血战到底 style these hands follow. The wall is 108 tiles. There are no honors, and there is no chi. A z tile is not a tile of this ruleset. Once a suit is declared missing, a tile of that suit leaves before any other tile, and the hand cannot win while one remains. House rules still differ on 血流成河, on the three-tile exchange, on a must-win rule, on whether seven pairs scores, and on the score cap. See Sichuan Mahjong.
Best cuts: 8m and 9m. Each is tenpai with 3 copies. Cutting 1p, or cutting 1s, is shanten 1 with 33 copies. The table has 14 rows. Under 定缺 man the ladder already throws a man. The 1s remainder was not re-measured. The cut table only supports the copy count 33.
Shanten 0. One kind, 3 copies: 8m×3. The hand still holds 8m, and the wait is 8m. Under 定缺 man that is not a legal win. Sequence accepts are not doubled. There is no chi, and a sequence can still win on a discard.
Shanten 0. One kind, 3 copies: 9m×3. The same problem on the other man. The structural tenpai and a legal hu are different questions while the missing suit remains.
Shanten 1. Ten kinds, 33 copies: 7m×4, 8m×3, 9m×3, 1p×4, 2p×3, 3p×3, 4p×3, 5p×3, 6p×3, 7p×4. No improvement rows. Both mans are still in the hand. Thirty-three copies are not a reason to throw pin or sou while a man remains.
The ladder and 定缺 agree on the first throw: a man leaves. They come apart on what that throw achieves. The resulting "tenpai" still waits on the missing suit. The next section is the hand after that suit is already gone.
川麻: after the missing suit is gone
Two suits, no honors. The missing suit is not in the string. The ladder ties two tenpai cuts, and a 51-copy one-shanten loses.
Best cuts: 1s and 8s. Each is tenpai with 9 copies. Also tenpai: 4s and 5s with 6 copies, and 2s and 7s with 3 copies. Cutting 9p is shanten 1 with 51 copies. The table has 14 rows. The 4s, 5s, 2s, and 7s remainders were not re-measured. Their kind lists stay unstated.
Shanten 0. Three kinds, 9 copies: 2s×3, 5s×3, 8s×3. Each winning tile completes sequences. 点和 can win that discard. The 9 is not doubled, because this ruleset has no chi. 查叫, if the wall ends in a draw, cares that this cut is tenpai.
Shanten 0. Three kinds, 9 copies: 1s×3, 4s×3, 7s×3. The keys match the 1s cut. The winning tiles differ. Both cuts stay in the best group. Both are sequence completions, so both can win on a discard.
Shanten 1. Sixteen kinds, 51 copies: 3p×4, 4p×3, 5p×3, 6p×3, 7p×3, 8p×3, 9p×4, 1s×3, 2s×3, 3s×3, 4s×3, 5s×3, 6s×3, 7s×3, 8s×3, 9s×4. No improvement rows. 查叫 compares tenpai with noten. It does not pay 51 over 9. The ladder rejects this row on shanten as well.
The two best cuts tie on all three keys. A player chooses between waits the ladder has already called equal. Pinfu, genbutsu, and furiten are not the vocabulary of this sidebar.
Seven pairs, on tables that score it
The analyzer's minimum includes seven pairs. A table that omits the pattern needs a different distance. This page did not recompute one. 立直 scores the pattern. 国标 lists it among the special patterns, and the point value is not invented here. 川麻 scores it only on some 血战到底 tables. The string below has no honor, so the tiles themselves are legal there. The yaku is the house rule. The 立直 page is seven pairs.
Best cuts: 8s and 9s. Each is tenpai with 3 copies. Cutting any of the six pairs is shanten 1 with 9 copies: 1m, 2m, 3p, 4p, 5s, or 6s. The table has 8 rows. Only the 1m remainder was re-measured. The other five pair-cuts keep the copy count 9 and do not inherit that kind list.
Shanten 0. One kind, 3 copies: 9s×3. Six pairs and a single 9s. The win is the seventh pair. The ladder keeps this tanki.
Shanten 1. Three kinds, 9 copies: 1m×3, 8s×3, 9s×3. No improvement rows. Nine copies at shanten 1 lose to three copies at tenpai. Breaking a pair is the wider one-shanten, and it is behind.
Cutting 9s is the other member of the best group, also tenpai with 3 copies on the cut table. That remainder was not given its own kind list. The measured tanki is the 8s cut, waiting on 9s.
Discard training and the ladder
The article's order is shanten, then copies, then kinds, on a mixed hand and on a man-only hand. Discard training is one suit, lengths 8, 11, and 14, with a 30-second clock. The green tile is the cut with the most winning-tile copies. A cut that is not tenpai scores 0. Kind count is not a tie-break. Tanyao, pinfu, furiten, and a safe tile are ignored there too.
On the man-only 14 in the kinds section, 7m, 6m, and 9m are all tenpai with 6 copies. The drill accepts all three. The analyzer's best group is only 7m, because that remainder has 3 kinds and the other two have 2. On the pinfu tie, the tanyao hands, and the South hand, the human reason is invisible to both the ladder and the drill. Only the sidebar carries it. When a narrow tenpai and a wide one-shanten are both available, both the ladder and the drill take the tenpai.
The one-shanten page is where the cut is chosen while the hand is already at shanten 1. The pictures there are a different exercise.
The analyzer's ordinary view of an 8-tile or 11-tile man hand fills unfinished groups with honor triplets so the distance matches a longer hand. That fill can print a short man line as a finished win, or as tenpai with an empty wait. Discard training does not use the fill. This page does not print those short lines. Open a 14, mixed or man-only, when you want the three-key table.
The later questions in Daily Challenge are one-suit 14s as well, graded by winning-tile copies, the same grade as the timed drill. The analyzer link under each hand is where kinds still break a tie.
What to practice
Read the row before you name the reason. Shanten, then copies, then kinds. If the best group has one tile, that tile is the structural throw. If it has several, the sidebar that matches your table picks inside the tie, or tells you why you are leaving the ladder on purpose.
- The distance, including 0 and −1, in How to Count Shanten.
- Kinds, once each, and hand-only copies, in Counting Effective Tiles. A wall subtraction lives there.
- The groups, in five-block theory. A floater is not a block until it sticks.
- The cut at shanten 1, in One-Shanten Discard. Floater strength and overlap are in sticky tiles.
- The wait as a shape, in Wait Types, after the cut has reached tenpai. Fu on a kanchan and a penchan is the same +2, so it does not split the tie on this page.
- 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.
Then cut tiles in discard training. The drill's green tile maximizes winning-tile copies. Bring a mixed 14 back to the analyzer when the third key, or a yaku, is the question you actually have.