Tests are our safety nets. If we don't trust on their integrity, we will be in great danger.
TL;DR: Don't write non-deterministic tests.
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Should tests verify the internals (private fields) of a class?
I've seen many test cases that assert every internal variable. I don't like that.
My reason is: Every time you refactor the class you have to rewrite the tests. However, tests are supposed to ensure the external behaviour of a class doesn't change unexpectedly. If the tests are rewritten, it's hard to confirm whether the external behaviour changed.