There are a total of 4 mini-games available to play: Jewel Bingo, Find bombs, MU Roomy and Balls and Cows.
How to play a mini-game
In order to play any of them you must collect 24 card pieces that drops from monsters lvl 32 and higher. Once you complete 24 card pieces it will turn into a deck which allows you to play one mini-game.
You must click the mini-game banner and click start game. You can read mini-game instructions and details there.