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RACKING A PICKED TILE IS NOT MANDATORY (Article 10)
Commentary: When players pick a tile from the wall, they are not required to rack it. The only exception is when a player wants to do a joker exchange with one of their concealed tiles. They must first rack the picked tile from the wall before they request a joker exchange with a different tile, or they will have less than 13 tiles on their rack (MJME 2024 page 16 #1).
Another consideration on this topic is the WINDOW OF OPPORTUNITY FOR THE LAST DISCARD (Article 107).
Question from a player: Is a player required to rack a picked tile from the wall?
Answer from the League: Racking is not mandatory, although recommended after a player has picked a tile. The tile previously thrown is still ‘in play’ and may be called until the picked tile has been placed in the sloped portion of their rack or has been named and discarded.
Sources: Mah Jongg Made Easy (2020 page 21, #18); National Mah Jongg League Bulletin (2022)