Can you give more details ? About what games you didn't play, what games you did ? Also the lenght of the song from what you remember ?
The only one I'm thinking of right now that sounds like a casino song is this one, which is from the slot machines :
https://www.youtube.com/watch?v=Cvxn4ECxTnI
ok here's a list i compiled of all mario games ive played & haven't played from the DS & up! (not counting any mario arcade games)
i have played:
new super mario bros (DS)
super mario 64 DS (DS)
mario kart DS (DS)
mario party DS (DS)
mario hoops 3-on-3 (DS)
mario kart wii (wii)
new super mario bros wii (wii)
mario party 8 (wii)
super mario galaxy 1 & 2 (wii)
new super mario bros 2 (3ds)
DDR mario mix (GC)
paper mario thousand-year door (GC)
mario sports mix (wii)
mario super sluggers (wii)
(also if we're including mario-related games related to mario but not part of the main series like smash bros i have played all except wii u)
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i haven't played:
any mario game on wii u (i don't have a wii u yet!)
super mario sunshine (GC)
luigi's mansion (GC) (also haven't played the 3ds game)
any GC mario party game
mario kart double dash (GC)
any of the 3ds or DS mario & luigi series games
paper mario sticker star (3ds)
super paper mario (wii)
any mario golf or tennis game on wii,3ds,or DS
(if we're counting sub-series of mario like wario,donkey kong,yoshi,etc then i have played: wario land shake it (wii),warioware DIY (DS), wario master of disguise (DS),donkey kong country returns (wii),donkey kong jungle beat (GC),donkey konga 3 (GC),DK jungle climber (DS),i haven't played any yoshi-centric games on DS,wii,3ds,gamecube,or wii u!)
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hopefully this can give you an idea of what im looking for! as for the length of the song itself idk exactly but i'd say probably about 2 or 3 minutes!