Tenpai

Tenpai is the state of being exactly one tile away from a complete, legal winning hand: every group is finished except for one, and a single specific tile (or one of several) will complete the hand. A hand in tenpai is 'ready' to win, and identifying when you reach tenpai, and on which tiles, is one of the most fundamental skills in mahjong. The term is Japanese but the concept applies to every variant.

Tenpai matters both for winning and for the end-of-round settlement. In Japanese riichi, you may only declare riichi from a closed tenpai hand, and at an exhaustive draw (when the wall runs out with no winner) players who are tenpai receive points from those who are not (noten penalty). So even a hand that never wins can profit simply by being ready when the wall empties. A tenpai dealer also typically keeps the dealership through a draw.

The shape of a tenpai hand is described by its wait: the set of tiles that complete it. Common waits include the two-sided ryanmen (e.g., 4p-5p waiting on 3p or 6p), the closed kanchan (4p-6p needing 5p), the edge penchan (8p-9p needing 7p), the single tanki pair wait, and the shanpon dual-pair wait. Wider waits are generally better, both because more tiles complete the hand and because of furiten considerations.

For example, a hand of 234m 567m 234p 88s with 4s-5s in hand is tenpai, waiting on 3s or 6s to finish the final chow. Until one of those arrives, you are one tile short; the instant a 3s or 6s is drawn or discarded, the hand is complete and you may win.