The branching factors and unknown information in civilization are far larger than chess. They are possibly far larger than go.
With 50 units, each can move in one of 8 different directions, or do 2 or so actions not-moving. That is on the order of 10^50 possible "next moves".
If you order the movement of the units canonically (which removes some useful strategic options), every turn the first unit movement of units still generates a branching factor of 500: still far larger than chess. (and most units can move more than 1 unit of distance)
So the game has to have lots of heuristics to decide what kinds of moves one should do.
And one can often not determine what the results of a set of actions are: you don't know where the enemy troops are, if the enemy will produce more units, or how the enemy will react to your movements.
Hence heuristic strategies. The AI makes a plan based off of heuristic rules and develops it based off heuristic rules.
To test these rules, you put them up against human and AI players, and see how the AI performs. Does the AI act like you want a nation to act? Is it an effective challenge?
Hahah, been awhile since I took Probability and Statistics!!
Aye, the number of possibilities is certainly prohibitive. But I can't help but think there's not a way to break it down into simpler models. Perhaps on a local battlefront using just the units present, and making an educated guess about what units might be just out of sight based on the enemy's tech levels, production levels, etc. Also, instead of iterating based on 50 specific units, use small stacks based on types, such as spearmen, archer, mounted, axemen, siege weapons.
Another possibility is to creat a cut-off for how many units the Ai may calculate iterations for. Many skirmishes occur with perhaps a handful of units, and the AI often blunders woefully. I see no reason in these situations that iterations couldn't be used instead of strict heuristics. I suspect there has to be a way to make at least some better use of the computing power available. Instead of iterating all the specific units and specific move combinations, perhaps find a way to iterate outcomes with various 'power assignments' such as occupying a forrested hill with access to a nearby road, or a nearby contested town or resource.
Bigben34