Except the game uses Chebyshev distance, so as long as they're within 30 feet in the x, y, and z dimensions, they're within 30 feet. Though for area damage spells, it's much, much more complicated. You don't just have to find the Euclidean distance from them to the center. You have to calculate how much of their square is within that distance.

That is one reason I don't like D&D, it is a glorified boardgame the hides it's wargame roots under a very thin layer. I like tactical rpg on the computer but investing that level of math and detail in a pen & paper game is so boring, for me at least.

IMHO, one of the more intriguing effects of streaming live-play series thriving these days has been the rise of TotM elements, if not entire games. Whereas my on-ramp to the hobby, et al, was finding a garage sale copy of the red box, the new crowd is cutting their teeth as spectators — and avid, creative spectators that most often are inspired to then recapture that feeling in-person or live online with others. I love that imagination is winning out over consumerism, at least in this small corner.

Depends how tall they are.

i wish that it was more common to refer to the metrics in terms of what they are instead of who discovered them. i can’t ever remember off the top of my head if the chebyshev one is supposed to be the diamond metric (L^1^) or the square metric (L^∞^).

Playing combat on a grid is actually presented as an optional rule and not the default for 5E, despite its popularity

So are feats, and point buy.

Personally I find Euclidean easy to remember because it matches the much more general Euclidean geometry. So you just remember "this is like, real maths". Manhattan distance is easy to remember because it does basically "refer to the metrics in terms of what they are", so long as you remember that Manhattan famously is a grid. Chebyshev is the hardest, but for me it's a simple matter of "the one that's left over". I have no idea, based on the name, what diamond and square metrics are supposed to be.

My group plays pretty loose goosy with the rules. We just look at it and make a quick estimate of whether something looks in range. They also have little range finder tools that are helpful for quickly determine cones, spheres, etc. We're also the kind of party that doesn't really keep track of gold. Apparently gold has a weight? For this reason I actually don't like playing one shots with people I don't know, because they don't play by all of our house rules, lol.

There's no grid in the sky, though

Holy shit it does. The halfling and dwarf are out of luck. Human stands a chance.

If you actually have to use that much math more than once in a blue moon, you're doing it wrong.

Fair point. I actually don't know what, if anything, the D&D (or Pathfinder) rules say on this matter. I've always just treated it as a natural 3D extension of the 2D grid rules. If they're three squares in one direction, same square in the other, and 10 feet up, I'd treat that as 15 feet away because of Chebyshev rules.

The opposite of that happened to Achilles

i think that’s a good point and that is a nice way to remember them. i think a lot of it just comes down to personal preference. i like calling them the diamond/square/circle metrics because those shapes describe the sets of points that have distance 1. i’ve found this wikipedia picture to be very helpful, and the diamond/square/circle terminology is my way of paying my respect to the picture. 

It is not really the math, but what I find boring is that 90% of the rules (measured by feeling) are about battle.

If the cleric is 30ft in the air, and the allies are 20ft away but on the ground, then the allies are probably 10ft tall

In general I don't really like Pen&Paper RPGs where you need miniatures (and for worse range finder tools) to play them. But that is a me thing, don't read my words as that I want to say D&D should change. Far away from that, D&D is a great game and I love it on the PC (where it IMHO only works, not at the table)

Happy cake day!

And multiclassing.