When can we have an AI that plays Third Reich? But not too well, I want to at least have a chance.

I'm actually not joking. I wonder how much different it would be to teach an AI like this how to play more complex games. I imagine Axis and Allies wouldn't take much, but Third Reich is notoriously complicated. The quickest war-length game I've played took a week of playing 3-4 hours per day and games like that seem to me to be much more similar to real world problems, with multiple different sorts of trade offs that interlock with each other.

Are neural AIs like this actually feasible to train for problems like that or are other AI techniques better suited to it? What about games with multiple different game systems, like board games with a card game element to them like Settlers of Catan? Would you need to use several different types of AI to optimize different parts of the game?

The hard part is probably writing a program to encode the rules of the game. Then, you can figure out how to represent the state (i.e. the board and the player's cards/resources etc) as a matrix or array (i like how this is done in NLP, they tend to represent each character/word/token as a 1-hot vector and then reduce the dimensionality of these (normally really sparse) inputs.

OpenAI's gym is probably a good place to start, as you can crib how they do it for a whole bunch of games. https://github.com/openai/gym