Key takeaways
- Visible means you can identify the tile and count, not merely that it is in a discard row.
- Copies in your own hand must be removed because they cannot be drawn again.
- Every tile in a chow, pung, or public kong is counted by type.
- Four visible copies create kabe; three leave one unknown copy.
- Unknown means location is hidden, not that the tile is certainly in the live wall.
Why are visible tiles foundational?
Theoretical shape tells you the maximum acceptance. Play asks how many copies remain unseen.
The block 45m theoretically accepts eight tiles. If another 3m is in your hand, two 3m are discarded, and an open group contains one 6m, only one 3m and three 6m remain unknown: four live copies, not eight.
Without visible correction, an explanation keeps counting tiles that cannot be drawn.
What should be counted?
Your own hand
This is commonly missed. If you hold two 5p and another shape lists 5p as effective, only two copies remain unknown.
Every discard row
Discarded tiles have left concealed hands and the wall. If a discard is called, its public location changes, but it must still be counted only once.
Chows and pungs
A pung exposes three copies of one type. A chow exposes three consecutive types. Add each tile to its own visible count.
Kongs
An exposed kong or publicly identified concealed kong reveals all four copies and forms kabe. If a ruleset does not reveal the identity of a concealed kong, an observer cannot assume its type.
Public indicators
A Riichi dora indicator is itself visible. The following tile is dora, but visible-count subtraction applies to the indicator tile, not automatically to the dora.
Flowers and other public tiles
Flowers may not be structural effective tiles, but their exposure changes wall and replacement-draw accounting. Include them only in the part of the model they affect.
Building a visible-tile table
Create one cell for each of the 34 basic tile types and start at zero. Scan:
- Your hand
- All discard rows
- Every call and kong
- Public indicators
- Other identified public areas
Increment the matching cell for each physical tile. A normal type exceeding four signals an input or counting error; stop using the result.
Calculating live copies
For each effective type:
unknown copies = 4 - visible copies
Then sum distinct effective types. Build the union first so the same 4m accepted by 23m and 56m is not counted twice.
| Effective type | Visible | Unknown |
|---|---|---|
| 1m | 1 | 3 |
| 4m | 3 | 1 |
| 7m | 0 | 4 |
Total live acceptance is eight, not the direct sum of each block’s theoretical total.
How do kabe and one-chance appear?
- Visible count 4: complete kabe; no opponent can conceal the tile.
- Visible count 3: one-chance; one unknown copy remains.
- Visible count 2: two unknown copies remain and the condition is neither.
Kabe removes routes that require the tile. One-chance reduces their copy count but does not delete them.
Unknown tiles versus live-wall tiles
Tiles hidden from your perspective may be:
- In the drawable wall
- In opponents’ concealed hands
- In a rules-specific dead area
- In an unidentified concealed kong
“Three unknown” does not mean “three in the wall.” With public information alone, state the unknown maximum or calculate a conditional model with explicit assumptions.
Correcting second-order ukeire
Visible counts affect future development too. If candidate A’s advantage requires drawing 5m into a three-sided shape but all four 5m are visible, that second-order route does not exist.
Candidate B can therefore be stronger even when the immediate theoretical totals match.
Supporting defense
- Four visible creates kabe and removes concealed blocks requiring that tile.
- Calls reveal fixed opponent melds.
- Discards can supply genbutsu or suji evidence under the relevant rules.
- Visible honors constrain pung and double-pair possibilities.
These are exclusions, not complete risk estimates. Visible tiles prove some structures impossible but cannot prove which remaining structure is present.
Common errors
- Counting only discard rows.
- Counting a called discard once in the row and again in the meld.
- Subtracting dora instead of the indicator.
- Treating three visible copies as complete kabe.
- Locating every unknown copy in the wall.
- Correcting immediate acceptance but not future routes.
Scope and limitations
This article assumes four copies of each ordinary type. Red fives replace ordinary fives within the same four-copy total. Flowers, wall structure, and concealed-kong visibility vary by rules. Visible information is never complete information.
Practicing live-tile correction with Tingpai Lab
Write theoretical effective tiles first, then subtract the hand, discard rows, and calls by type. If candidate order changes, identify the exact count or future route that disappeared. This builds a transferable process rather than a memorized “dead tile.”
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