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Advanced Strategy: Minimum Attacking Ratio

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Advanced Strategy: Minimum Attacking Ratio Empty Advanced Strategy: Minimum Attacking Ratio

Post  Everdan on Thu May 16, 2019 9:05 pm

Deciding when and where to attack is a core part of AWBW strategy. A large part of this is being able to calculate your attack - in other words, being able to determine the outcome of your attack before you even make a move.

I use the term "engagement" to refer to any duration and location in which battle is occurring. Sometimes, engagements are small, short, and decisive; it's easy to see what the outcome will be. But other times, engagements may last several turns, or require dozens of units, and the outcome isn't obvious from the outset.

In this post I present one useful tool for trying to calculate the outcome of your attack: the minimum attacking ratio (MAR).

Minimum Attacking Ratio


In AWBW, the goal of all attacks is to turn a profit. Quite often this simply means doing more damage than you take - if you take out 2 tanks with your attack wihle only losing 1 on the opponent's counterattack, you've made a favourable attack.

It's natural to ask the question: if my opponent has X units, how many units do I need to attack into that, given that I have first strike?

Intuitively, if I have many more units than the opponent, it will be favourable to attack. Conversely, if I have many less, it will be unfavourable. We can conclude that there is some threshold value below which it is unfavourable to attack, and above which it is favourable to attack. In other words, when I have this many units, attacking is neutral - neither favourable nor unfavourable (remember this for later!). This threshold will be some fraction Y multiplied by X. I call Y the minimum attacking ratio (MAR).

It's difficult to pin this value down exactly, but we can roughly guess what range it falls into. For example, consider the case where I have 20 tanks and my opponent has 10 tanks - attacking destroys all his units, which is surely favourable, since no counterattack is possible. Now consider the case where I have 4 tanks, and my opponent has 10. Then no matter how I attack, I can only destroy 2 tanks, leaving 8 of my opponent's alive, and then all 4 of my tanks will be destroyed upon counterattack - surely unfavourable.

This gives us a rudimentary estimate: 0.4 < Y < 2. But can we do better?

Solving for the MAR


Suppose my opponent has X units and I have YX units. Recall that in this case, attacking is neutral - I don't gain or lose by attacking. We can use this fact to solve for the MAR.

Here I make some assumptions which give us an equation for calculating Y:
1. We consider a single unit type with base damage 55 against itself. In practical terms, this means that every 2 attacking units can destroy 1 opponent unit.
2. Ignore counterattack damage
3. No reinforcements, no CO powers

On my turn, I have YX units, so I destroy YX/2 enemy units.
On the opponent's turn, my opponent has X - YX/2 units, so he destroys X/2 - YX/4 of my units.

Since neither of us gained from that attack, we must have XY/2 = X/2 - XY/4, which gives Y = 2/3 = 66%.

In other words, if you can get first strikes more than 66% of the total number of enemy units, you will profit from the attack, whereas if you can only attack for less than the MAR, you will incur net losses from the attack.

Limitations


Before you apply this to your games, it's worth noting that this value of the MAR rests on several crucial assumptions. Notably, the single unit type assumption, the 55 base damage, and the ignoring of counterattack damage. In practice, the variety of unit types, the presence of CO powers that increase attack or defense, and the fact that counterattack damage exists changes the value of the MAR. However, the 66% is a good "rule of thumb" to keep in mind.

You can apply this approach to specific game situations by following the same general approach we used here, and modifying the equation to account for counterattack damage, CO powers, etc.

Everdan
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