Counting Effective Tiles

Ukeire is the set of tiles you can draw that lower shanten. Kinds are how many distinct ids are in that set. The count is the sum of the copies still left of those kinds only. This page counts both for the ordinary win of four melds and one pair. Scoring and safety sit beside the count. They change with the ruleset.

This site sorts a discard by lower shanten, then more ukeire copies, then more ukeire kinds. mjlab uses that ladder and does not run an expected-value engine. The frame is tile efficiency. The distance is shanten. At shanten 0 the same test lists the winning tiles, the step from 0 to −1.

What the count is

On 13 tiles the analyzer reads shanten, then tries one extra copy of each kind the hand holds fewer than four of. If shanten falls, that kind is ukeire. Kinds are the size of the set. The count sums, over that set only, four minus the copies already in the hand.

On 14 tiles it tries each discard and runs the same test on the 13 that remain. A cut row prints shanten and the copy total. It does not print a kind count, and this page does not invent one.

The default subtraction is the hand alone. Discards, melds, and indicators are not removed. The pond arithmetic appears in one labeled section below. Every other figure here is hand-only.

A kind that completes two blocks is still one kind. Overlapping Taatsu is the shape page. Block slogans are maxima for one block with the rest of the hand fixed. For ryanmen, kanchan, and penchan, the copy column also assumes that none of the accept tile is already held.

Those lines are not the hand's ukeire until the whole 13-tile hand is recomputed. A draw that pairs a loose tile in an unfinished group can lower shanten even when no one block's slogan named it.

The ladder is this site's sort. A deficiency paper's discard rule is a step-k completion probability under a knowledge base, not this ladder. A published 立直 sample player keeps shanten and maximizes the number of necessary kinds. This site maximizes copies, then breaks ties on kinds. That is a choice of key, not a measured win rate.

Same shanten, wider ukeire

Both hands are shanten 1. The first key ties, so copies decide, then kinds.

1s×3, 2s×3, 3s×3, 4s×1, 5s×2, 6s×2, 7s×4, 8s×3, 9s×2. Every sou kind counts. 7s contributes 4 because none are held. 4s contributes 1 because three are held, and that last copy still lowers shanten.

1s×1, 2s×3, 3s×4, 5s×3, 6s×2, 7s×4, 8s×2. 4s is absent because all four are in the hand. 9s is absent too: four sit outside the hand, and drawing one does not lower shanten. A leftover copy is ukeire only when the shanten test says so.

23 copies and 9 kinds rank ahead of 19 copies and 7 kinds. That is wider ukeire at the same shanten. A 立直 yaku, a 国标 fan family, or a 川麻 suit you are clearing can still prefer the narrower shape. Write the count, then name the ruleset in Discard Strategy.

Lower shanten beats a larger count

A larger copy total does not buy a step you failed to take.

East is the only tenpai cut, so it wins on the first key. The 24-copy lines rank behind it.

The 13 tiles after East are this ryanmen: 2 kinds, 8 copies.

31 against 23 is the same-shanten comparison. 35 against 31 is shanten first: 35 is larger, and shanten 2 loses.

1m×3, 2m×4, 3m×4, 1s×3, 2s×3, 3s×3, 4s×1, 5s×2, 6s×2, 7s×4, 9s×2. The floating 1m adds acceptance: 1m, 2m, and 3m are on the list, and 8s is not. Cutting 1m instead returns the pure sou shape, 9 kinds and 23 copies. That is a value choice. The ukeire sort picks 8s.

立直. Keep the sou tiles when the plan is chinitsu, or when tanyao is the yaku you are protecting. 国标. The same cut can serve 实质进张 for a one-suit fan, with the man tile off that plan. The ladder's best cut remains 8s.

At tenpai, the count is the wait

At shanten 0, ukeire and the wait are the same set. Each hand below is shanten 0, and a tenpai hand has no improvement list.

Ryanmen wins on copies, 8 against 4. Shanpon ties kanchan and penchan on copies and wins on kinds, 2 against 1. Kanchan and penchan tie on both keys.

