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If we decide the evidence is strong that there is an Intelligent Designer, what tests would we be able to run, what would we expect to find upon further investigation, to support the theory?
Yup, that's the crux of the question.
Your post about the rigged card game is an interesting one. We could, following that idea, get a sample of the number of "shuffles" (planets in the universe), and if we knew all the variables that determine whether a planet supports life, and had a large enough observation window (number of eons), we might be able to compare the actual number of life-evolving planets with the predicted number based on the variables.
The only problem is, as difficult as that experiment would be, even THAT doesn't count as a testable theory for ID, because if the prediction were different from the result, it doesn't automatically point to a creator. It might, for example, point to an incorrect assumption about one of the variables.
How do you test whether the game was rigged in the case of the card shark dealer? You try to observe him shuffling. Perhaps watch him with a high-speed camera. How do we apply that analogy to testing the ID hypothesis? How can we check, scientifically, whether God is keeping the Ace on the top?