by all odds vs definitely

by all odds and definitely both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by all odds	No	No	No	Yes
definitely	No	No	No	Yes

As adverbs, by all odds and definitely are synonyms defined as:

Other synonyms of by all odds include decidedly, emphatically, in spades, unquestionably.

by all odds (adverb)	definitely (adverb)
without question and beyond doubt	without question and beyond doubt