Here scientific background information is provided. Be aware that the following chapters have not yet been proofread as thoroughly as they should. They are for courageous readers only.
Well yes, it seems our dear project has to do with about all other branches of mathematics one can think of, but a little bit of hands waving is necessary as well. We aren't mathematical crackpots, are we?
Perhaps some things here might turn out as mere mess. Since we are non-experts in the fields addressed, some inaccuracies are of course unavoidable. Anyway it is crucial to be able to explore the unknown terrain by using computation (that's how the saying goes).
But there is no reason for a too submissive behavior either. On one hand one can try to use information from other parts of science for our concrete strategy games. And on the other side in return, one might even ask if by the help of computational trial / error and learning by doing we address some interesting mathematics valuable in its own right. General theorems emerge starting from shared properties of a wealth of examples.
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