Implement the game logically, implement different players with possible strategies, let the different combinations play out thousands of games, see if alle strategies win roughly the same time, else tweak values.

If you haven't done that before: create a function or even better a class for the game, make classes for different playstyles. Each game has to have n players, the game class should have a method that plays the game, most likely executing a round method until the win or end condition is triggered. Each call of round should ask the player objects what they do, e.g. call the players play_round method, whilst giving them the information about the state of the game, these methods return the actions to the game, making dice rolls or whatever during their turn. The game objects shall collect all the informations you want to observe.

Depending on the complexity of your game this is quite an effort, but you will get premium knowledge about balance and once it is done, changes and tweaking balance are easy and almost trivial.