run a risk vs take chances

run a risk and take chances both are verbs.

Word	Noun	Adjective	Verb	Adverb
run a risk	No	No	Yes	No
take chances	No	No	Yes	No

As verbs, run a risk and take chances are synonyms defined as:

run a risk and take chances: take a risk in the hope of a favorable outcome

Other synonyms of run a risk include adventure, chance, gamble, hazard, risk, take a chance.

run a risk (verb)	take chances (verb)
take a risk in the hope of a favorable outcome	take a risk in the hope of a favorable outcome