How far away from a town do you need to be to cast Town Gate?

tl;dr: in order to cast Town Gate in combat, your army must be at least 9 squares away from the entrance of at least one of your towns.

More precisely, you can use Town Gate to escape to a town only if your army is outside the circle with radius 9 squares centered on the northernmost entrance square of that town.

I did a series of experiments using a setup with a single town and a Scroll of Town Gate.

There are a few questions we need to answer in developing a theory of how Town Gate works.

• Does the distance measurement use Euclidean or taxicab distance?
• Is distance measured from the center of the town, or from the entrance?
• Is distance measured to the hero's army, or to the enemy army?

My starting assumptions, which I will attempt to falsify, are:

• Taxicab distance falsified
• Measured from the center of the town falsified by Experiments 7–8
• Measured to the hero's army

Note: when I use the word "diagonal" in this writeup, I mean diagonal relative to the grid lines of the Adventure Map. Since the map is presented in isometric perspective, "diagonal" lines appear horizontal/vertical on the screen.

Experiment 1

• Setup: Hero is 9 squares diagonally away from the corner of the town (8 empty squares in between), attacking an army on the 10th square away from the corner.
• Result: You can cast Town Gate to escape from combat.

Experiment 2

• Setup: hero is 9 squares orthogonally away from the entrance of the town (8 empty squares in between), attacking an army on the 10th square away from the corner.
• Result: You can cast Town Gate to escape from combat.

Experiment 3

• Same as experiment 2, except the hero is only 8 squares away from the town entrance, not 9
• Result: You cannot cast Town Gate to escape from combat.

Experiment 4

• Same as experiment 1, except the hero is only 8 squares away from the corner of the town, not 9
• Result: You can cast Town Gate to escape from combat.

This implies that one of my hypotheses is wrong! This result appears inconsistent with the results of experiments 2 and 3.

Experiment 5

• Hero is 8 squares orthogonally away from the wall of the town (7 empty squares in between), on the side of the town opposite the entrance. (note similarity to Experiment 3)
• Result: You can cast Town Gate to escape from combat.

This implies that distance is measured from some point other than the geometric center of the town.

Experiment 6

• Hero is 2 squares orthogonally away from the wall of the town (1 empty square in between), on the side opposite the entrance.
• Result: You cannot cast Town Gate to escape from combat.

Experiment 7

• Same as Experiment 6, but hero is 4 squares away
• Result: You can cast Town Gate to escape from combat.

Experiment 8

• Same as Experiment 6, but hero is 3 squares away
• Prediction: you cannot cast Town Gate, because distance is measured from the nearest square containing a town entrance and you must be 9 squares away to cast.
• Result: You cannot cast Town Gate to escape from combat.