I believe that on higher difficulties the AI gets a combat bonus. I have played enough Deity games now to be sure that the combat outcomes are not just the ratio of the two units' combat power. I almost never win a fight which is even or when I am at a disadvantage. I lose surprisingly frequently when I have an advantage less than 2 to 1. I think that the AI gets a bigger bonus when defending. The occasions where I win an even fight are almost always when I am the defender.
While it may seem to be this way, it's really not. The AI does not get some hidden defensive bonus on Deity. It's just normal.
It may have to do with conditions being a little tougher for you to get the units to the other guy quick enough, or just a few unlucky battles, but it all evens out. Anything that's not overrun (7:1) has a chance to win, though it's rare to see anything over 3:1 lose.
Do you know this for a fact? Has anyone tested the game by repeating fight scenarios? I find it doubtful. I can tell you that, without a doubt, I win far less than half of my even strength fights on deity. And I almost never win a fight at less than even strength. I lose at 3:1 or more at least once per game, usually more. I know that Civ2 was riddled with special bonuses for/against the AI and the Barbarians, depending on what difficulty level you played. That was proven by objective tests by many players.
The one thing we can all agree upon is that an absolutely even battle should be a 50/50 proposition. As you suggest, elthrasher, it is possible that the formula for uneven fights is non-linear, so 3:1 odds would not mean the stronger side winning 75% of the time. Unfortunately, without a convenient cheat mode/map editor and given that battles always end the same way after save/load (naturally, I know this from others. I never do it myself. ) there really is not a convenient way to test the outcomes of battles with different odds. If someone wants to do the research, a string of 50 or so battles with exact 1:1 odds, repeated for different levels of units (1 vs. 1 warrior fights, 12 v. 12 with no mods, 12 vs. 12 Ninja Horse Army vs. dug in Archer army and so on) should tell us if there is an AI combat advantage.