15 ft diagonal movement...why?

[SangoProduction]

OK. I say a forum post (on another site) where they explained that diagonal movement is worth approximately 1.5 times the movement of moving on the sides because of Pythagoras's theorem - thus, to make all directions worth equal movement cost, every other diagonal movement is doubled every second diagonal move.

My question here is "why?" Is there some specific reason that the straight line approach is not suppose to be more efficient than doing a stair step movement? Is there a reason why it needed to be "balanced"?

[OldTrees1]

Um. Diagonals cost more so that it is realistic. No balance concerns. Merely trying to avoid "people bend spacetime when they move diagonally".

However you sound like you would like a Hex grid.

[Drelua]

Well, because it's a simple rule, and without it things make no sense. Just imagine there's a man 30 feet ahead of you. Then, 30 feet to your left of that man is a dog. If you don't count every other diagonal square of movement twice, then in order to move to either the man or the dog, you would have to move the same distance. This makes absolutely no sense.

Or, if you have some knowledge of trigonometry, this would form a right angled equilateral triangle, which is completely impossible.

[Gnoman]

The 1.5 square rule produces a vaguely circular range much like what you would get if you were simply using cartesian coordinates. Thus, you move roughly the same distance gong NW as you do N. If diagonal movement costs 1 square, you produce a square range, and going NW means you move 150% as far as you do going N in a straight line.

[Flickerdart]

Or, if you have some knowledge of trigonometry, this would form a right angled equilateral triangle, which is completely impossible.
Except, of course, upon a sphere.

[OldTrees1]

Except, of course, upon a sphere.

Well on a sphere you get wacky results too. Two paths of equal length that differ by 45 degrees(aka one is orthagonal and the other is diagonal) will end up separated by half their length. So either the man and the dog are closer together than you are to them, or neither one is diagonal from you.

[The Grue]

Um. Diagonals cost more so that it is realistic. No balance concerns. Merely trying to avoid "people bend spacetime when they move diagonally".

However you sound like you would like a Hex grid.

Incidentally, D&D ports rather well to a 5ft hex grid. No more having to remember what shape cones and spheres take of a given radius.

[OldTrees1]

Incidentally, D&D ports rather well to a 5ft hex grid. No more having to remember what shape cones and spheres take of a given radius.

Yeah. I love 6 of the 12 hex directions and don't care about 4 of them. However I can't make rectangles look right on a hex map.

[Drelua]

Except, of course, upon a sphere.

Err, it's impossible on a flat plane I mean. Stupid smart playgrounders, knowing more stuff than me... :smallwink:

[Tommy2255]

Yeah, I just use the "Pythagorous Was Wrong" approach to movement on a square grid. Diagonal costs the same as orthogonal. Basically, movement is as easy as on a hex grid, but you can have square buildings that don't end up being weird. Fireballs are square, cone of cold is half of a square, the threatened area of a reach weapon is square, the set of squares you can charge to is square. It's less realistic, but screw it, we've got dragons to kill, I don't have time for some Greek weirdo and his fancy geometry. It doesn't seem to mess up balance in my experience, so who cares?

[WeaselGuy]

and here my group is with a piece of string and a wet erase marker, drawing red circles whenever my wife casts a fireball, to see if the rogue is in the blast zone or not...

[Eldariel]

and here my group is with a piece of string and a wet erase marker, drawing red circles whenever my wife casts a fireball, to see if the rogue is in the blast zone or not...

Tip: Cut a paper the size of your most commonly used effects. You can just plant that on the grid and see what's affected.

[The Grue]

Tip: Cut a paper the size of your most commonly used effects. You can just plant that on the grid and see what's affected.

Alternative tip: Buy a stack of dollar store wire coat hangars and bend them into the appropriate shapes. Possibly with tools. Soldering them closed is optional.

EDIT:


Yeah. I love 6 of the 12 hex directions and don't care about 4 of them. However I can't make rectangles look right on a hex map.

