If you pay, you get 5 tries, but it's not guaranteed that you will get something at all! As for playing for free, you get an occasional free play or two, usually when a new set is released, but you can also earn some plays from the practice crane! In the practice crane, you grab dummy badges that are based on the day's main set, and if you catch 10 of them total, you get a free play for every 10 of them! The dummy badge counter carries over from one day to another, so if you get 5 dummy badges one day and then 5 the next time you play, you still get 1 free play! Additionally, every dummy badge you grab has a chance of being a special one that awards you 2 play coins, but it won't be added to the dummy total and, while already rare but still possible to get two at once, each special one you get drastically decreases your chances to find another one! Finally, there is just one upside to paying for plays, if you have payed for 10 or more plays, then you can occasionally get free themes!
PS: Just a heads up, if you leave the arcade, you lose all your plays! If you have any plays at all, you are forced to use them right away!