Shapes worth keeping: 3456, 3445, 334 and ryankan

The 6 hanging off your 345, the second 4 in a 3445, the 7 next to a 35: each one looks like a spare, and spares feel like the first thing to cut. Count the draws each one adds, though, and it usually beats the loose (isolated) tile you'd keep instead. These compound shapes, three or four tiles working as one group, take more draws than their size suggests.

Three tiles that take more than two

A partial set is two tiles one draw from a set. A ryanmen (two-sided) takes 8 tiles, and a kanchan (middle) or a penchan (edge) takes 4, as the partial-sets lesson counted. Put a third tile in the right place and the same block takes more.

A pair plus a partial set. pair plus ryanmen is the ryanmen 34p with a second 3p. A 2p or a 5p still makes a set, and now a third 3p does too: 3 kinds, 10 tiles. Join a pair to a kanchan or a penchan, as in pair plus kanchan or pair plus penchan, and 4 tiles become 6.

These counts assume a head somewhere else. Then the 33p is a second pair, and a third 3p makes a set while your head stays put, as Pairs: two is right, three is one too many showed. If the 33p is your only pair, it's busy being your head, and the 334p works as a head with a spare 4p.

A ryankan. ryankan is two kanchans sharing the 5p: the 35p waits on the 4p and the 57p on the 6p. Together that's a ryankan (両嵌), 2 kinds and 8 tiles, as many as a ryanmen. It costs three tiles instead of two and finishes like a kanchan: if the rest of your hand fills first, you cut one end to reach tenpai and wait on a kanchan. Far from tenpai, keep all three tiles. Any three tiles spaced two apart make one: 135, 246, 357, 468, or 579.

Shape	Example	Draws that make a set	Tiles	Without the extra tile
Pair plus ryanmen	pair plus ryanmen	2p, 3p, or 5p	10	8
Pair plus kanchan	pair plus kanchan	6s or 7s	6	4
Pair plus penchan	pair plus penchan	1m or 3m	6	4
Ryankan	ryankan	4p or 6p	8	4

Four tiles: a set with a spare that isn't loose

Add a fourth tile to a set and the extra one looks spare. It isn't loose, though. A loose tile has nothing within two of it in its suit, and this one touches the set. Draws around the group give it a partner and turn the shape into a set plus a partial set.

The strongest is four in a row, four in a row. Read it as 345m and a 6m, or a 3m and 456m. Every tile from the 1m to the 8m makes it a set plus a partial set: a 2m gives 23m and 456m, a 7m gives 345m and 67m, a 3m gives the 33m pair beside 456m. That's 8 kinds and 28 tiles. At tenpai the same four tiles are the nobetan, a single wait on either end, from Mahjong waits. The Tenhou game review calls the shape by its Japanese name, yonrenkei (四連形), and keeps it because so many draws improve it.

Shape	Example	Takes	Tiles
Four in a row	four in a row	1m to 8m	28
Run with a tile two away	run with a tile two away	2m, and 5m to 9m	22
Aryanmen	aryanmen	2m to 7m	20
Four in a row at the edge	four in a row	1m to 6m	20
Nakabukure	nakabukure	2m to 6m	16
Run with a tile two away, at the edge	run with a tile two away	4m, 7m, 8m, and 9m	14

Two more have Japanese names. The aryanmen (亜両面), a run with a pair on one end, is the shape you met as a wait in Mahjong waits. The nakabukure (中膨れ) is a run with its middle tile doubled. Four of its five kinds leave a ryanmen: a 2m gives 234m and 45m, a 6m gives 456m and 34m. Left as it is at tenpai, though, it waits only on its middle tile, the 4m, with 2 copies left.

Now count a loose tile the same way, as What to discard first did: the draws that give it a partner. A loose honor takes 3 tiles, a 1 or 9 takes 11, a 2 or 8 takes 15, and a 3 to 7 takes 19. The top four shapes in the four-tile table beat any loose tile. The nakabukure and the 5679 beat a loose honor or terminal, but a loose 3 to 7 takes more than either, and a loose 2 or 8 tops the 5679 by one tile.

Count before you cut

You draw the 8m and finish 678m. That gives you five blocks: the 678m set, the 23m ryanmen, the 246p ryankan, the 344s, and the 99p head. The 9s touches none of them. A 7s, an 8s, or a 9s would give it a partner, but you already hold a partial set for every set you still need, so that partner would only make a spare shape, and its 11 tiles count for nothing. The hand is 2-shanten, and the cuts that keep it there aren't worth the same.

Cut	What it costs	Tiles
	Nothing: it touches no block	28
or	The ryankan becomes a kanchan	24
	The 344s becomes a plain ryanmen	24
	The 344s becomes a pair	20

Cut the 9s and you keep 28 tiles: 8 for the 23m, 8 for the ryankan, 10 for the 344s, and the last two 9p. The 9p counts because the two pairs work as a team: draw it and 999p is a set, with the 44s as your head. Cut a 4s and the 9p stops counting as well, since the 99p is now your only pair. That's why one 4s costs 4 tiles, not 2. The hand analyzer opens this hand with every cut ranked. Here the 9s goes and every shape stays.

The two kinds of shape do different jobs, though. A three-tile shape's extra tile helps its partial set become a set, so it counts even with five blocks. A four-tile shape's spare works like a loose tile: it adds tiles only while your hand still needs a partial set. Once the rest of the hand holds five blocks, head included, the spare and a loose tile both sit outside them, and the count ties. In 2379m3456p2267s15z, cutting the 3p, the 6p, the East, or the White each keeps 20 tiles. The five-block method shows how to break that tie.

And a ryankan or a nakabukure that never improves leaves you a one-sided wait. 1-shanten: the step where hands are won shows what to do with a ryankan near the finish, and Headless and floating-tile 1-shanten shows when the nakabukure's better waits are worth a few tiles.

Practice

Find the tiles outside your sets, then count what each one brings.

Take these shapes to the tile efficiency trainer. Its hands hold no loose tile, so every cut breaks a shape. Name each three- and four-tile group and its count before you cut, then check the ranking.