When choosing your pieces in Checkers, choose the Yoshis in order to have the first move. In Checkers, you can press the space bar to force Mario to interrupt his thought processes and force him to make his move.
Go Fish Hint
In Go Fish, make note of the kinds of cards Mario asks you for. When you do draw one of those cards from the deck, make sure you ask Mario for that type when you next have the chance. You'll build up your own books and diminish Mario's opportunities to do the same.
Dominoes Strategy
A good Dominoes strategy is to use up all your doublets at the first opportunity. Also, try to first play pieces that display pictures that show up on other dominoes in your hand to maximise playing at length before you need to draw another piece from the boneyard.
Yacht Hint
In Yacht, let your first roll determine which scoring category you'll try to fill. If you roll four ones on your first turn, for example, it's worth spending your next two rolls trying to gain another one to score a Yacht (worth 50 points).