D&D 4E Non-Euclidean Geometry in 4E?

[Elder-Basilisk]

You might think so, but things are also REALLY different when you take the possibility of move+charge and the variety of possible "nearest" squares into account. In the half dozen or so DDM 2.0 games I've played thus far, it has only been in the most rare and constricted situations that I have been unable to reach and attack whatever of my opponents' pieces I want to attack without incurring an OA--at least that is when my opponent hasn't been running a band consisting of five or six thundertusk boars that block up every available path to anything else I might want to attack and on a map where there is a six square wide choke point for them to block.

I'll also note that this example features an open area with no other combatants in it. Things would be different in a dungeon and will also be changed by the introduction of other party members.

 

[Reaper Steve]

Well, this is accurate, but they don't want long movements to take too long to calculate if you have to re-do some of the movement.

Personally, I'd do:

All movement into a clear square costs 1.

The first diagonal movement of any move action costs an extra 1. All other subsequent diagonals in that move action cost 1.

Works pretty well, especially considering that the 1-2-1-2 scheme overcharges you slightly for diagonals.

Consider a human with a base move of 30' (6 squares) moving only in diagonal:

1-2-1-2: 4 squares, approximately 28'

1-1-1-1: 6 squares, approximately 42'

2-1-1-1: 5 squares, approximately 35'

A little more error than 1-2-1-2, but nearly all the simplicity of 1-1-1-1.

Now this is genius! It strikes a fine balance, effectively enhancing play with a simpler system than 1-2-1-2, while still being reasonably close to geometry as we know it.

DMShoe... if it's not too late, think about this one.
(BTW, thanks for your posts and thoughts. I appreciate your argument, but I still think that 1:1 isn't the best decision, especially when one like this is available.)

Ranges and area effects are all 1:1. then in the movement rules, add "the first (and only the first) diagonal move of a creature's turn counts one additional square of movement."

Puggins: thanks. I'll keep this in the hip pocket if I stand deal with pure 1:1 but don't want to go ll the way to diagonal = 1.5

 

[Stalker0]

Puggins, definitely an interesting compromise between realism and simplicity, a definite consideration for anyone not satisfied with the rules as written.

 

[Kobu]

This rule change is great. It's going to get more groups to switch to hexes.

The two arguments in favor of squares that I concede to go right out the window with 1-1 diagonal movement. These were:

1. Movement in certain directions on a hex is "weird". It's true, you have to abstract a bit to understand the zig-zag movement. The warped space with diagonals though is much stranger and there's no real way to justify it. When rotating the grid alignment makes all the difference in the world for tactics, something is very wrong.

2. Circles for large AoEs are better emulated on square grids. The larger the spread, the better it approximates a circle. Large spreads on hexes tend to end up looking more like hexagons or triangles. It doesn't come up much where anyone will notice, but firecubes will come up every single time. Cones too are either horribly warped or have to use a system that doesn't match movement.

 

[Nom]

Hexes do not cause problems.

Actually, they cause a variety of problems, some of which are not shared by square grid metrics.

Hexes constrain in exactly the same way that manhattan distance (orthogonal only) squares do. It's just not quite as noticeable because you have 3 axes of freedom rather than two.

I've also noticed some people running the 'diamond' argument. That applies to hexes too. Set up two guys on a spline. Any path from one to the other is the same length, which means that a guy in the middle can be bypassed for no additional movement cost unless he can block the entire width.

Similarly, a hex grid ends up in exactly the same situation as square grids vs distance on and off prime axis (oddly, the diagonal axes becomes the prime axes under the 4E system). I've played a number of space combat games on hexes, and one always ends up manoeuvring around the splines. Admittedly, those games including 6-direction facing.

No grid can achieve an exact distance measurement. It's not accurate vs non-accurate; it's about how much inaccuracy you are willing to put up with.

There are other advantages of hexes:

Many hex maps have little dots in the middle of the hexes, so it makes it easy to determine whether 50% of the hex is available for use or not.

Many hex maps have numbers on them which make identifying where an invisible PC is. For example, a player can write down the number of the hex where his PC is moving to and hand it to the DM, and the other players do not know where the invisible PC is located.

