We found one dictionary that defines the word throw one's hat over the wall:

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1. throw one's hat over the wall: Wiktionary

Definitions from Wiktionary (throw one's hat over the wall) ▸ verb:  (idiomatic) To commit fully. ▸ Words similar to throw one's hat over the wall ▸ Usage examples for throw one's hat over the wall ▸ Idioms related to throw one's hat over the wall ▸ Wikipedia articles (New!) ▸ Words that often appear near throw one's hat over the wall ▸ Rhymes of throw one's hat over the wall ▸ Invented words related to throw one's hat over the wall