Yes, tui is a Scrabble word!
...and is worth 3 points in Scrabble, and 4 points in Words with Friends
Tui is a valid Scrabble word.
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What Scrabble words can I make with the letters in tui?
Words that can be created with an extra letter added to tui:
There are 7 words that can be made by adding another letter to 'tui'.