For drawing terrain? I just draw things without regards to the grid, and adjudicate on the fly whether a given hex is open ground or not. My players are aware of this and seem to keep their tokens out of the "iffy" hexes unless they have a really good tactical reason to move into one, so it rarely comes up.

[OldTrees1]

For drawing terrain? I just draw things without regards to the grid, and adjudicate on the fly whether a given hex is open ground or not. My players are aware of this and seem to keep their tokens out of the "iffy" hexes unless they have a really good tactical reason to move into one, so it rarely comes up.

More like Dungeons where I want to use 30, 45, 60, 90, 120, 135, 150 and 180 degree angles between corridors and I want it all on one grid. I don't know how to do that without making iffy hexes.

[Chronos]

If you use a square grid with diagonals costing the same as orthogonal movement, then hexes are better (closer to geometric truth, do a better job of modeling reality). If, however, you use a square grid with diagonals counting as 1.5, then the square grid is better than the hex grid. The square grid also makes it a lot easier to accommodate square rooms, right-angled corridors, etc., which come up fairly often.

[Psyren]

Well, because it's a simple rule, and without it things make no sense. Just imagine there's a man 30 feet ahead of you. Then, 30 feet to your left of that man is a dog. If you don't count every other diagonal square of movement twice, then in order to move to either the man or the dog, you would have to move the same distance. This makes absolutely no sense.

Or, if you have some knowledge of trigonometry, this would form a right angled equilateral triangle, which is completely impossible.

All of this. Just mentally count "5-10-5-10..." while moving diagonally up to your movespeed and you're there.

[Vhaidara]

My question here is "why?" Is there some specific reason that the straight line approach is not suppose to be more efficient than doing a stair step movement? Is there a reason why it needed to be "balanced"?

It is still more efficient.

A single stair step would cost 10ft of movement. A single diagonal costs 5.
A double stair step would cost 20ft of movement. A double diagonal costs 15
Triple stair = 30. Triple diagonal = 20.

It makes it so that you can't double your movement by going diagonally. Because does it make any sense that you can literally cover twice the distance by running diagonally.

[Curmudgeon]

Incidentally, D&D ports rather well to a 5ft hex grid.
Perspectives differ on that. As a DM, it would greatly reduce effectiveness of mob attacks against PCs if there were only 6 surrounding spaces instead of 8. So no, D&D doesn't port at all well to hex grids from that viewpoint.

[137beth]

Perspectives differ on that. As a DM, it would greatly reduce effectiveness of mob attacks against PCs if there were only 6 surrounding spaces instead of 8. So no, D&D doesn't port at all well to hex grids from that viewpoint.

BUT if you use a hex grid, then as a side effect the party wizard might turn into a lizard!


At one point I tried making 'more accurate' diagonal movement rules: moving from square (x,y) to square (x+m,y+n) costs 5*Ceiling(Sqrt(m^2+n^2)) feet of movement.
Then I and my group decided it wasn't worth it, and went back to the default diagonal rules. And ultimately, it isn't accurate either way, since rounding takes place every turn, leading to somewhat odd results. It's just more convenient.

For the record, in 4e, they changed the default to be the L-Infinity metric: diagonal movement costs the same as orthogonal movement.

[Necroticplague]

In the game, a diagonal costs 1.5 times normal movement in an attempt to represent that in reality, it would be about 1.21 times the straight movement. So, like in life as we know it, the rules recognize that moving diagonally is faster then moving in a step-pattern, but less effective than devoting all movement to one direction or the other.. If diagonal and non-diagonal had the same costs, then pi=4 and sqrt(2)=1, squares and circles are the same thing (and spheres and cubes are also identical). It has jack squat to do with balance, its with a vague attempt at simulation. 4e did away with it because its more of a pain than its worth (thus, firecubes).

[Chronos]

In the game, a diagonal costs 1.5 times normal movement in an attempt to represent that in reality, it would be about 1.21 times the straight movement.
Typo: That should say 1.41 .

