A C3 random walker will start on a tile touching its building and will usually return to its building and finish on a tile touching or almost touching its building (unless the finishing point is on an unconnected road). A school child will not return to its building. Sometimes an engineer, tax collector, or entertainer will not return to its building even if he is connected to the finishing point, but that is not discussed here.

In terms of starting and finishing points, bridges are treated as roads--in this post, "road" means "road or bridge". Gatehouses are sometimes treated as roads.

A connected road network includes all connected roads, gatehouses, non-corner tiles of granaries, north tiles of warehouses, and elevation change ramps. If two connected road networks have the same number of tiles then the one with a road or gatehouse that is the most northeast is considered the larger, and if they both have road or gatehouse tiles that are equally far northeast then the one with the northeasternmost road or gatehouse tile that is the most northwest is considered the larger.

Random walkers fall into five categories based on their starting point: 1) most random walkers, 2) prefects, engineers, and tax collectors, 3) walkers from hippodromes, 4) citizens from warehouses, and 5) citizens from granaries. However, the finishing point of any random walker who returns to its building is essentially the same (although for some buildings only a part of the building is used), so the finishing algorithm is discussed first.

Results will be described and presented in diagrams. In all diagrams, the road tile with the lowest number is used, and north is diagonally up and to the left.


Finish Point

For hippodromes and warehouses, only a part of the building is used to determine the finishing point. See the appropriate section below.

A random walker will usually finish its walk by returning to its building on a road or gatehouse tile. The finishing tile is the one adjacent to the building (even to just a corner) that is furthest northeast, and if that selects multiple tiles then the finishing tile is the one of them that is furthest northwest. If no roads or gatehouses are adjacent to the building then the finishing tile is one separated from the building by 1 tile that is furthest northeast, and if that selects multiple tiles then the finishing tile is the one of them that is furthest northwest. If there are no road or gatehouse tiles either adjacent to or separated by 1 tile from the building, the random walker disappears instead of returning to its building.

The finishing road or gatehouse tile for random walkers from a 3x3 building (north is diagonally up-left):

17	18	19	20	21	22	23
24	1	2	3	4	5	25
26	6	3x3			7	27
28	8				9	29
30	10				11	31
32	12	13	14	15	16	33
34	35	36	37	38	39	40

Common Random Walkers

This behavior applies to all random walkers except for prefects, engineers, tax collectors, walkers from a hippodrome, citizens from a warehouse, and citizens from a granary.

A common random walker starts in the largest connected road network that has a road tile adjacent to a side (not a corner) of the building. The starting tile is the first road tile of that connected road network encountered when beginning at the tile northeast of the north tile of the building and going clockwise.

The starting road tile (selecting from the largest connected road network) for common random walkers from a 3x3 building (north is diagonally up-left):

.	1	2	3	.
12	3x3			4
11				5
10				6
.	9	8	7	.

Unless the road system is changed during its walk, a common random walker who returns to its building finishes on a tile adjacent to the building but not on the tile directly south of the south corner of the building.


Prefects, Engineers, and Tax Collectors

A prefect, engineer, or tax collector starts on the road or gatehouse tile that would finish his walk. Since there must be a road that the citizen can use, the starting tile must be adjacent to the building but not directly south of the south corner of the building.

The starting road or gatehouse tile for a forum tax collector (north is diagonally up-left):

1	2	3	4
5	Forum		6
7			8
9	10	11	.

Unless the road system is changed during his walk, a prefect, engineer, or tax collector finishes his walk on the same tile that he started.


Hippodrome Walkers

A citizen or chariot from a hippodrome starts in the largest connected road network that has a road tile adjacent to a side (not a corner) of the hippodrome. If that network has a road tile adjacent to a side of the northwest third of the hippodrome, then the starting tile is where a common random walker would start considering the northwest third as a 5x5 building. If that network does not have a road tile adjacent to a side of the northwest third of the hippodrome but does have a road tile adjacent to a side of the middle third of the hippodrome, then the starting tile is where a common random walker would start considering the middle third as a 5x5 building. Otherwise, the starting tile is where a common random walker would start considering the southeast third as a 5x5 building.

