Iishanten

Iishanten is the state of a hand where one tile is needed to achieve tenpai. This is the closest state to tenpai.

Four main types

The four types are based on the possible configurations regarding complete and incomplete tile groups.

Yojouhai

Waiting for: (to form a sequence)

Floating tile iishanten 「余剰牌」 is a hand with two complete groups and a pair, with two incomplete groups waiting to be completed. One tile (the East tile in the example hand) does not contribute to any group, and so is said to be floating.

Kanzenkei

Waiting for: (to form a sequence), (to form a triplet)

Complete iishanten 「完全形、完全イーシャンテン」 is an improvement on floating iishanten where all tiles in the hand contribute to the iishanten. In the example hand, the 223s group now has three tiles working together.

This hand is also an example of perfect iishanten. Perfect iishanten is a complete iishanten with two ryanmen groups, thus guaranteeing a ryanmen wait.

Atamanashi

Waiting for: (to form a sequence), (to form a pair)

Headless iishanten 「頭なし、ヘッドレス」 is a hand with three complete groups, no pair, and one/two incomplete groups. An ideal headless hand, as shown above, will have two ryanmen groups waiting to be completed. If either ryanmen is completed, the hand enters tenpai with a tanki wait. If any of the four tiles are paired, the other tile of its group can be discarded, forming a wait with the other ryanmen. (E.g. if a 2s is drawn, discard 3s to enter a ryanmen tenpai.)

With a triplet

Waiting for: (to form a sequence), (to form a pair)

Headless iishanten + closed triplet is a stronger version of headless iishanten. Here, if either ryanmen is completed, then the triplet can be discarded (turning it into a pair), thus retaining a ryanmen wait.

Assuming the hand has two ryanmen groups:

A headless iishanten without a triplet has better tile acceptance than a perfect iishanten, but there are fewer tiles that lead to a ryanmen wait at tenpai.
A headless iishanten with a triplet has better acceptance than perfect iishanten, and has more tiles that end with a ryanmen wait. Thus, headless iishanten + triplet is an overall stronger wait.

Kuttsuki

Waiting for: (to form an incomplete group), (to form a triplet)

Sticky iishanten 「くっつき」 is a hand with three complete groups, one pair, and two floating tiles. It seeks to form an incomplete group. This type of iishanten tends to accept the most tiles, but many of those tiles lead to a non-ryanmen wait.