[ahenobarbi]

If diagonal and non-diagonal had the same costs, then pi=4

Actually pi is still 4 with current rules.


For the record, in 4e, they changed the default to be the L-Infinity metric: diagonal movement costs the same as orthogonal movement.

L-1 (no diagonal movement), pseudo L-2 used in 3.5, L-infinity (diagonal movement costs the same as straight) and hex grid are all I są w used. L-1 is unintuitive, pseudo L-2 makes for ugly shapes and hex is annoying (when you move straight but have to move "a little ahead and to left" then next step "a little ahead and to right"). L-infinity results in square circles but seem to be the best.

EDIT: I forgot about actually measuring distances. I never player like that but it seems like a lot of extra time added to each round.

[Nibbens]

OK. I say a forum post (on another site) where they explained that diagonal movement is worth approximately 1.5 times the movement of moving on the sides because of Pythagoras's theorem - thus, to make all directions worth equal movement cost, every other diagonal movement is doubled every second diagonal move.

My question here is "why?" Is there some specific reason that the straight line approach is not suppose to be more efficient than doing a stair step movement? Is there a reason why it needed to be "balanced"?


Yeah, I just use the "Pythagorous Was Wrong" approach to movement on a square grid. Diagonal costs the same as orthogonal. Basically, movement is as easy as on a hex grid, but you can have square buildings that don't end up being weird. Fireballs are square, cone of cold is half of a square, the threatened area of a reach weapon is square, the set of squares you can charge to is square. It's less realistic, but screw it, we've got dragons to kill, I don't have time for some Greek weirdo and his fancy geometry. It doesn't seem to mess up balance in my experience, so who cares?

"The trees are squares?"

After having played with a DM who used this method, I started DMing for a different group. The group I was DMing for began to question my ability to draw circles because instead of a 20 foot diameter circle, I drew a 4X4 square. I was confronted with the above question. My PC's thought there was some special reason the trees were pruned in squares... I never heard the end of it...

Truthfully, it doesn't change the experience as long as everyone is on the same page - but it does make for some weird looking circular objects...

[Rijan_Sai]

(thus, firecubes).

Sorry, I have nothing relevent to the topic to add...(all the math has been done by those better then I.)

However, the above quote alone would almost make using 4e "L-infinity" movement rules worth it!

[aidenn0]

I didn't see anybody mention this, so here's a really easy rule for any straight-line distance:

Count how far up, and how far over you move. Divide the smaller number by 2 (round down), and add the larger number to the result. This gives you the same value as the 5/10/5 rule for diagonal movement, and is faster in many cases (including is Eilamil the Ranger in the radius of a 30' effect).

Example:

What's the distance to my target if he is 5 squares up and 10 squares over from me?

5/2=2; 2+10=12 so 12 squares or 60 feet.

For movement, this doesn't come into play much unless you are using expeditious retreat, or polymorph into something that flies, but this is really useful for finding ranges and "am I in the radius of effect X"

[Kingsnake]

Well, because it's a simple rule, and without it things make no sense. Just imagine there's a man 30 feet ahead of you. Then, 30 feet to your left of that man is a dog. If you don't count every other diagonal square of movement twice, then in order to move to either the man or the dog, you would have to move the same distance. This makes absolutely no sense.

Or, if you have some knowledge of trigonometry, this would form a right angled equilateral triangle, which is completely impossible.

Now this is just silly. The distance between you, the man, and the dog is exactly the same- 30 feet. 30 feet to the north is not somehow less than 30 feet the northwest. The fact that a square grid doesn't model movement in eight directions doesn't change the basic underlying laws of reality.

[Vhaidara]

Now this is just silly. The distance between you, the man, and the dog is exactly the same- 30 feet. 30 feet to the north is not somehow less than 30 feet the northwest. The fact that a square grid doesn't model movement in eight directions doesn't change the basic underlying laws of reality.

