numbers pool vs numbers game

numbers pool and numbers game both are nouns.

Word	Noun	Adjective	Verb	Adverb
numbers pool	Yes	No	No	No
numbers game	Yes	No	No	No

As nouns, numbers pool and numbers game are synonyms defined as:

Other synonyms of numbers pool include numbers, numbers racket.

numbers pool (noun)	numbers game (noun)
an illegal daily lottery	an illegal daily lottery