Mahjong Fundamentals 2: Starting Hands & Five Block Theory

Mahjong is a fast-paced game – most of the time you’ll be expected to complete each turn in around 5-10 seconds or faster, which doesn’t give a lot of time for complicated calculation on what the best move might be. This is especially true if you’re a beginner, as you won’t have the experience or knowledge in situations to see answers that more experienced players will intuitively know to be the correct choice.

Early on in the hand there is a lot to think about all at once. How fast is your hand looking to be? Which yaku should you pursue? If someone discards a specific tile, do you want to call it this early on? What is the dora? And of course, on your turn, which is the best tile to discard? This article is intended to help with the last of those questions, to allow you to free up a bit more of your attention for considering the other aspects, which we’ll cover in the next article.

An Introduction to Five Block Theory

One of the key hand-building techniques in mahjong is known as five block theory. When you get your starting hand (often called haipai) using five block theory is incredibly useful to identify the general shape of your hand and which tiles you should discard first. The general principle is based on the fact that your final hand can be expected to be four sets of three and a pair, which is five blocks in total. Thinking about your hand in terms of forming those five blocks is something that most players will already do intuitively, but five block theory helps structure this thought process.

In the early hand, you will have a mixture of complete sets (mentsu), incomplete sets, and isolated tiles. Obviously complete sets typically are the most useful to keep in your hand, and isolated tiles are typically the least useful, so we should discard isolated tiles first. Using five block theory helps us work out which tiles are isolated and therefore which we should discard.

Let’s try an example starting hand:

This hand has two complete sets, along with two incomplete sets (a proto-run and an complex shape), which gives us four blocks in total. We can split the hand up like this:

This gives us three isolated tiles: , and .

Lets consider the fact that the hand currently has four blocks in total. This means we should expect our fifth and final block to build around one of the three isolated tiles, by progressing it to an incomplete set and then a complete set. The question is which one is the least useful for forming this fifth block and should be discarded?

For the two dragon tiles, they can only progress to an incomplete set if we draw another of the same tile, of which there are 3 tiles left for each one. On the other hand, for the it can progress to an incomplete set if we draw any of , , , and – this is five different types of tile and a total of 19 potential tiles to advance the hand.

19 potential tiles to improve is much larger than 3, so in this case we should definitely keep the , and discard either the or tile.

Another example:

This hand has two complete sets, and two incomplete sets (a proto-run and a pair), so again we’re at four blocks (technically the 11234p group should be considered two merged blocks in a complex shape, but for this article we’ll just consider them separately). Again we have some isolated tiles, from which we’ll need to form our fifth block: , , and .

So which one do we discard first?

Looking at the potential to form the fifth block:

can accept x4, x4, x3, x4, x4 = 19 tiles total

can accept x4, x4, x3 = 11 tiles total

can accept x4, x4, x3, x4, x4 = 19 tiles total

can accept x4, x4, x3, x4 = 15 tiles total

We can see from efficiency that the has the lowest chance to join up with a tile you draw and form an incomplete set, and so we should discard . Also note that is more useful to keep than the , but still less useful than the or .

One last example:

This hand has one complete set, along with four incomplete sets (a 24 proto-run, a 78 proto-run, and two pairs), so we already have the five blocks that we need:

In this case all three isolated tiles (, , ) can be considered somewhat useless as we don’t need another block, so from a pure efficiency perspective it shouldn’t make a huge difference which one we discard first.

However in this case it is worthwhile holding onto the , due to the weakness of the block, which can only accept a to complete. If we keep the and manage to draw or later, then the new or block it forms will accept more tiles than the block already in the hand, and gives us a subtle benefit to our tile efficiency.

Even with hands that already have five established blocks, it can still be helpful to discard terminals and honour tiles before more central suit tiles.

Typical Priority for Discarding Isolated Tiles

Five block theory gives us a good tool to identify the general shape of the hand, and which tiles are isolated and therefore can be discarded. You will find in a lot of cases that you have several isolated tiles, and therefore need to work out which one to discard. However, going through and working out the tile acceptance for each isolated tile is time-consuming, and difficult to do when you first see the hand.

Luckily, for isolated tiles the acceptance doesn’t change from hand to hand, so we can just use the following general discard priority, in order of what should be discarded first:

  1. Winds that are not your own or wind of the round (valueless winds)
  2. Wind of the round (if not your wind)
  3. Dragons
  4. Your own wind
  5. 1 and 9 (terminal tiles)
  6. 2 and 8
  7. 3,4,5,6,7

There will be situations where this order will change to allow you to chase certain yaku and increase your hand value (e.g chanta, pinfu, or honitsu), but the above works as a general rule of thumb to allow you to make your initial discards quickly without damaging your tile efficiency. As you improve as a player you can start understanding the situations where breaking away from the usual priority is worthwhile, and we’ll begin to look at value in the next article in this series.

One last point of note is that the wind of the round is the first value honour tile you should discard if it’s not also your own wind. This is because it’s worth one han for you, but two han for one of your opponents (as it will be their wind also), and so compared to dragons or your own wind it’s best to discard it early to minimise the chance that they can get a pair and call pon.

If you’d like to read more on haipai efficiency and the order to discard tiles from your starting hand, then is covered in further detail in these two articles by Muller:

Haipai efficiency part 1
Haipai efficiency part 2

In the next article we’ll go into 5 block theory in a bit more depth, and look at some of the basic shapes that make up mahjong hands.

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