# Ceasar's Mind

## Flanking – Part 1

With the math behind pricing in mind, it’s obvious that forces grow in strength exponentially with each unit in the party. Not only is our force stronger though, but we take less damage. However, party strength is limited by space. If a unit can’t get the enemy in range, he can’t help the party.

Basics

The basic idea here is rather simple. All of that math explained before assumes that all units in a force can attack. But that isn’t necessarily the case. What battles are really all about are creating situations where you have more units attacking than your opponent does.

The simplest and perhaps most common of these scenarios is the flank of a line formation. In the image to the right, the black army is positioned to flank the white army. All three of the black units can attack the bottom white unit, but only the bottom white unit can strike back. The other two white units don’t have any targets in range.

If white does not react quickly, black will fight each unit individually, and crush all three of them losing only one unit in the process.

(Line formations are extremely effective at flanking because of their ability to wrap around vertices, but their vertices are also extremely vulnerable.)

The Impact of Formation

Besides the actual size of units, formation can affect the effectiveness of an enemy flank. Consider the two images presented here.

In the image above, four black units are surrounded by an army of white. Due to their shape, they reduce up to 16 attacks down to 8.

Now consider this second image.  In it, an army of nine black units fend off a larger army of white. Due to their shape however, they reduce up to 36 attacks down to 12.

Notice the number of vertices stays the same despite the increasing amount of units. Side length increases instead, decreasing the percentage of your units being flanked. Consequently, bigger shapes are better. Furthermore,  if the terrain is favorable, it can sometimes be possible to construct a straight line from one impassable point to another, eliminating vertices altogether!

This knowledge is particularly useful when using units that are expensive since, at least in my experience, they are balanced assuming that the enemy strikes in full force. By rearranging your army’s formation or exploiting impassable terrain, you can force enemy units to strike individually and increase the effectiveness of your units exponentially!

The Impact of Range

Besides collision size, the other factor that affects a player ability to flank is range. Basically, more range means more unit can sit along the circumference of the range from the target, and increase the effectiveness of a flank. Furthermore,  if a group of units possess a range greater than their targets, not only will they able to position themselves along a wider circumference, but units can position themselves in a series of lines, drastically increasing the effectiveness of their attacks.

In the picture above, the white army has a small range, and the circumference along which they can align is also fairly tiny.

Compare the above picture to the previous one. In this, the white army has significantly increased attack range, permitting many more units to join in the attack.

Because of this property of Range, it can easily disrupt the balance of games. Given enough time, a patient player might construct an large army of long-ranged units that knock-out enemy units before receiving any return fire, instantly spelling defeat for his opponent. (I’ve seen this happen in many Tower War games, including my own Expansion. But this is not at all an uncommon phenomenon.)

Conclusion

So basically, at this point, it should be obvious that besides collision size, formation and range can impact the effectiveness of a flank.

Written by Ceasar Bautista

2010/06/17 at 21:33

Posted in Uncategorized

Tagged with , , , ,