Math Matters

Ironaically enough, you just take either the horizontal or the vertical distance (whatever is longer) instead of calculating. I hate that rule and never use it, but that's what RAW says.

Depends how tall they are.

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

RAW yes, they're 30 feet away.

As a home rule, I'll sometimes run total distance = long distance plus half the short distance. That also correlates nicely with making every other diagonal count as 10'

Used it in practice in my head the other day - even nailed the sqrt to a decimal point. I have created human life, but I think I was more proud of this lol

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.

If you actually have to use that much math more than once in a blue moon, you're doing it wrong.
- If I think more about it i come to conclusion that is not really the math per se, but what I find boring is that 90% of the rules (measured by feeling) are about battle and battle takes such a huge and detailed part in the game.
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.
- I think you'd like how Exalted handles money. (Note: I'm talking about second edition here; I never got familiar with third edition.)
  In Exalted, wealth is represented by a Background called Resources. Backgrounds are essentially stats that represent useful things your characters has in a general sense like wealth, fame, contacts, or a mentor. They go from zero to five.
  Resources is a vague representation of wealth. At Reduces 1 you're one meal away from total poverty. At Resources 5 you have something that passively generates substantial amounts of money for your character, whether that's ownership of a lot of land or an army of accountants maintaining your investment portfolio. Whatever is is, it works without you having to deal with it.
  In terms of game mechanics it's easy to use: Prices are expressed as Resource scores. If you want to buy something you just compare your score to the item's.
  If yours is higher, you just get the item as the price doesn't affect your wealth significantly.
  If both scores are the same you get the item but have to reduce your Resources by one. This represents you having to liquidate a large amount of your assets to cover the price.
  If your Resources score is lower than that of the item, you can't afford it.
  It's a nice system for a game that doesn't want resource management to get in the way of epic adventure.
- 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)

But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to approximate Euclidean.

Happy cake day!
- Thanks!
Me at 20: I'm never going to need Chebyshev distance in real life. Why am I learning this?
- Happy cake day!
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.
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 (L¹) or the square metric (L^∞).
- 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.
- Chebyshev distance can also be called chessboard distance if you want something more descriptive.
There's no grid in the sky, though
- 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.
Is that so? Why would some spells specify geometry then? For example fireball says it is a 20 ft radius while Hallucinatory Terrain specifies that it affects a 150 ft cube which, under Chebyshev distance, would be the same as a sphere right? My understanding was that D&D 5e uses euclidean distance with a minimum threshold of a square that has to be covered to be counted.
- D&D's targeting rules are quite strange, but yes, it's very explicit that Chebyshev is used in 5e by default, if playing on a grid. On page 192 of the 5.0e PHB:
  To enter a square, you must have at least 1 square of movement left, even if the square is diagonally adjacent to the square you're in.
  The DMG presents, on page 252, an optional variant of the optional grid rules, which is to treat it the same as Pathfinder 2e does (alternating 5 ft and 10 ft):
  The Player's Handbook presents a simple method for counting movement and measuring range on a grid: count every square as 5 feet, even if you're moving diagonally. ... This optional rule provides more realism.
  When measuring range or moving diagonally on a grid, the first diagonal square counts as 5 feet, but the second one counts as 10 feet. This pattern...continues when you're counting diagonally even if you move horizontally or vertically between different bits of diagonal movement.
  As for the value of cube vs sphere in the context of Chebyshev ranges, there are two key differences.
  First, cubes measure side length, spheres measure radius. A 10 ft cube covers 4 squares. A 10 ft sphere covers 16.
  Second, and more importantly (since the above could easily be translated by using only cubes or only spheres throughout the system, with either half or double the numbers), cubes are cast from one side, whereas spheres are cast from the centre. If you're standing in the front line with enemies in front of you and allies behind, a cube cast with you as its origin point will hit either allies only or enemies only, but not both. A sphere cast with you at its origin point will affect both allies and enemies. Note that the rules for cube, on page 204 of the 5.0 PHB say "A cube's point of origin is not included in the cube's area of effect, unless you decide otherwise." So you could include yourself and your allies, or you could include enemies but not yourself, if you so desired. Or, less likely, you could include allies but not yourself, or enemies and yourself.
  From memory, cube spells are mostly cast from a range of "self", which is where this becomes an important distinction. If a spell has a range of X feet and cube, then the main difference is just that its area is smaller but its reach is longer than a sphere with the same numbers.
- Fireball says radius, but in a non-Euclidian geometry radius doesn't translate to a Euclidian sphere. Embrace the cube of constant radius!

If the range of Bless is 30ft and the Cleric is 30ft in the air, then any non-zero horizontal distance would technically put them out of range. You don't need to calculate that they are 36.06ft away to know if they are out of range or not.

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.
- Though for area damage spells, it’s much, much more complicated.
  That's an optional variant rule described in Xanathar's Guide. The default rule for grids is simpler: just do Chebyshev.
But do their feet need to be in range or just a single part of their body?
- Depends on which part of them needs to be blessed?

Do some people actually playing RPG care that much about range ? Rather than some guesstimate ?

I actually find the Ryuytama range management pretty cool, where you simply say whether your character is at contact/short-range/long-range/away and that's it.

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. 🤘🏼🤓
A wild Ryutama reference is crazy. What a charming system.
It always comes up at some point. Most DMs will either handwave or give a generous approximation. Inexperienced DMs (or those that just run a tight ship) will actually calculate it.
Some do. I like positioning on a grid as a part of combat. It rewards tight play and understanding the mechanics. When I DM though, it depends on the playgroup. I think most people prefer guesstimating and just applying the rule of cool