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A math snag I've hit concerning hexcrawls and such.

Started by beejazz, May 08, 2013, 08:14:28 PM

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Justin Alexander

Quote from: beejazz;653922Book of the River Nations. It's a supplement that compiles the rules from Kingmaker.

On this topic, in particular, the Book of the River Nations is broken.

Let's start with Kingmaker. Paizo defined the size of a hex like this: "Each hex on the map of the Stolen Lands is 12 miles across (between opposite corners) and covers just under 150 square miles of area."

First, the opposite corners thing is weird because it pretty much cripples your ability to use the hexmap effectively. (You can't move by counting hexes. Whenever the group arrives at the next corner, there's no way to actually tell what hex they're moving into. And, worst of all, it warps and distorts movement even more than a hexmap normally does.)

Second, the square miles figure doesn't make any sense. If it's 12 miles between opposite corners, the length of the side is 6 miles and the area is 93.5 miles. That's not "just under 150 miles square miles". (If we assumed it was 12 miles between opposite faces, then the area would be 125 square miles. That's closer, but still far enough off that it's not just a typo.)

So Kingmaker itself is inconsistent on this point and its method is completely without utility at the gaming table. However, the movement charts included in Kingmaker are accurate for the listed distance of 12 miles.

Okay, now let's look at Birth of the River Nations. BotRN defines the size of a hex like this: "Each hexagon of land has sides 12 miles long. That translates to an area approximately 375 square miles."

You'll notice that they've changed how they're measuring hexes. Unlike Kingmaker, BotRN correctly calculates the area of the hex. (A hex with a 12 mile side does, in fact, have an area of 375 square miles.)

But despite doubling the size of each hex, they kept the exact same movement charts for crossing a hex. These, of course, are now completely inaccurate.

Plus, as I've mentioned before, measuring a hex by the length of its side makes no sense because you will never, ever use the length of a hex's side at the gaming table. Measuring things in a way which forces you to perform complicated mathematical equations in order to translate them into a useful value is not good practice for a roleplaying game.

The whole thing is a mess.

The shortest path to a coherent, usable standard in all this would be to treat each hex as being 12 miles from face-to-face, drop the area for each hex to 125 miles (which is fairly close to the original figure), and then use the movement charts as published for face-to-face or middle-to-middle movement.
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Daddy Warpig

#16
Quote from: Justin Alexander;653925First, the opposite corners thing is weird because it pretty much cripples your ability to use the hexmap effectively. ...
Second, the square miles figure doesn't make any sense. ... But despite doubling the size of each hex, they kept the exact same movement charts for crossing a hex. These, of course, are now completely inaccurate. ... Plus, as I've mentioned before, measuring a hex by the length of its side makes no sense because you will never, ever use the length of a hex's side at the gaming table. ... The whole thing is a mess.
It's things like this that bother me whenever I write something up. I can't learn everything, and no matter how much research I do, I know mistakes will creep in.

It worries me.
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beejazz

I'll have to check again to see if you're right about the differences and errors. It's kind of disappointing to see this sort of thing in (what is supposed to be) a tier one or tier two gaming company's product.

Personally, my plan is to shrink hexes significantly. There's a reason I want to have lots of smaller hexes rather than a few bigger ones. Part of the reason is that the search time for the area of a hex seems weird. The area (IIRC) was described as being the size of six Washington DCs. Besides that, there are things like a hex filled entirely with traps (an area the size of six Washingtons). Additionally, it might mesh better with the custom domain management rules I'm fleshing out in the other thread. I've got a few problems there too (currently there are a lot of incentives to build up within your borders, but few reasons to expand your borders).

soltakss

In my opinion, you don't need exact measurements for hexes.

If you can move 30 miles per day, say, and each hex is 4 miles across, then you can move around 7 or 8 hexes a day. If the hexes are 6 miles across then you can move 5 hexes a day. It doesn't really matter whether you go straight across hexes or that the straight-line distance is different, if you have hexes then you move in hexes.

Also, knowing the actual area of a hex won't really help in your hex search, unless you are doing a fingertip search of an area of grass. Terrain and contents matter far more than the area of the hex. Searching open plains is easy, searching forest is harder, searching forested mountains containing caves is harder and searching a city block full of slums is harder still. Don't bother searching a city slum on the forested slopes of a mountain with caves beneath them.

I really wouldn't bother working this kind of stuff out. Use hexes per day for movement and have a set time period for searching a hex at a certain level. Life's far too short to mess about with that kind of thing.
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