That's not a feature of hexes. That's just because you are using military wargame style hex maps. I have seen square maps with the same features.

Hexes allow 5 foot circular area effects to include 1 hex, 10 foot 3 hexes, 15 foot 7 hexes, etc. Cones are easier with hexes than squares, pick two hex lines and shape the cone down them.

Assuming you are happy with "circle" = "hex" and "cone" = "60 degree triangle". Which is fundamentally the same abstraction as "circle" = "square" and "cone" = "45 or 90 degree square/triangle". D&D 3.5 at least produced shapes that were significantly more circular / conic than the grid.


Hexes do have one failing that is unique - they are not monotonic to intersecting lines.

Draw any line across a square grid. Unless it lies on a grid line, there is always a single crossing point from any row or column to the next row or column. In contrast, many lines on hexes will spend some time in the zig-zag between two hexrows. This becomes a pain when trying to calculate sight lines or cover, as the "direct path" between two hexes is non-unique.


It's important to consider the difference between hexes, manhattan (orthogonal) squares, cheybeshev (diagonal = 1) squares, and the diagonal = 1.5 squares approximation. Hexes and manhattan squares are mathematically identical with the exception of 2 vs 3 axes of movement. Non-manhattan square models offer 4 axes of movement, but with artefacts on distance metrics.


As for other models, I've played a couple of games with the '1st diagonal costs double' model (eg a mini-game in Star Frontiers' Volturnus series, which incidentally normally counted hexes as 1). It ultimately plays almost identically to diagonal = 1, except that:
(1) slower creatures suffer a greater penalty.
(2) one ends up with a concave movement area (diamond with extra bits on orthogonals), which is the opposite of a "realistic" convex area.
Thus, you end up with a "quirky" mechanic without really gaining anything.

The opposite alternative, which I rather like in terrain-rich environments, is that diagonals count not double but +1. It means that a diagonal in clear terrain is the same as orthogonal (unless the orthogonal is blocked!), but you gain speed moving over difficult terrain.

For me, though, the most telling argument is the unification of movement distance and range. Any model that penalises up-front means that an adjacent diagonal is range 2 while an adjacent orthogonal is range 1, which then means we need a 3.5-esque exception to handle that case.

 

[Deset Gled]

I believe I woud file this change under "mistakes not learned from".

In 3.5, they wanted Power Attack to be more powerful. If you follow the math that is consistent with the rest of the game and is most balanced, you would change it so that light weapons add 0.5 damage for each point of penalty spent, one-handed weapons give 1, and two-handed weapons give 1.5. But, since that would make the math more difficult, WotC decided it was best to damn the math and go with 0-1-2 (respectively) instead. The result was one of the most controvertial changes of 3.5. The rounding caused PA to be *the* way for just about every melee build to deal more damage in 3.5. I was such a lopsided feat that WotC eventually denounced it as a bad idea (while also not learning that any opened ended bonus is a problem - but that's another rant).

Here, again, they have decided to sacrifice realism for the sake of quick playability that requires less math, in a way that will be amazingly controvertial, and allows players to munchkinize rounding errors. IMO, they have gone too far in search of simplicity, to the point that it will actually make things more complicated when people learn that they can play games with diagonals. Also, like PA, it probably won't be much of an issue at low levels, when all movement is 2D and not many bonuses to speed are available. But at higher levels the problems will be much larger, as the unbounded rounding error gets greater over longer runs, 3D movement, and larger spell areas/ranges. It also gives me flash backs to an N64 FPS (I'm pretty sure it was Perfect Dark) that failed to normalize the joystick vectors properly, and made you run faster on a diagonal than straight forward. The results were very silly.

This is the only mechanical change in 4e so far that I completely disagree with.

 

[KarinsDad]

Actually, they cause a variety of problems, some of which are not shared by square grid metrics.

Wow. Where to start? So many claims ...

Hexes constrain in exactly the same way that manhattan distance (orthogonal only) squares do. It's just not quite as noticeable because you have 3 axes of freedom rather than two.

