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An example where the rules are simple but there's no strategy is matching pennies, an example where there are expected rules which aren't necessarily always followed is the coordination game. In more realistic examples nothing is so simple.

(Phrased differently) Without asking a new question (the only question asked is in the first sentence), at what point are agents beyond using explicit calculations and their proofs and we are better off letting the program write its own equations (learn the questions to ask, and how to solve them). There's a couple of examples below where the program knew nothing, it's only input was the pixels on the screen (and the score), still it was able to decide what the rules must be and how best to exploit them; beating human players.

An example where the rules are simple but there's no strategy is matching pennies, and an example where there are expected rules which aren't necessarily always followed is the coordination game. In more realistic examples nothing is so simple.

(Phrased differently) Without asking a new question (the only question asked is in the first sentence), at what point are agents beyond using explicit calculations and their proofs and we are better off letting the program write its own equations (learn the questions to ask, and how to solve them)? There's a couple of examples below where the program knew nothing, it's only input was the pixels on the screen (and the score), still it was able to decide what the rules must be and how best to exploit them; beating human players.

Definition: Approximation Theory

There is an interesting Q&A on Stats.SE titled: "The Two Cultures: statistics vs. machine learning?" which contains a few excellent points:

• "Methodological Statistics papers are still overwhelmingly formal and deductive, whereas Machine Learning researchers are more tolerant of new approaches even if they don't come with a proof attached."

• "The biggest difference I see between the communities is that statistics emphasizes inference, whereas machine learning emphasized prediction. When you do statistics, you want to infer the process by which data you have was generated. When you do machine learning, you want to know how you can predict what future data will look like w.r.t. some variable."

• "Ken Thompson quote: ''When in doubt, use brute force''.
  In this case, machine learning is a salvation when the assumptions are hard to catch; or at least it is much better than guessing them wrong."

(Phrased differently) Without asking a new question (the only question asked is in the first sentence), at what point are agents beyond using explicit calculations and their proofs and we are better off letting the program write its own equations (learn the questions to ask, and how to solve them). There's a couple of examples below where the program knew nothing, it's only input was the pixels on the screen (and the score), still it was able to decide what the rules must be and how best to exploit them; beating human players.

Definition: Approximation Theory