numbers game vs lottery

numbers game and lottery both are nouns.

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

As nouns, lottery is a hypernym of numbers game; that is, lottery is a word with a broader meaning than numbers game:

numbers game: an illegal daily lottery
lottery: players buy (or are given) chances and prizes are distributed by casting lots

Other hypernyms of numbers game include drawing.

numbers game (noun)	lottery (noun)
an illegal daily lottery	players buy (or are given) chances and prizes are distributed by casting lots
	something that is regarded as a chance event