Preferring kanchan over penchan, because the closed wait upgrades to a ryanmen more often, is common 立直 and sequence teaching about ryanmen upgrades. It is not a second analyzer number. The shapes are drawn in Wait Types.

Ryanmen wins on copies here. Equal counts among kanchan and penchan are not ranked by the analyzer. On these four tenpai hands the ladder stops at kinds and copies, so a closed wait does not outrank an edge wait when those two keys match. Those two keys are the whole sort on this site: lower shanten, then the hand-only copy total, then kinds. When kinds and copies both match, this page stops. It does not invent a third key that would place the closed wait ahead of the edge wait.

立直. Furiten can remove a kind you already discarded, while the hand-only list still prints it. Declaring riichi freezes the closed hand, so later shape changes stop. Both sit on top of these counts. See Riichi Mahjong.

Count each kind once

Count a kind once, then add the copies that remain.

Two of each wait are already held, so each kind contributes 4 minus 2. The total is 6. Counting 3×4 = 12 invents six tiles.

All four 4s are in the hand, so 4s cannot be ukeire. The seven kinds are 1s×1, 2s×3, 3s×4, 5s×3, 6s×2, 7s×4, and 8s×2.

1s×4, 2s×4, 3s×3, 4s×4, 5s×2, 6s×3, 7s×4, 8s×4. The 35 side and the 56 side both accept 4s, and the list still has 4s once. 5s is ×2 because two are held. This hand has improvement rows. They keep shanten at 1 and raise the kind count. They are not added to the 28.

Hand-only copies, and the tiles you can see

Neither wait is in the hand, so the slogan and the 13-tile test agree on 8.

Each wait is already held twice. The slogan of eight assumed that none of the accept tile was held.

The pond is a side calculation this site does not run. The analyzer prints the hand-only count and has nowhere to put the pond. On the ryanmen, if two 3m are already in the pond, 3m (4−0−2) + 6m (4−0−0) = 6, while the analyzer still prints 8. After you subtract everything you can see, unseen copies may sit in other hands or the dead wall. The visible count is an upper bound for comparison, not the live wall. Drills here score the hand-only 8.

An improvement draw is a second list

Acceptance lowers shanten. A shape improvement does not. Adding the two lists mixes a step already taken with a step that only widens the shape, and this site does not add them. This site lists an improvement only when shanten stays the same and the number of kinds rises. A draw that keeps the kind count flat is not listed, even when the future wait looks easier. That is narrower than "any better shape." Tenpai hands have no improvement list. The three equal hands in the next section have no improvement rows. Those two wordings are not claimed to be the same definition.

Ukeire is 2m×4, 3m×3, 4m×3, 5m×4, 4s×3, 5s×4, 6s×3. 3s is not in that list.

Ukeire is 2m×4, 3m×3, 4m×3, 5m×4, 3s×3, 4s×4, 5s×3. 2s is not ukeire. Do not add 24 and either improvement into one total.

Ukeire is 1m×2, 9p×2, 3s×3, 6s×3, 9s×4. The ten improvement kinds are 2m, 3m, 7p, 8p, 1s, 2s, 4s, 5s, 7s, and 8s. Each goes from 5 kinds to 6. None of the ten is in the ukeire list.

Equal totals do not rank a closed wait against an edge wait

Each hand is shanten 1, with 3 kinds and 8 copies, and has no improvement rows. Shared accepts are 9s×2 and East×2.

The analyzer ties all three. It cannot see that 46m upgrades to a ryanmen more readily than 12m. Preferring that upgrade is common 立直 and sequence teaching about ryanmen upgrades. Label it 立直, and label it general sequence pedagogy. It is not an analyzer result.

国标: structural ukeire, scoring draws, and empty tenpai

国标 reads a fan plan on top of the structural list. This section does not compute a fan total. The analyzer returns every kind that lowers shanten. In the Canada MCR association's glossary, 实质进张 advances the core fan (主体番种), 型听 is structural tenpai under the minimum fan to win, and 改良进张 leaves xiangting unchanged while the wait widens.

The pin body and the white-dragon triplet are finished. The only winning tile is 1s. For a one-suit plan, structural ukeire is 1s×3 and 实质进张 is empty. The association's 2020-07-16 lecture, 如何打好国标麻将, would also call the finished hand 型听 if it is under the minimum fan. This is not a 国标 win until that check. The fan total is not computed here.

