Ryanmen, kanchan, penchan: partial sets ranked

Sort a fresh hand and much of it comes in twos: a ryanmen here, a kanchan there, a penchan at the edge. Each needs one more tile to become a set, but they aren't equal. Eight tiles finish the 67m. Four finish the 46p or the 12s. That gap tells you which part of your hand to give up first.

The four partial sets and what finishes them

Almost every winning hand is four sets and a pair, as How to play riichi mahjong showed, and Your first ranked games told you to keep the tiles close to a set. Those are partial sets. A partial set, or taatsu (搭子), is two tiles that need one more to become a set. There are four kinds.

Name	Example	Finished by	Tiles
Ryanmen (two-sided)	ryanmen	or	8
Kanchan (middle)	kanchan		4
Penchan (edge)	penchan		4
Pair	pair		2

Count the same way every time: four copies of each tile that finishes the shape, minus the copies in your own hand. That's why the pair gets 2. You already hold two of its four.

Two details catch new players. Any two in a row from 23 up to 78 is a ryanmen: 23 waits on the 1 and the 4, and 78 on the 6 and the 9. Only 12 and 89 are penchan, because nothing sits below the 1 or above the 9. A kanchan, two tiles with a one-tile gap, can sit anywhere from 13 to 79.

The pair is the odd one out. As a partial set it's the narrowest, with 2 tiles left to finish it. But every standard hand needs exactly one pair, the head, so a pair has a second job the other three can't do. How many pairs to keep gets its own lesson.

Why a ryanmen is worth two of the others

Eight tiles against four makes each draw twice as likely to finish a ryanmen as a kanchan or a penchan. And you can chi either tile that finishes it when the player on your left discards one.

The gap matters most once you're tenpai. Your wait is usually the last partial set you have left, as in the problem above. Keep a ryanmen to that point and you wait on 8 tiles. A kanchan or a penchan leaves you on 4. Mahjong waits covers the waits wider than a ryanmen.

That gap shows up in results. The wait win rate page follows the first riichi of each hand in Tenhou's top room (Houou). It counts turns from zero, so its turn 8 is your ninth discard. A riichi on a two-sided wait at that turn wins 52% to 57% of the time. A one-sided wait on a 5, like the 46 kanchan, wins 33%.

Good shapes pay more, too. Pinfu, one of the everyday yaku from the yaku lesson, needs a two-sided wait, so a hand that ends on a kanchan or a penchan can't have it. And every penchan holds a 1 or a 9, so the set it makes rules out tanyao.

Kanchan beats penchan because it can grow

A kanchan and a penchan both wait on 4 tiles, so the finishing count can't split them. The draws that don't finish them can. Add a to kanchan and you hold , with the ryanmen ryanmen inside it and the 6p spare. A works from the other side: holds the ryanmen ryanmen.

Kanchans differ among themselves. An inner kanchan (35, 46, or 57) can grow from either side. An outer kanchan (13, 24, 68, or 79) grows from one side only, the side away from the edge: 79 needs a 6, and 68 needs a 5.

No single draw turns a penchan into a ryanmen. Add a to penchan and you hold . The 24s inside it is an outer kanchan, still a one-sided wait. Only a 5s on top of that gives you the ryanmen 45s, so the penchan needs two exact tiles, a 4s and a 5s, before it becomes a ryanmen.

Shape	Finished by	Turned into a ryanmen by
Inner kanchan: 35, 46, 57	4 tiles	8 tiles (46 takes a 3 or a 7)
Outer kanchan: 13, 24, 68, 79	4 tiles	4 tiles (79 takes a 6)
Penchan: 12, 89	4 tiles	none in one draw

So while you build a hand, the order runs ryanmen, inner kanchan, outer kanchan, penchan: first by the tiles that finish a shape, then by the draws that turn it into a ryanmen.

That order is for building, while a draw can still change a shape. Once you're tenpai and about to riichi, growth no longer counts, and the tile you wait on decides. On the same win rate page, a one-sided wait on a 3 or a 7, the tile a penchan waits on, wins 38% at turn 8. A wait on a 4, 5, or 6, where an inner kanchan waits, wins 33% to 36%. Choosing your wait covers that step.

Visible tiles can also change the order. If three 5m and three 8m already sit in the discards, your 67m has 2 tiles left, and a kanchan with all four of its tiles unseen is worth more. Tile acceptance shows how to count what you can see.

Label every tile before you discard

Before you choose a discard, give every tile a label: set, partial set, pair, or loose tile. A pair is a partial set too, but it gets its own label because it can also be your head. A loose (isolated) tile has nothing within two of it in its suit, or it's an honor with no partner. You'll also see it called a lone tile. It needs two more tiles to become a set: one to make a partial set, then one to finish it.

Label the finished sets first, then the partial sets and the pair, then check what's left over.

• Set: 234m. It's done, so leave it alone.
• Partial sets: the ryanmen ryanmen (8 tiles), the kanchan kanchan (4), and the penchan penchan (4).
• Pair: pair, your head for now.
• Loose tiles: the and the East wind . Nothing sits near either one.

The 6p and the 9p are three apart, too far to work together, so the kanchan and the pair are separate parts. Between them, the three partial sets have 16 tiles that finish a set. Open the hand in the hand analyzer and it lists the same 16: the 5p, 3s, 5s, and 8s, four of each. The 9p isn't on the list. A third 9p makes a set but uses up your only pair, so the hand gets no closer to tenpai.

With the parts labeled, your next discard narrows to the two loose tiles. What to discard first puts loose tiles in order. A loose terminal or honor usually goes before any partial set, even a penchan, because the penchan is one tile from a set and the loose tile is two. When nothing is loose, break the weakest partial set on the ranking and keep your only pair. With three pairs, a pair is usually the part to break. How many pairs to keep explains why.