The minigames in Romancing SaGa 3, I believe, are the best ones out there.  There are 3 minigames, 2 of them are only available to Mikhail.

The Business Game

Thomas's Business Game- you'll need Thomas to start it, but don't need him to finish it.

The Ruling Game

Mikhail's Ruling Game- Mikhail must be your main character.  This is his attempt to rule Loanne and is the most difficult and frustrating game out of all of them.

The War Game

Mikhail's War Game- a subsection of Mikhail's ruling game.  These are his campaigns against various foes.  Personally, it's my favorite of his games.  Harid also has the first 2 battles of Mikhail's war game during his introduction.

War Game Tactics

This is just a list of the various tactics you may get in Mikhail's Ruling Game.