Efficiency: Square vs. Hexagon

Many players argue that the best way to place production buildings around storehouses is in the following manner:

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That certainly is a fine use of space but let's take a closer look at the efficiency in that system. Before we begin we have to get one thing clear: The points are more important than the squares themselves. What does that mean? Think of deposits. A tree, fishing spot, or meat spot consists of one point. This matters when you consider that the average production building takes up 9 such points. The only one of those points that matters is the front-center for every building. The task for resource buildings is to make sure that point is as close to the resource point as possible. This could be as easy as placing the front-center of the building directly on that point. The result is an astounding 2 seconds from the workyard to the deposit (a settler spends 2 seconds for every point he travels).

From workyard to storehouse is a little different. We all know that the shortest distance between two points is a straight line so placing the buildings to the right and left of a storehouse is the first best place to look. Our square shaped model holds up well here (3 points between storehouse's front-center to productions front-center= 6 seconds). What about the row of buildings north and south of the storehouse?

Those 6 buildings are all 5 points away from the storehouse for a total of 10 seconds each. Let's do some math! =D

All 8 production buildings together add up to 36 points from building to storehouse. It takes nine building licenses for the square model so divide points by licenses and you get a total of 4 points for every license that the settlers have to travel. That certainly is good considering few points per license means less wasted travelling time for the production chain.

Let's see what happens when we use a staggered (or Hexagonal) model. If you stagger the rows north and south of the row of the storehouse you will get something like this:

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Now each of those buildings has to travel 4 points to the storehouse. All together we have 22 total points divided by 7 building licenses for a total of 3.14 points a settler has to travel per license. Now look at the following chart.

Cycles.....Hex........................Square
..............Time.......Product....Time......Prod uct
1........... 22.......... 6........... 36.......... 8
2........... 44......... 12.......... 72.......... 16
3........... 66.......... 18.......... 108........ 24
4........... 88.......... 24.......... 144........ 32
5........... 100........ 30.......... 180........ 40
6........... 122........ 36.......... 216........ 48

As you can see the hex model can crank out 30 products in the amount of time the square model cranks out about 24. It also goes through 5 hypothetical production cycles in the amount of time it would take the square model to do about three (this is all assuming we use the same building in both examples for the same base time).

Now, not only does the Hex model save you building licenses and cuts down time but in the long run it can produce more than the standard square model.

Problem with hex method is it is reliant on having the 4 spaces next to the 8s' spots available - 12 sec spots. There is only so many spaces on the map that will accommodate the full hex strategy. I use a mix of square and hexes- and sometimes square on top and hex below depending on space available.

I certainly agree that the map has a lot of restrictions on what strategies you can use. And another problem is even if the environment in some spots can allow for you to overlap a couple of hexes it involves going overboard on extra storehouses to take care of those 12 second spots. Nobody wants to use licenses on more storehouses than neccesary. This post is a precursor to a future thread I'm going to make when I have enough numbers to back up a theory I have for another layout strategy.
A lot of novice players haven't yet figured out how the travelling time is determined so it was neccesary to start a discussion on these kinds of strategies because the idea that I'm building up towards is a little controversial and will probably generate a lot of dicussion.

Your right when you say some people have not figured out just how bad it is to not place buildings properly. Looking at advanced players islands can give you ideas and thoughts on how to best place buildings. Some over emphasize rebuilding with all of one type of building together- when you should really be focused on cutting down travel times for most buildings (farms and wells less so).

Quote:

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Some over emphasize rebuilding with all of one type of building together

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So true. I see Cutters in one large group and all the trees in that area gone. To avoid stuff like this, for example, I make sure my cutters and foresters are a proportional distance away from the same tree and I'm able to have a self-containg cell that I never have to worry about again. It's nice. But I will admit that I'm running out of spots were I can do that with the shortest production time. Eventually you just gotta work around what nature gives you.

This would be correct if you don't take into account the time each building actually takes to produce things. If we use 3 minute buildings (the general best case for the hex over square since travel time hits them hardest) we get:

Production time per building: 180 seconds (3 minutes)

Square:
Trip distance total: 2 * 2 + 6 * 4 = 28 segments
Round trip time total: 28 * 2 trips * 3 seconds = 168 seconds total
Round trip time average per building: 168/8 = 21 seconds
Average total production time per building: 21+ 180 = 201 seconds
Average end production time per building license: 201 / 9 = 22 1/3 seconds per license to produce a single good

Hex:
Trip distance total: 2*2 + 4*3 = 16 segments
Round trip time total: 16 * 2 * 3 = 96 seconds total
Round trip time average per building: 96 / 6 = 16 seconds
Average total production time per building: 196 seconds total
Average end production time per building license: 196 / 7 = 28 seconds per license to produce a single good

Square pattern pulls ahead farther with higher time to work buildings, but really this an effect of the production buildings:storehouse ratio than the layout used. You want to put your low production time buildings close to the storehouse, in whatever layout allows you to most effectively cram around 15-20 buildings per storehouse, with the higher production time ones father away. Only using the small hexes or squares listed in the op get pretty inefficient with higher production time buildings which are better to array up to 3-4 squares out from an existing storehouse rather than building more storehouses.

You might build more storehouses for the short term next to expensive buildings as a cheaper way to squeeze some more out of them, but in the theoretical very long term when everything is upgraded, storehouses surrounded by 15-30 buildings each will win.

Fir cutters and coal mines get special mention of their 1.5 minute production time, but it's difficult to work a small hex of fir cutters to be extremely close to both the storehouse AND the trees for this ideal, and similar for coal mines for obvious reasons.

It also matters if you are using the 12s spaces with the hex where you would be using the 14sec spaces on the square.

The square is still going to be on average better anyway between unless you happen to have fir cutters or coal mines arranged to fit on that hex perfectly just due to the 8:1 vs 6:1 production building:storehouse ratio. You might be able to squeeze 6 fir cutters and ring it with 9 fir foresters around a storehouse somewhere on the map without needing an extra forester in which case I'd suggest a hex layout of fir (specifically fir only) cutters then ringed around that with foresters rather than a square a square layout that allows a single extra building to be placed, but there is nowhere with coal mines that fit that. That said, there are notches in the map where buildings 2 across (or some even number of buildings wide) is all that will fit and it's best to take the offset layout for those as opposed to keeping them square to save the 6 seconds each building in the round trip.

You're also not going to be able to make perfectly extending squares nor hexes due to the map so you can't just prescribe either layout but extended out one or two radii either. My rule of thumb currently is putting as many buildings will fit in a roughly 14x14 square area (7x7 building lengths) around each storehouse. This is never a perfect square or hex so you don't get 49 buildings, but going out to at least a 10x10 square or 5x5 building length area per storehouse is a good idea over sticking to the patterns in the OP.

And put the quickest production time buildings closest to the storehouses.

the hex layout is one of the best options to use for certain buildings but it doesn't apply to everything. also, have a hex figure will require more investment in store houses and with the limited availability of building licenses, this option may not be the most feasible one. many buildings have been destroyed in my quest to find the most optimal setup. nice work on the numbers. :D

I have a mix of both on my island, but truely I just use whichever keeps all my resources at a even and increasing rate :)