There is no such thing as "too many cases to test". If the code to handling a set of cases can be written, they need to be thought. If they can be written and are thought, they code that test them can we written as well. In average, for each 10 lines of (testable) code that you write, you can add a constant factor of testing code associated to it.
Of course, the whole trick is knowing how to write code that matches the testable description.
Hence, you need to start by writing a test for all the cases.
if there is a big, let's say for the sake of discussion that you have a countable set of possible cases to test (i.e: that add(n,m) == n+m for all n and m integer), but your actual code is really simple; return n+m. This of course is trivially true but don't miss the point: you don't need to test all the possible moves in the board, TDD aims so that your tests cover all the code (i.e: the tests exercise all the if branches in your code), not necessarily all possible values or combinations of states (which are exponentially big)
a project with 80-90% of line coverage, means that your tests exercise 9 lines out of each 10 lines of your code. In general if there is a bug in your code, it will in the majority of circumstances be evidenced when walking a particular code path.