Voltorb Flip is easily my favorite mini-game in the series.
I normally avoid the Game Corners. If there's something there that I want, I usually just grind until I can buy enough coins to buy it, since I detest the slot machine games. The slots are some combination of luck and twitch timing (some of them have been almost pure luck, while others have added some amount of perfectly timed button pressing - the latter's better than the former, but not by far).
At least Voltorb Flip is an actual puzzle, so it rewards thinking, rather than just relying on luck and a bit of twitch skill. It still comes down to luck a bit too often - too many of the puzzles, and particularly at the higher levels, come down to a point at which there's a "box" of choices left. There'll be two columns left with, say, one 2 each, and there will similarly be two rows with one 2 each. That means that one of the 2s is at the intersection of one row and column and the other one is at the intersection of the other row and column, but the other two intersections are 1s at best, and quite possibly Voltorbs, and there's absolutely no way of knowing which is which. So all you can do is pick one and hope.
Ah, but that's not all you can do, and that's the other thing that I like about Voltorb Flip. If you get down to that point and don't feel like gambling on a wild guess, you can just take your winnings and go on to the next game.