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skeptical_lurker comments on After Go, what games should be next for DeepMind? - Less Wrong Discussion
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What about chess? See if a DNN based AI beats a conventional chess AI running on the same processor power. Many people are interested in chess, and if it could push forwards chess theory, then that would be very interesting.
Why not check out the AGI capabilities of Alphago... It might be possible to train chess without architectural modifications. Each chessboard square could be modelled by a 2x2 three-state Go field storing information about chess figure type. How good can Alphago get? How much of its Go playing abilities will it loose?
This isn't at all the same thing, but it might amuse you: Gess the game.
http://arxiv.org/abs/1509.01549 is relevant.