Mathematics and Civ Mechanics

I have a few mathematics questions that pertain to Civilization IV... I realize that they may have already been asked, but a cursory Google didn't show anything. So, here goes:

How exactly is the probability of winning a battle calculated? Does anyone know the exact equation? Is it hidden in a Python file somewhere?

How exactly is the yield of a trade route calculated? Again, the exact equation would be nice.

Do bonuses stack multiplicative or additive? Likewise, do bonuses in battle add to your strength, or subtract from an opponents strength?

Also, in the second question there (battle bonuses), which would be preferable? I can't exactly tell because I don't have an equation...

Combat odds are simple

A warrior versus an archer.

Warrior has 1 strength. Archer has 3.

Variables: Warrior is defending on a forested hill across the river from the archer.

Now the warrior has 1.75 strength and the archer has 2.25 (Approximately).

The odds are gained by dividing 1.75 by 2.25 and multiplying it by 100. The archer has a 77.7 percent chance of victory.

Nah it's more complicated than that. PieceOfMind is the man who knows how combat works.

Trade route value is calculated differently in BTS compared to vanilla and Warlords.
Theres an article explaining trade route values in the war academy, here

Similarly theres an article explaining how combat works in the war academy. Not sure if this one goes into exactly how odds are calculated as they are complicated, I only ever bothered to understand the significance of the 'R' value, the ratio of strengths.

Jarlaxe Baenre said:

Combat odds are simple

A warrior versus an archer.

Warrior has 1 strength. Archer has 3.

Variables: Warrior is defending on a forested hill across the river from the archer.

Now the warrior has 1.75 strength and the archer has 2.25 (Approximately).

The odds are gained by dividing 1.75 by 2.25 and multiplying it by 100. The archer has a 77.7 percent chance of victory.

Click to expand...

Where did you get those values? First off Warriors have 2 strength and an Archer attacking a Warrior on a forested hill would look like this;
Warrior 2 + 25% (river crossing),+75% terrain defence) so 3(Archer) vs 4(Warrior). Geting odds from this is going to be more difficult as Archers have a First Strike to take into account too.... but ingame WB tests show 73.3% in the Warriors favour.

Oops, I mixed up. I recently played a mod with a 1 strength warrior.