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I decided to quickly test whether or not C3C armies enjoy any combat bonuses, as mentioned in the strategy guide on the Bonus CD and also referenced by a few beta testers.
Short answer: They do!
Longer answer: I only tested armies on offense, and only tested whether or not they enjoy the base 1/6 bonus refenced, not the 1/4 bonus with the construction of the Military Academy.
How does the 1/6 base bonus work? You add the raw attack values of all the constituent units. You divide the total attack values by 6, and round down the result (or so it has been stated elsewhere). The rounded result is added to the army's attack value for purposes of combat resolution. For example, an army composed of 3 knights would have an effective "attack value" of 6 rather than the knights' normal 4. (3 units with 4 attack = 12 combined attack; 12/6 = 2; 2 added to knight attack of 4 = 6). So that 3 knight army becomes a 12HP, 3-move, 6 attack, 4 defense, blitz-enabled, pillage-without-cost war machine.
As alexman said in a related thread, think about an immortal army early in the ancient age
Again, I haven't tested defense, nor have I tested the effects of building the military academy (nor do I plan to).
In the interests of "civ scholarship" the following quote describes the test parameters I used so others can verify I haven't overlooked anything or made a mistake, and I'll post the .biq test scenario if anyone wants it.
Let the "armies too strong" debates begin 
Catt
Short answer: They do!
Longer answer: I only tested armies on offense, and only tested whether or not they enjoy the base 1/6 bonus refenced, not the 1/4 bonus with the construction of the Military Academy.
How does the 1/6 base bonus work? You add the raw attack values of all the constituent units. You divide the total attack values by 6, and round down the result (or so it has been stated elsewhere). The rounded result is added to the army's attack value for purposes of combat resolution. For example, an army composed of 3 knights would have an effective "attack value" of 6 rather than the knights' normal 4. (3 units with 4 attack = 12 combined attack; 12/6 = 2; 2 added to knight attack of 4 = 6). So that 3 knight army becomes a 12HP, 3-move, 6 attack, 4 defense, blitz-enabled, pillage-without-cost war machine.
As alexman said in a related thread, think about an immortal army early in the ancient age
Again, I haven't tested defense, nor have I tested the effects of building the military academy (nor do I plan to).
In the interests of "civ scholarship" the following quote describes the test parameters I used so others can verify I haven't overlooked anything or made a mistake, and I'll post the .biq test scenario if anyone wants it.
I established a small landmass where both Rome (human) and Egypt (AI) have one city. The land is RR'd. All unit experience levels have 10 HPs in order to eliminate the effects of promotions and in order to generate more separate combat results from each monotonous attack than 4 HPs provide. Longbows are modded to have an attack value of 22 and 2 moves (revenge of the longbows 
); Infantry are modded to have a defense of 20. The Egyptian AI has a stack of ~40 infantry, unfortified on grassland -- with the grassland bonus, the infantry have an effective defense of 22. The Roman human has 30 longbows and 10 armies -- these are combined into 10 armies of 3 longbows each. Then it is just a matter of launching repeated attacks against the infantry stack with longbow armies, and keeping track of how many HPs are lost by each side.
If there were no army combat bonus, we should expect (with sufficient trials) a roughly 50 - 50 win - loss ratio between an army attacking at 22 offense against a defender with an effective 22 defense. If the 1/6 base bonus is present, we should expect the longbow armies to win about 60% of the time (3 longbows at 22 offense = 66 attack points; 66/6 = 11; 11 added to the attack of 22 means an effective atack of 33; 33 attack versus 22 defense = 33/55 = 60% win expected).
Out of 977 total individual combat die rolls (HPs), the armies lost 393 HPs while the infantries lost 584 HPs, meaning the infantries lost, and the longbows won, 59.775% of the combats - pretty darn close to the expected 60 - 40 split.
); Infantry are modded to have a defense of 20. The Egyptian AI has a stack of ~40 infantry, unfortified on grassland -- with the grassland bonus, the infantry have an effective defense of 22. The Roman human has 30 longbows and 10 armies -- these are combined into 10 armies of 3 longbows each. Then it is just a matter of launching repeated attacks against the infantry stack with longbow armies, and keeping track of how many HPs are lost by each side. If there were no army combat bonus, we should expect (with sufficient trials) a roughly 50 - 50 win - loss ratio between an army attacking at 22 offense against a defender with an effective 22 defense. If the 1/6 base bonus is present, we should expect the longbow armies to win about 60% of the time (3 longbows at 22 offense = 66 attack points; 66/6 = 11; 11 added to the attack of 22 means an effective atack of 33; 33 attack versus 22 defense = 33/55 = 60% win expected).
Out of 977 total individual combat die rolls (HPs), the armies lost 393 HPs while the infantries lost 584 HPs, meaning the infantries lost, and the longbows won, 59.775% of the combats - pretty darn close to the expected 60 - 40 split.
Catt
Good to have you hanging around the forums again. 
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