Application of Block Theory – Part 1
By now I’m sure you’ve learnt about five block theory and how it works, but how do you actually apply the theory to determine what’s the best tile to discard? How do you make your decisions systematically and consistently?
Today’s lesson is taken from Hirasawa Genki’s よくわかる麻雀の勝ち方 (Yoku Wakaru Maajan no Kachikata).
Count your blocks
The first step is to count the number of blocks you currently hold. Do you have four or less, five, or six or more? Mahjong is a game of comparison, and what you compare will depend on the answer to this question.
Four blocks or less
This is usually how things are at the start of the round. At four blocks or less, you need to create more blocks in order to form a complete hand. In order to do so, you need to compare “floating tiles” – these are single tiles that you hope to use to create another set. For example, take the following hand:
This hand can be divided up into four blocks as follows:
The leftover are floating tiles from which you need to make one more block. The easier it is to create a block from a floating tile, the more valuable that floating tile is. The various types of floating tiles are ranked in value here:
- Yonrenkei (shapes such as or , with four consecutive numbered tiles) and nakabukure (shapes such as or , wherein a sequence has two of the tile in the middle) and other consecutive shapes.
- Tiles numbered 3 to 7. You can form a block with a if you draw anything from to .
- Tiles numbered 2 or 8. You can form a block with a if you draw anything from to .
- Tiles numbered 1 or 9. You can only form a block with a if you draw one of , and none of these give you a particularly good wait.
- Honor tiles. You can only form a block with an honor tile if you draw another of the same tile.
- Tiles numbered 1 or 9 when you already have the middle suji (that is, 4 or 6). If you have , you can discard the and still make use of or .
Some additional modifiers also come into effect:
- Dora tiles increase in value by about two ranks. This one is important, so don’t forget it.
- Tiles that are next to a triplet such as the in decrease in value by one rank. This also applies to tiles that you can see elsewhere on the table, such as in the discard pond, other players’ called tiles, or the dora indicator. This is simply because there are more tiles in that area that are used up, and therefore there are less tiles that you can use to create a block with that floating tile.
- Tiles that are nearby to a completed sequence increase in value by one rank. For example, the in becomes more valuable because, in addition to , you can also form a block with it by drawing . Similarly, the in is more valuable than a regular isolated as you can form a ryanmen wait by drawing or a kanchan wait by drawing or .
- Among nakabukure and yonrenkei shapes, the closer they are to the middle, the better. For example, is a more valuable nakabukure shape than because it forms a ryanmen wait if you draw any of , while the latter only forms a ryanmen upon drawing . Similarly, is a more valuable yonrenkei shape than as you can form a ryanmen with any of , but with the latter you can only form a ryanmen with or .
- Similar to point #6 above, tiles numbered 2 or 8 where you hold a 5 are relatively less useful than other tiles numbered 2 or 8. However, they’re still more valuable than 1 or 9 tiles. Treat them as half a rank down.
At six blocks, you’ve got one too many and you’ll need to discard one. For that purpose, you’ll need to compare your blocks to determine which is the weakest one – the one least likely to form a completed set. The various types of blocks are ranked below:
- Ryanmen waits or better
- Shapes waiting on five or more tiles, such as , , or
- Kanchan, or a pair when you have two pairs in your hand
- Pairs, when you have three pairs in your hand
As with before, a few modifiers come into effect:
- Blocks with overlapping waits decrease in value by half a rank. This refers to shapes such as , which share an overlapping wait on the .
- You should maintain six blocks if (and only if) all your incomplete blocks are the same rank and you absolutely cannot choose between them. For example, with a hand like
you should discard to maintain six blocks. You can’t tell which of your incomplete blocks will be completed first, so rather than choosing to break one up, you should take a wait and see approach.