fan tan vs game of chance

fan tan and game of chance both are nouns.

Word	Noun	Adjective	Verb	Adverb
fan tan	Yes	No	No	No
game of chance	Yes	No	No	No

As nouns, game of chance is a hypernym of fan tan; that is, game of chance is a word with a broader meaning than fan tan:

fan tan: a Chinese gambling game; a random number of counters are placed under a bowl and you gamble on how many will be left (0, 1, 2, or 3 modulo 4)
game of chance: a game that involves gambling

Other hypernyms of fan tan include gambling game.

fan tan (noun)	game of chance (noun)
a Chinese gambling game; a random number of counters are placed under a bowl and you gamble on how many will be left (0, 1, 2, or 3 modulo 4)	a game that involves gambling