The starting road tile (selecting from the largest connected road network) for a hippodrome citizen or chariot (north is diagonally up-left):

.	1	2	3	4	5	16	17	18	19	20	26	27	28	29	30	.
15	Hippodrome															31
14																32
13																33
12																34
11																35
.	10	9	8	7	6	25	24	23	22	21	40	39	38	37	36	.

The finishing tile is determined using the northwest third of the hippodrome as a 5x5 building. The walker will not return to a tile touching the southeast third of the hippodrome or some of the middle third of the hippodrome.

The finishing road or gatehouse tile for a hippodrome citizen or chariot (north is diagonally up-left):

20	21	22	23	24	25	26	27	28	.	.	.	.	.	.	.	.	.
29	1	2	3	4	5	6	7	30	.	.	.	.	.	.	.	.	.
31	8	Hippodrome															.
32	9																.
33	10																.
34	11																.
35	12																.
36	13	14	15	16	17	18	19	37	.	.	.	.	.	.	.	.	.
38	39	40	41	42	43	44	45	46	.	.	.	.	.	.	.	.	.

Warehouse Citizens

If there is a road tile adjacent to a side (not a corner) of the north corner (covered area) of the warehouse, a citizen from a warehouse starts where a common random walker would start considering the north tile as a 1x1 building. Otherwise, the citizen from a warehouse starts where a common random walker would start using the whole warehouse.

The starting road tile (selecting from the connected road network touching the side of the north corner if one exists, otherwise selecting from the largest connected road network) for a warehouse citizen (north is diagonally up-left):

.	1	3	4	.
2	W.H.			5
12				6
11				7
.	10	9	8	.

The finishing tile is determined using the north tile of the warehouse as a 1x1 building. The citizen will not return to a tile touching the southeast or southwest sides of the warehouse.

The finishing road or gatehouse tile for a warehouse citizen (north is diagonally up-left):

6	7	8	9	10
11	1	2	3	12	.
13	4	W.H.			.
14	5				.
15	16				.
	.	.	.	.	.

Granary Citizens

The citizen from a granary starts his walk on the road or gatehouse tile that is adjacent to the middle side of a granary. Of those tiles, the preference is the same as for the starting tile of a common random walker.

The starting road or gatehouse tile for a granary citizen (north is diagonally up-left):

.	.	1	.	.
.	Granary			.
4				2
.				.
.	.	3	.	.

Unless the road system is changed during his walk, a citizen who returns to his granary finishes on a tile adjacent to the building but not on the tile directly south or southwest of the south corner of the granary.

Off-topic note: A granary will generate a citizen (and therefore can be staffed and store food) when it is adjacent to a gatehouse but not a road. However, a market will only send its buyer to a road tile adjacent to a granary (or warehouse). If a market wants to get food from a granary that is adjacent to a gatehouse but not a road, it will not find a road tile adjacent to the granary and will not send its buyer there (or anywhere else).

[Edit: included elevation change ramps in connected roads.]

[This message has been edited by Brugle (edited 04-22-2018 @ 02:58 PM).]

According to reply #1 above, under "The starting road or gatehouse tile for a forum tax collector (north is diagonally up-left)" and looking at the picture the starting point is at number 1, as expected.
I expect the finish point to be the same number 1 in the picture according to "tax collector finishes his walk on the same tile that he started". Maybe, I would expect possible finish point to be the number 2 in the picture, that is also not the case.
But not, the finish point is actually point 3 in the picture, six tiles away from the building which is not mentioned in this thread.
There is something that has not been revealed or I don't still understand the mechanics of the game.
can you explain?

Picture taken from Brugle's Palace Peaks:


thanks

The last sentence of the first paragraph of reply #1:

Sometimes an engineer, tax collector, or entertainer will not return to its building even if he is connected to the finishing point, but that is not discussed here.

I'd rather not clutter up this thread with extraneous material, so please don't reply to this here. If you want to discuss this topic some more, start a new thread.

Since I'm already posting here, the best explanation is probably in the Pharaoh forum. The last paragraph of reply #25 of Walkers and teleporters from pavilions may be helpful.

I added elevation change ramps to connected roads in reply #1.