As has been stated before, over the long run you can not win against the house. The only game in the on board casino that you can actually win, as you are not playing against the house, is poker.
Having said that, gambling can be fun and reducing the odds for the house make it even more fun as you will loose less. The best games in the casino with the lowest house odds (on board) would be craps and black jack.
It is easy to Google and find the best methods to play these games. For craps the easiest way to play and lower the house odds is to put a minimum bet on the pass line. When the point is established, make an odds bet. If the point is a 6 or an 8 bump the odds bet up. The odds bet is the best bet on the table.
For black jack you can print out a "cheater card" on how to best play, when to hit, stand, double down, etc. Short of card counting, which most people don't take the time to learn, the card can teach you the best moves to make to lower the house odds.
My personal system is to win money at the poker table and then loose it at the crap table. It works well for the casino and keeps me from carrying around all that extra money.