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Understanding Waits

One of the most interesting aspects of Mahjong play is constructing flexible waits.

Having an almost complete hand (lacking only one tile to win) is called waiting or fishing. Being one tile away from a waiting hand is simply called 1 away (or 2 away, etc).

Note: The furthest you can ever be from a waiting hand is 6 tiles; this is all it takes to produce a wait for Seven Pairs.

Most mahjong hands require 4 sets and a pair.

Consider the following waiting hand:

It is nearly complete, as it already has 3 sets and a pair:

There are also the tiles Circle 7 and Circle 9 which can be interpreted as an incomplete Chow. If we were to draw (or another player would discard) a Circle 8, we could use this tile to complete the Chow 789 and win the hand.

This is called a closed wait. It is not very flexible since Circle 8 is the only tile we can win on. There are only four of these in play; some are probably tied up in other players hands, or they may all have been discarded already.

What if we had a duplicate Circle 9 instead of the Circle 1?

This hand is also nearly complete, as it has 3 sets and two pairs:

Either of the pairs could be completed with one more of its kind, making it a Pung and fulfilling the 4 sets + pair requirement. This is called an open wait since it lets us win on multiple tiles. However, this is still not a very flexible hand: while there are 4 of both Circle 9 and South, we already have 2 of each in our hand. This still leaves a total of only 4 tiles available to win on, though with slightly better chances.

Let's have a look at yet another variation:

The difference is tiny, but this hand is a lot more powerful than the previous two. The Pung of East and pair of South remain the same, as do most of the Circle tiles. With a Circle 9 we could complete the Chow 789. We could also use a Circle 6 to form the Chow 678. Are there any other options?

It might not be obvious at first, but this hand is also waiting for a Circle 3. Since all the tiles are concealed, we may still choose how to arrange them. With an additional Circle 3, we could form the Chows 123, 345 and 678! The way we mentally structure the hand has a huge impact on our play.

Since there are 3 tiles we can win on we call this a 3-way wait. If we break it down to individual tiles, there are 4+3+3=10 tiles we are potentially waiting for (we already have one each of Circle 3 and 6).

Note: Just because a hand is waiting it might not always be worth enough points to win. For simplicity the hands shown here can go out on either of the tiles mentioned; Half Flush and Pung of East are enough to go out in most rulesets. Ideally you would want the full sequence 123456789 to score a Pure Straight as well.

Wait flexibility is taken to the extreme with the special hand Nine Gates:

As the name suggests there are nine possible tiles to win on, depending on how we arrange the sets (for clarity, the pair has been moved to the right).

This leaves a massive total of 23 potential winning tiles. This hand is considered "special" for a reason; you will most likely never see it in a real game. It is included in the rules mostly as a thought experiment.