In Caesar 3, how many tiles do school children run?

The supposed 'randomness' of random walkers in the impressions games isn't actually completely random. There are some patterns to be observed.

The game generates 4 walks for each building, which depend in a somewhat strange way on your road layout. Consider the north-most square of your building your 'origin' square. There are 4 target squares: the squares exactly 8 tiles away from the origin square in the four directions. The game will search for roads within 6 tiles of these target squares in a predictable pattern. If it finds one then the walker will walk to that tile, then back to the building it came from.

That means if your city is connected well enough, each walker building will repeat a cycle of 4 patterns. However, if the game cannot identify a route, it is too long, or it's blocked by a gatehouse, then a walker may go into 'random mode', and all bets are off what they will do, except return to their building after some pre-determined x steps.

School-children are a bit weirder even than the regular walkers:

• they disappear after either 11, 16, 21, or 26 tiles³ (index based), and
• their index is used to determine which route they take¹
• Their routes may feature doubling back on itself².

1: The index part means that on phase 1 of 4, child 1 may take route 1 2 takes 2, and so on while on phase 2, these selections are permuted (there are 256 combinations!).

2: Due to a bug with multiple walkers from the same building the walkers affect eachother. That means when child 1 is deleted, the game may re-assign (shuffle) the walk targets, which may cause the other 3 children to change directions. It's similar to pharaoh's teleporters. Similarly when the children are created walk targets may be changed.

3: Schoolchildren behave like other random walkers, except that they do not have a 'return home' phase. They disappear after reaching their target tile or their travel limit (which is a 'short walk' or 26 tiles, or sometimes shorter due to multiple-walker-interference bugs). Your experiment results may be less due to counting tiles differently.

I do not know yet whether these walk patterns actually overlap or not. To investigate whether the patterns overlap, try building a school within a tight grid layout (say a 3x3) which extends at least 10 tiles in all 4 directions and manually count the patterns.

It may also be interesting to investigate exactly how the walkers affect eachother. As a starting point, try reading what's already known from the in-depth ambulomancy article written for Impressions games.