Explain Civ IV first strike concept?

[Deathcon5]

I have owned Civ IV for years and have never figured out exactly how the First Strike effects the odds. I have read the manual and can't find a good explanation of how it works. My basic understanding is that the unit with the most number of first strikes gets a number of chances (the difference between the 2 units' numbers of first strikes) to damage the other unit before the other unit gets to shoot back. How would this be better than the 10% strength upgrades?

[Ruxton]

Here's my understanding of how first strike works..

Both characters have a chance to strike first, if both have first strike buffs then both their chances increase. Whoever wins strikes first, If both win the chance to strike first, the one with the higher chance wins.

[Deathcon5]

It has to be more than just going first in the calculation. If you have a level 3 first strike, then you should get 3 damaging attacks before the battle starts, giving quite an advantage. But if the other unit has 2 and yours has three, you would get only 1 shot (3 minus 2) before the other unit shoots. That would make sense but I'm not sure how it actually does change the battle math.

EDIT:
I found this explanation online that sheds some light:

"The Basics

Just to level set, I wanted to explain how the battle works in CIV 4 leaving all bonuses and promotions aside. Assuming 2 units are equal strength and full health, when they go to battle, each battle is a series of rounds. Each Round has a victor (and only one). The loser of each round has the opponents hit points subtracted from their health. The rounds continue until one unit has 0 or less health remaining. A unit with 100% health will have 100 hit points available. A unit that is listed at strength 3.0 of 6.0 would have 50 hit points available. Obviously, if a unit starts a battle injured, it has a higher chance of losing that battle. Overall, if units have equal strength, there is a 50-50 chance that each unit will win the battle. A stronger unit will have a better chance over a weaker unit, but there are always exceptions.

The Computer (not actually the AI, because the same thing will happen when the AI attacks) will select the best defender vs. the attacker. This will be the unit with the best chance. Frequently, this will be the strongest unit, but occasionally may be a unit with specific advantage vs. the attacking unit. This means if you change attacking unit types (mounted to melee, or Swordsman to Archer), your unit may face a different defending unit.

First Strikes: 1 round where the unit with the first strike can only win (reducing the opponents available hit points). The odds of winning a first strike round are the same as any round, but if the unit loses the first strike round, the unit's hit points do not get reduced (meaning it can only win).

First Strike Chance: 50% chance that there will be an additional first strike.

Now, before the rounds above, there could be first strike rounds. Only some units start with first strikes or first strike chances. First, the first strike chances are determine to be first strikes or not. Each chance has a 50-50 chance of being a first strike each time a unit goes to battle. Now, the first strikes for both units are subtracted. If they are equal and subtract to 0, then there are no first strikes. If one unit has more, than that number of rounds will take place where the unit with first strike can not be injured."