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Let's propose, that I can define the state of a board in a board game, with 234 neurons. In theory, could I be able to train a neural network, with 468 inputs (two game boards), and 1 output, to tell me which board state is 'better'? The output should give me ~-1 if the second board is better than the first, ~0 if they are equal, and ~1 if the first board is better than the second.

If yes, what could be the number of ideal neurons on the hidden layers? What could be the ideal number of hidden layers?

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    $\begingroup$ one issue is that a comparison function defined by what's essentially a random oracle is not guaranteed to be transitive, antisymmetric or even reflexive. It needs to be all three. $\endgroup$ – John Dvorak Jan 25 at 13:11
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For optimal performance, the network complexity should fit the complexity of the game. Since we do not know the latter, your question is not answerable.

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    $\begingroup$ I am very new to AI, and neural networks. What do you mean by the complexity of the game? If I would, for example, write down the ruleset of the game, would that help? $\endgroup$ – Adam Baranyai Jan 25 at 13:11
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    $\begingroup$ @AdamBaranyai: No that would not help, because there are no well-understood rules that can convert a written set of rules into a network architecture. There are general concepts and understanding e.g. a more complex function with more inflection points and high-frequency components will require a neural network with more neurons in hidden layers. Finding working architectures for new problems usually consists of a search, guided by experience from similar problems. $\endgroup$ – Neil Slater Jan 26 at 14:10
  • $\begingroup$ I would say that even if we knew the complexity of the game, we probably could not suggest the ideal number of neurons or hidden layers. With that view, then the first half of this answer is accurate, but the second half is misleading in that it implies if someone was to describe a game in detail, that they could get an answer. This is only going to be true when the game is one that has already been studied in detail. $\endgroup$ – Neil Slater Jan 26 at 14:16

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