Heh... I wanted to do something similar in the weekend. You beat me to it, Solver

[edit: for a more comprehensive post, look 10 posts down]

So allow me to contribute:

How do first strikes work?

First, in order to determine how many first strikes a unit A actually got, you need to look at the combatting unit B. If B ignore first strikes, unit A will have 0 first strikes. (very important early on!) If both A and B have first strikes (say A has 3, B has 1) it's the difference that counts (A gets 2, B gets 0).

Once battle is fought, each first strike gives a free round of battle. That means that a round is fought normally, but in case A has a first strike, he can't lose the round. If B would be hit, he gets hit. If the result is negative, it is ignored.

Notice that the base strength of the units is unaffected: if A has a strength (or hp) of 4, first strikes of 2 after modifiers, and B has a modified strength of 6, the first 2 rounds still have a 4/(4+6)=0.4 chance of succeeding, taking 0.2*6*(3*4+6)/(3*6+4)= 0.98 off the strength of B each time they hit. B, however, has 6/(4+6)=.6 chance of succeeding, but instead of taking .2*6*(3*6+4)/(3*4+6)=1.46 off the strength of A, it doesn't hit anything.

Once first strikes are over, combat continues as usual. At most, B has been hit once (but it could be twice or not), which would mean its strength is now at 5. (the average would be a bit higher) A is still at 4. The numbers in the formula don't change, though, so B still has a .6 chance of winning the next round, while A only has .4. With those numbers, B is almost certainly going to win, even if he was hit a little during first strikes.

You would be tempted to think that first strikes are thus unimportant. Nothing is farther from the thruth, you only need to use them well. If the situation is reversed, and a unit C has 6 strength and 2 first strikes, while unit D has 4 strength, the results are very different.

C will hit D in 60% of the cases, and it will do 0.97 damage. D can hit C in 40% of the cases, and will do 0.8 damage. With those numbers, C will hit D once or twice, doing at least 0.97 damage and reducing D to 3.03. Another 4 hits and he's dead... C still needs 6/.98= 6.1 or 7 hits.

(due to roundings, this is a bad example. In reality the number of rounds left will be 3 for C and 6 for D)

If you compare the battle of C with one without first strikes, you would see that C has a much higher chance of not getting damaged, with a sligthly higher chance of actually winning. The bigger the difference in strengths between C and D, the extremer this effect. Adding 2 first strikes to a unit that is already twice as superiour will mean he will win most battles undamaged. As your damage directly affects your strength in the next battle it is very important to keep a good health.

OTOH, if the difference between the strengths decreases, first strikes give a small advantage. You can use that to win fights where e.g. you have a 10% disadvantage. Once the difference is too large, first strikes won't help you to win, though.

First strikes should be used for two different types of units: those that defend and the overwhelming attackers. As defenders are most likely stronger because of the bonusses, they are helped as they can fend of multiple attacks, still remaining strong. It's very annoying to have dozens of units attack a city, where one single defender just shrugs of the attacks.

For the overwhelming attackers, it can keep you going. This especially applies to pillagers: they will remain healthy long enough to pillage that resource far inside the foreign borders, where units with the same strength but no first strikes will get slowly damaged over time to a point where an older unit can win. A tank which is damaged to strength 1 will most definately lose from a spearman of modified strength 5.

DeepO

[edit: wrong damage]

[edit again: wrong damage In this example only a 2% in damage change, though, and no effect on how many rounds are actually needed to win.]

[edit 3: this time I will get it ]

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