Yes the map size plays a part, but do a little experiment -
Play the first 100 or so turns with 2 civs on "Tiny", and then play the same 100 or so turns with 2 civs on "Huge". The huge map certainly does not take exponentially more time per turn, it takes marginally more time.
But then compare the Huge map with 2 civs versus 16 civs, and you'll find that the time does go up significantly.
Which supports the idea that it is the units, not the map which is the largest factor.
Play the first 100 or so turns with 2 civs on "Tiny", and then play the same 100 or so turns with 2 civs on "Huge". The huge map certainly does not take exponentially more time per turn, it takes marginally more time.
But then compare the Huge map with 2 civs versus 16 civs, and you'll find that the time does go up significantly.
Which supports the idea that it is the units, not the map which is the largest factor.
There is a very big point in checking the ai performance on the late game and not the early game: Civ3 is unfinishable for me because late game it takes forever and a half to compute its moves whereas it's ok in the early game.
You can say that early on the ai will be civ-intensive and later on it will be map-intensive. But this 'later on' is when most of the time is spent anyway.
Just to deemphasize the processing power point of view, I want to say that MrBaggins's post was spot on. The difficult thing is to think of everything you have to manage, assess every danger and opportunity, and make bids as to which course of action is the best and what resources should be allocated to it.
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