From Hawaiian Pidgin craps slang, meaning “to wager everything on one roll”: one would be broke, bankrupt if one loses.
Popularized by the movie Go for Broke! (1951), which is named for the 442nd Infantry Regiment’s unit motto.
go for broke
- To wager everything.
- (idiomatic) To try everything possible or do last thing possible in a final attempt.
See also 
- ^ The movie Go for Broke!, which popularized this phrase, gives this etymology.