What to Discard: Five-Block Theory and Spotting Useless Tiles

In a what-to-discard problem, deciding which tile to cut becomes faster and more accurate if you first look at the skeleton of your hand — its blocks — before counting tile acceptance. If acceptance (ukeire) is the 'count' decision, block theory is the 'structure' decision. This article covers the structure.

A hand is made of five blocks

A winning hand is 4 melds + 1 pair. In other words, your hand is built from five blocks (melds, partial sets that will become melds, and the pair candidate). Seeing what-to-discard as 'keep the tiles forming these five blocks, cut the overflow' narrows your candidates fast.

When you have six blocks, the cut reveals itself

You only need five blocks, so if you are holding six meld-candidates, you break the weakest one. Which one to break is decided by block strength. From strongest to weakest:

• Completed meld (a run or a triplet) — strongest; it is already done.
• Two-sided partial set (ryanmen, e.g. 4-5 accepts both 3 and 6 = 2 kinds = 8 tiles) — the widest candidate.
• Closed wait (kanchan, e.g. 4-6 accepts only 5) and edge wait (penchan, e.g. 8-9 accepts only 7) — 1 kind, 4 tiles, narrow.
• A pair (pair candidate / triplet candidate) — tends to be spare once your pair is secured.
• Isolated (floating) tile — weakest; not yet a block.

If your pair is already secured, break a sixth weak partial set (a kanchan or penchan) or a spare pair first. When you have several ryanmen forming six blocks, you sometimes drop the ryanmen least likely to grow (the one closer to the terminals).

Discard order for isolated tiles

Isolated tiles that are not part of any block should be cut lowest-value first. A common priority (order to discard) is:

• Non-value honor tiles: cannot form a run and have the least room to grow — cut first.
• Terminals (1 and 9): extend in only one direction (penchan at best).
• 2 and 8: grow somewhat, but less than middle tiles.
• Middle tiles (3-7): can grow into a two-sided shape on either side, so they are the most valuable isolated tile — keep them.

There are exceptions. A value-honor (yakuhai) pair candidate, dora and tiles next to dora, and tiles of a suit you are collecting for a flush all gain value even when isolated. Learn the basic order first, then weigh hand value and yaku once it is second nature.

Decide together with acceptance

The practical procedure is simple: (1) use blocks to narrow the 'cut candidates' down to a few tiles, then (2) among those, choose the discard with the largest tile acceptance (see the companion article). Structure (blocks) does the big narrowing; count (ukeire) makes the final call. This two-step approach is the fast, hard-to-miss way to think about what to discard. On TsumeDojo each what-to-discard problem shows the accepted tiles and count after you answer, which helps with step (2).