I believe it is non-deterministic. If you go digging behind the game, a Mogma will pop up and give you hints on how to play. He says that smaller value rupees have fewer bad holes around them and that higher value rupees have more bad holes. This leads me to believe that the game builds each field randomly. There isn't a set of pre-defined fields the game rotates between.
The only thing that affects the field is the level at which you choose to play: Beginner, Intermediate, and Expert.
If you want some help playing the game, there is the Thrill Digger Assistant/Solver that will let you see the probabilities of finding good holes based on what you've dug up.