Tactics

Tactics (from Greek taxis "arrangement" + -ics "study of") refers to direct maneuvers to achieve a goal.

Contents

1   Substance

The goal of tacts is to

A flank is a weak point of a formation. Flanking refers to moving toward the enemy to take advantage of their weak points.

2   Formations

2.1   Line formation

Line formations limits the weak to edges of the line. If an enemy line is shorter than an allied line, then allies on the edge will be able to

2.2   Column formation

A column formation is when allies move toward an enemy in a straight line pointed at the enemy.

The column formation has several advantages:

  • When attacking ranged enemies with low accuracy, it reduces the chance that a shot which misses its target will hit an ally.

    The Allies used this tactic in World War I when attacking German machine guns. The Germans responded by spacing machine guns apart, and having them attack columns that were attacking other machine guns.

3   Arrangement

3.1   Order

Units with the highest durability and the least attack power should be placed in front, where they can absorb damage. Units with high attack power and low durability should placed in protect positions where they cannot be directly attacked.

4   Retreat

A unit under attack from multiple ranged enemies with equal attack power and ranges should always retreat from the center of all of them in order to escape with the least damage.

There are intuitive reasons to flee from the closest, which is probably the greatest threat, or the further so as more quickly reduce the numbers of attackers. However, these are problematic in different scenarios.

4.1   Between

static/images/retreat_between.png
static/images/flee_direction_visual_proof.png

Consider the case where a unit is inside a triangle formed by the location of enemy 1, enemy 2, and the intersection of their ranges. Let's say the unit is closer to enemy 1 than enemy 2.

If the unit flees from the closest, it will flee until both attackers are equidistant, in which case its programming will cause it to get stuck.

Retreating from the furthest causes the unit to get very close to the closer attacker.

Let's let the range of attackers be 2x. I am looking to prove:

\begin{equation*} 2 * (EJ - DE) + JL > 2 * (FK - DF) + KM \end{equation*}
\begin{equation*} EJ = x \end{equation*}
\begin{equation*} 2x - DE + JL > 2 * (FK - DF) + KM \end{equation*}

We can calculate JL as follows:

\begin{equation*} BC = BJ = 2x \end{equation*}
\begin{equation*} CJ = \sqrt{{BC}^2 + {BJ}^2 - 2\times{BC}\times{BJ}\times\cos(CBJ)} \end{equation*}
\begin{equation*} CJ = \sqrt{8x^2 - 8x^2 \times \cos(CBJ)} = 4 |x| |\sin(CBJ \div 2)| \end{equation*}
\begin{equation*} JL = 2x - CJ \end{equation*}

We can calculate FK as follows:

\begin{equation*} BF = x \end{equation*}
\begin{equation*} BK = 2x \end{equation*}
\begin{equation*} FK = \sqrt{{BF}^2 + {BK}^2 - 2\times{BF}\times{BK}\times\cos(FBK)} \end{equation*}
\begin{equation*} FK = \sqrt{5x^2 - 4x^2\times\cos(FBC)} = |x| \sqrt{5 - 4\cos(FBK)} \end{equation*}

Let E be the point the intersection of FG and the line perpendicular to FG that intersects D. Then:

\begin{equation*} \sin(DFE) = DE / DF \end{equation*}
\begin{equation*} DF = DE\sin(DFE) \end{equation*}

So:

\begin{equation*} 2x - DE + JL > 2 * (FK - DE\sin(DFE)) + KM \end{equation*}
\begin{equation*} JL = 2x - CJ \end{equation*}
\begin{equation*} CJ = \sqrt{8x^2 - 8x^2 \times \cos(CBJ)} = 4 |x| |\sin(CBJ \div 2)| \end{equation*}
\begin{equation*} (4 - 4\sin(CBJ \div 2))x - DE > 2 \times (FK - DE\sin(DFE)) + KM \end{equation*}
\begin{equation*} FK = |x| \sqrt{5 - 4\cos(FBK)} \end{equation*}
\begin{equation*} (4 - 4\sin(CBJ \div 2))x - DE > 2 \times (|x| \sqrt{5 - 4\cos(FBK)} - 2DE\sin(DFE)) + KM \end{equation*}

This proof is incomplete. I need to find the relation between DJ and DK. It may be useful to know that we know some angle because of the equilateral triangle.

The damage taken during the time to escape the closer attacker when out of range of the further attacker is greater than the damage that would taken under fire from when escaping from both.

4.2   Aligned

static/images/retreat_aligned.png

When the attackers are roughly in the same direction, the best choice is to flee from the farther one, but the difference between retreat from all and the farther one is negligible.

5   Ethics

In a fight between two closely-matched combatants, the fighter who is willing to do dirtier tactics will win. David Sirlin calls "playing to win". "The Mittani", leader of the most successful faction in EVE Online, observed this as well and pushed members to do dishonorable things. [1] This is also called realpolitik_.

Many people instinctively feel a sense of "honor" when fighting. For example, in video games many players will refuse to exploit glitches.

6   Surround

Surround the enemy group has different advantages and disadvantages. The advantage is that if an enemy tries to flee, they will move into range of another ally. The disadvantage is that the enemy group could push toward an ally, and then kill him.

7   References

[1]https://www.rockpapershotgun.com/2011/04/07/eve-online-audience-with-the-king-of-space/

In chess, until players reach the skill level of "master", tactics tend to ultimately decide the outcome of games rather than strategy. Many coaches thus emphasize the study of tactics as the most efficient way to improve one's results in competitive play.