1) Speed and Precision
The "button" factor -- fast and precise execution of commands in real-time. Completely irrelevant to Civilization, but a major factor in for example sports, racing, fighting and RTS games (and DOTA too?)
On this front humans can never outperform optimized AI, since a program can perform pixel-precision tasks with 100% accuracy.
To counteract that advantage is actually very easy.
Sample the click rates and accuracy from a lot of players, and then construct
appropriate probability distributions. (There's definitely no shortage of data
for StarCraft for a huge range of player abilities and in-game situations.)
In short, the AI's click rates and accuracy can be forced to be, on average, the
same as the class of player(s) it is playing against. It is easy to add or
subtract small random time increments from that average click rate (with the
same variation around the average as the human player), and to make it more or
less precise.
There are many other effects that can be included: e.g. tiredness, hesitation,
time since last coffee, nervousness or calmness about the current position in a
tournament, etc, etc.
Many facets of Esports science have similarities and exact counterparts to those
in well-established physical sports sciences.
2) Combinatorics
Volume of information to process, relevant when all information is available to both players. Again, humans don't stand a chance in games like chess. A factor in Civilization, especially combat tactics, but not huge.
Not quite.
If I asked you to find the shortest path around 4 random cities on a map of the
USA without visiting any of them twice you coud probably do that very easily.
All information is known to you and an "AI".
If it was 512 cities (a standard travelling salesman problem benchmark), you
would struggle to beat the best distance found by some cheap hardware and freely
available algorithms.
However, there are also many similar situations where humans can outperform
computers...
3) Judgment
This is where things get more complicated.
So much so that we could spend years discussing it!
Yes, computers can out-grind the best players in the world in chess and some
simple board games. However, there are many situations, where a human can size
up a position on the board in a fraction of a second, whereas a computer might
never find the solution.
In Civ, you might want to stop another civ from knowing about a certain part of
the map. You know that you can just buy a tile and the AI won't get into that
region for a long time, if ever, without declaring war. Computer algorithms can't
do that.
We are able to imagine future situations. For example, suppose that there were
mirrors at the ends of a chess board, and that pieces could move off the end
of the board and land back where they were reflected in the mirror.
Humans can see possibilities and difficulties with such a rule change in a very
short time. Computers cannot.
Great questions, by the way!