American Mahjong Addition Hands Explained
Addition hands arrange numbered tiles so the values form an arithmetic relationship shown on the card. The equation helps identify the ranks, but the hand is still built from exact tile groups with fixed spacing, suits, and joker rules.
The arithmetic identifies ranks, not loose substitutions
If a line represents one number plus another number equaling a third, the rack must contain the exact printed ranks in the exact group sizes. You cannot substitute a different equation merely because it produces the same total.
Printed colors still determine suit relationships. The addends and result may need one suit, two suits, or three suits according to the line.
Read both layers of the line
Arithmetic layer
Identifies the number relationship among the groups.
Mahjong structure layer
Controls suit colors, group sizes, flowers, dragons, exposure status, and joker eligibility.
Addition-hand verification
- Confirm the exact equation printed on the current card.
- Map each number to its required tile group.
- Assign printed colors consistently to suits.
- Keep pairs natural.
- Do not merge separated groups for joker use.
- Verify all fourteen positions before declaring mahjong.
Addition-hand questions
Can I use any numbers that make the same total?
No. Use the exact ranks and arrangement printed on the current card.
Does a plus or equals sign represent a tile?
No. It communicates the arithmetic relationship; only the tile symbols and groups are collected.
Can jokers be used in addition hands?
They may be used only in eligible matching groups of three or more unless the line or rules impose a stricter requirement.