Scrabble Dictionary

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Yes, betrothal is playable

...and is worth 15 points.

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Enable (Words with friends)
SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Betrothal" Definition

noun

A mutual promise to marry; an engagement: announced their betrothal the next day.
The act of betrothing or the fact of being betrothed.
The act of or fact of being .
A mutual promise or contract for a future marriage.