No, what he's saying if you have

M_30ft_D
|
30ft
|
Y

Now, if you don't have 1.5 diagonal movement, the distance from you to the dog is also 30ft. When it isn't

[137beth]

More like Dungeons where I want to use 30, 45, 60, 90, 120, 135, 150 and 180 degree angles between corridors and I want it all on one grid. I don't know how to do that without making iffy hexes.

I go back and forth depending on the environment. In an artificial dungeon or building, square grids. In the wilderness or sometimes a natural cavern, hexes. If an encounter takes place partly in a building and partly outside (or just around the building), then I use squares.

[NNescio]

In the game, a diagonal costs 1.5 times normal movement in an attempt to represent that in reality, it would be about 1.21 times the straight movement. So, like in life as we know it, the rules recognize that moving diagonally is faster then moving in a step-pattern, but less effective than devoting all movement to one direction or the other.. If diagonal and non-diagonal had the same costs, then pi=4 and sqrt(2)=1, squares and circles are the same thing (and spheres and cubes are also identical). It has jack squat to do with balance, its with a vague attempt at simulation. 4e did away with it because its more of a pain than its worth (thus, firecubes).

sqrt(2) ≈ 1.414

Not 1.21.

(Trivial to check, 1.3^2 = 1.69 < 2)

[Judge_Worm]

Do what my group does- ignore the boxes. You don't need em. Use construction paper cutouts for effects and a marked tongue depresser for your movement. One of the members of my group plays a lot of warhammer 40,000 and came up with the idea. It makes the whole world more fluid.

Or else you could always just ignore the diagonal movement restriction.

[Necroticplague]

sqrt(2) ≈ 1.414

Not 1.21.

(Trivial to check, 1.3^2 = 1.69 < 2)

Somebody else already pointed this out.

[137beth]

sqrt(2) ≈ 1.414

Not 1.21.

(Trivial to check, 1.3^2 = 1.69 < 2)

Someone else pointed this out earlier in the thread. See what I did there :)

[Kanthalion]

and here my group is with a piece of string and a wet erase marker, drawing red circles whenever my wife casts a fireball, to see if the rogue is in the blast zone or not...

The other DM in our group, who's house we game at, made metal wire rings of the appropriate size for that very purpose. The 20 foot one gets far too much use from that stupid web spell I now regret talking the sorcerer into taking.

[Kanthalion]

Alternative tip: Buy a stack of dollar store wire coat hangars and bend them into the appropriate shapes. Possibly with tools. Soldering them closed is optional.

EDIT:

For drawing terrain? I just draw things without regards to the grid, and adjudicate on the fly whether a given hex is open ground or not. My players are aware of this and seem to keep their tokens out of the "iffy" hexes unless they have a really good tactical reason to move into one, so it rarely comes up.

Looks like I should have read the whole thread before mentioning the ring thing. I do the same thing with the maps on the grid. Then where appropriate I will usually have them do a balance check or the like if they want to go on a partial square.

[Vhaidara]

The other DM in our group, who's house we game at, made metal wire rings of the appropriate size for that very purpose. The 20 foot one gets far too much use from that stupid web spell I now regret talking the sorcerer into taking.

My uncle actually gave me a set of metal frames that mark out 10ft and 20ft circles, and 2 30ft cones (right angle and straight ahead) sized to the grids of the dry-erase surfaces he gave me. Best Christmas present ever.

[Kanthalion]

My uncle actually gave me a set of metal frames that mark out 10ft and 20ft circles, and 2 30ft cones (right angle and straight ahead) sized to the grids of the dry-erase surfaces he gave me. Best Christmas present ever.

Sounds like an awesome uncle. We just have the rings, but that sounds like a good idea to make something for the cones.

Oh, and I suppose to the actually topic of the thread, I agree that it is just a simplifying abstraction and is better not to think about too hard. I was once playing a d6 Star Wars game and one of the other players got into an argument with the DM about the physics of jumping because the game rules weren't in line with reality.