bad luck vs mischance

bad luck and mischance both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad luck	Yes	No	No	No
mischance	Yes	No	No	No

As nouns, mischance is a hyponym of bad luck; that is, mischance is a word with a more specific, narrower meaning than bad luck:

bad luck: unnecessary and unforeseen trouble resulting from an unfortunate event
mischance: an instance of misfortune

As nouns, bad luck and mischance are synonyms defined as:

Other synonyms of bad luck include mishap.

bad luck (noun)	mischance (noun)
unnecessary and unforeseen trouble resulting from an unfortunate event	an instance of misfortune
an unpredictable outcome that is unfortunate	an unpredictable outcome that is unfortunate
an unfortunate state resulting from unfavorable outcomes