penny ante vs poker game

penny ante and poker game both are nouns.

Word	Noun	Adjective	Verb	Adverb
penny ante	Yes	No	No	No
poker game	Yes	No	No	No

As nouns, poker game is a hypernym of penny ante; that is, poker game is a word with a broader meaning than penny ante:

penny ante: poker played for small stakes
poker game: any of various card games in which players bet that they hold the highest-ranking hand

Other hypernyms of penny ante include poker.

penny ante (noun)	poker game (noun)
poker played for small stakes	any of various card games in which players bet that they hold the highest-ranking hand
a business deal on a trivial scale