Then deconstruct the enemy civ and see if it was in any way likely that what happened could within the bounds of probability. For instance, in one game I was deconstructing one of the enemy cities defended by LBs and axes. On two separate occasions, an axe beat a full strength modern armor unit!? The odds are of course, 99.9 so it could possibly happen once, but twice?? The odds are literally a million to one.
Even though the most likely explanation for this was that you reloaded the game to try the battle again (hence getting exactly the same result due to the preserved random seed) as mentioned earlier, losing 2 99.9% battles in a row may be
slightly more likely than for a pure random number generator (in fact is is probably
less likely). The pseudo random number generator used by the game cannot be perfect - no PRNG can be - and as a result streaks could be very slightly more likely. However, there is no way there can be any bias that depends on whether the player is human or AI.
The combat calculation in civ4 has undergone statistical analysis and it is proven to not be biased against the human player. The distribution of odds behaves exactly as it should.
It *IS* biased, but only because the AI gets such a massive discount on troops. You have far more dice rolls at 70% attacking to fail on than the AI

. That's just how it is when you attack 20 troops rather than 10...your odds of losing multiple 70% battles are that much higher.
That's not the same as bias. If you roll a 6-sided die that has only the numbers 4, 5 and 6 on it, just because the numbers are different from the standard 1to6 die doesn't mean it is biased. Bias is when certain outcomes are made more likely than one should reasonably expect. If you're rolling an unusual die you have to change what outcomes you expect.
The worst is early on though, when 20% odds for that barb unit attacking yours can really hurt, because the barbs keep getting freebies. The worst by far is galleys, which have > 30% odds no matter what you do, and will come en masse' on higher difficulties with some starts...completely unstoppable in a reasonable time frame.
What do you mean by barbs getting freebies? And where are you getting the 30% odds for galleys? These sound like numbers that are completely explained by combat mechanics.
In fact, on Prince and lower, when you still have free wins vs barbs remaining, the odds calculator lies to you by under-estimating your odds vs. barbs, making it biased in the
human's favour. It's funny that I have never ever seen anyone complain about the RNG when playing at lower levels!

So many players must have won absurbly unlikely battles vs. barbs only because they still had free wins left.