3s, 6s, and 9s stay with the sou body. 9p and 1m lower shanten by completing a triplet in another suit. Which of the five are 实质进张 depends on the core fan. The analyzer returns the union.

The ten improvement kinds, each from 5 kinds to 6, match the association's 改良进张 only under "xiangting unchanged and the wait widens." This site's test is "the kind count rises," which these ten pass. The wordings agree on this hand. They are not treated as one definition for every hand.

The association's 2019-01-05 continuation, 国标麻将浅识（续）, counts 当量 as pedagogy. A pair's remaining copies are multiplied by 4, for a self-draw and a pong. A sequence tile is multiplied by 2, for a self-draw and a chi from the left only. Their sketch is 2×4 = 8 for a pair with two left, and 4×2 = 8 for a sequence tile with four left. That ×2 is not 立直 ukeire, not 川麻, and not what the analyzer prints. Which competition year applies, and whether 8 fan is the minimum, is not locked here. Name the edition from Chinese Official Mahjong.

川麻: the missing suit can be the whole wait

川麻 here follows 血战到底-style pages: DoubleWin, the World Mahjong Tour 血战到底 rules, and the Sichuan Mahjong Mobile guide. House rules differ, including 血战到底 versus 血流 and whether a late win is compulsory. Name 血战到底 when you use the continuing deal. The set has 108 tiles and no honors, so these hands use none. There is no chi, so do not multiply a sequence accept by the 国标 当量 ×2.

The wait is the missing suit, and a pin tile is still in the hand. The 33-copy one-shanten is not a reason to cut a sou while a pin remains. 定缺 says the pin goes first. After it goes, the structural tenpai is still illegal, because the only wait is 1p.

Two suits only. This is the picture after 定缺 is cleared. The best cuts are legal tiles, and meld-and-pair ukeire applies inside the suits you kept.

Sichuan Mahjong is the rules page. The analyzer does not choose 定缺, and it does not delete an illegal wait from the list.

川麻: an exhaustive draw pays tenpai

During the hand, the shared sort still prefers lower shanten. At an exhaustive draw, 查叫 compares tenpai with noten, not the wider count. On 血战到底, play continues after someone else wins, so a narrow tenpai can still be the practical goal. That is table economics, not a change to the 13-tile formula.

Only sou and man are held, so a 定缺 of pin is already clear, and the wait is not the missing suit. Three copies is a small tenpai. It is tenpai.

It has more ukeire, and it loses 查叫 to the tanki if the wall ends now. Once 定缺 is an empty suit, this hand is not 花猪. It is noten.

Seven pairs changes the set

Count seven pairs (七对) only on tables that include that win. 立直 includes it. 国标 includes it as a special pattern. 川麻: the fetched 血战到底 pages score 七对 at 2 fan, and other Sichuan tables may omit it. Kokushi is a 立直 pattern. These hands are not kokushi, and kokushi is not a legal win in 国标 or 川麻.

Six pairs plus a 9p singleton. The wait is the seven-pair tanki. This page did not recompute the hand with seven pairs turned off.

A seven-pairs-only reading sees 7p×3. The extra 1p and 4p win as a standard hand. "Count the pairs" undercounts this hand. "Always add seven pairs" is wrong on a table without that win. The standard-only waits were not recomputed here.

What to practice

1. Shanten, including 0 and −1, in How to Count Shanten.
2. Kinds and hand-only copies on this page. Name every kind in one-shanten training. Cut by the copy total in one-shanten discard.
3. The cut, in One-Shanten Discard and Discard Strategy.
4. The wait as a shape, in Wait Types.
5. Overlap, still one kind, in Overlapping Taatsu.
6. The table. Riichi Mahjong, Chinese Official Mahjong, or Sichuan Mahjong. Carry a 立直, 国标, or 川麻 sentence only into the ruleset it names.

The ladder's best cut is the efficiency best cut. A scoring plan, a missing suit, or an exhaustive-draw tenpai is an overlay you name before you play past the numbers.