Advanced Strategy: How Much is First Strike worth?

One of the big incentives for attacking in AWBW is the notion of first strike: by attacking your opponent's units first, you do more damage than you take in return. This makes it possible for a smaller force to successfully destroy a larger one, provided it has the advantage of going first. And yet, there's a limit to the power of first strike; you can't engage into an enemy army three times your size and expect to come out ahead.

In this post I discuss how much a first strike is worth.

Assumptions

To simplify the analysis, I make several assumptions:
1. We consider a single unit type, with base damage 55 against itself (quite realistic)
2. All units can attack on their turn (not always true)  
3. No CO powers

First Strike Value

One way of calculating first strike value is as follows: Suppose my opponent has X units and I have Y units, a smaller number, and I engage the opponent with a first strike. How big does Y need to be for our armies to trade evenly?

There are a couple ways of solving this - you could do it analytically by setting up the correct equations, and then solving them, or you could model this in Excel for several different values of X, Y. The first method gives an estimate of about Y = 0.78  X. In other words, the first strike allows this army to trade with an army (1/0.78) = 1.28 times its size. This means that the first strike is worth about 28% of your army value.

Conclusions

In conclusion, the first strike allows a numerically inferior army to fight on even ground against a larger army. Concretely, an army with first strike can evenly trade with an army 30% larger.

Appendix

The equations used to calculate the given value may be posted here in the future.