How so? You’ll have to illustrate this with an example. The directional constraints are a lot less than squares and the distance constraints are small. For example, moving 90 degrees to the left as opposed to straight up a line results only in about an 8% delta off of real distance (a little is lost on each hex as the movement zigzags). That's much better than the 29% delta of 1 1 1 1 diagonal movement on squares.

Who even cares about 8% for a 1 1 1 1 hex system (worse case scenario) when the harder to play 1 2 1 2 square diagonal system was off by 6%.

And, DND is not played with orthogonal movement only.

I've also noticed some people running the 'diamond' argument. That applies to hexes too. Set up two guys on a spline. Any path from one to the other is the same length, which means that a guy in the middle can be bypassed for no additional movement cost unless he can block the entire width.

This one is true. I'll concede this as an issue with hexes.

Similarly, a hex grid ends up in exactly the same situation as square grids vs distance on and off prime axis (oddly, the diagonal axes becomes the prime axes under the 4E system). I've played a number of space combat games on hexes, and one always ends up manoeuvring around the splines. Admittedly, those games including 6-direction facing.

I'm not sure what you are trying to say here. Please give an example.

Assuming you are happy with "circle" = "hex" and "cone" = "60 degree triangle". Which is fundamentally the same abstraction as "circle" = "square" and "cone" = "45 or 90 degree square/triangle". D&D 3.5 at least produced shapes that were significantly more circular / conic than the grid.

But they were hard to use. A lot harder to use than large hexes as circles and large triangles as cones. And cones are only 90 degrees in 3.5, not 45 degrees. Granted, a cone could be 45+ degrees on a square grid system, but 3.5 doesn't do that. Course, cones can be 30+ degrees on a hex system up a spline and a row.

And, speaking of their cones. 15 foot cones in the DMG:

XXX
XXX
OXO

or

OOX
OXX
XXX

The first one looks like a tree and the second a triangle. It isn’t until really large size that the 3.5 cones becomes vaguely cone-like. Even the 30 foot cones look mostly like a triangle (or more like a Stealth bomber, but not a cone).

And, circle = square is a lot less circular in shape than circle = hex.

Hexes do have one failing that is unique - they are not monotonic to intersecting lines.

Draw any line across a square grid. Unless it lies on a grid line, there is always a single crossing point from any row or column to the next row or column. In contrast, many lines on hexes will spend some time in the zig-zag between two hexrows. This becomes a pain when trying to calculate sight lines or cover, as the "direct path" between two hexes is non-unique.

I wouldn't call that a pain. Draw a line or hold a string up. Cover exists if a hex has 50% or more of it on the side granting cover. That’s just as easy of a rule as "if a line drawn through any" of 3.5 for squares.

I fail to see this as hindering game play in any way.

I think you are stretching here. It's a feature of hexes, but it is not a failing. It doesn't really affect game play.

 

[Hussar]

Meh, if you think it will break the game that much, test it. Try to run your next adventure with this system of counting squares. Pick a module at random, use 4 pregen PC's and test it out.

Come back when you've finished and share your results. Right now I'm seeing all sorts of hypothetical sitations that are just that - hypothetical. The real test is in play.

 

[AZRogue]

I wouldn't have a problem with suspension of disbelief. I'm already at a table half covered by snacks playing a game with magic, monsters, and elves. I can, and have, had problems with consistency, or with metagaming, but not with suspension of disbelief.

My problem with the 1 for 1 diagonal movement rule would be that it too easily allows for characters and/or monsters to bypass the defenders and SEEMS to negate a lot of the tactical positioning that I associate with playing on a grid.

Now, I'm not shattered or anything because I won't be using a grid for most of my encounters, but I DID plan on using one now and then for large, or special, tactically interesting, ones. This somewhat lessens the appeal.

One way that would solve the problem, in my mind, would be if the Defenders were allowed a Shift or Move of some kind when it WASN'T their turn. If there was an ability that allowed a Defender to step between a monster and its target then the 1 for 1 rule would be fine with me. I guess I'll have to wait and see.

 

[TwinBahamut]

I just thought of another odd quirk of this new system. I guess I will explain with an example:

An X represents a person or object, while an O represents empty space. Compare the two situations:

OOOOO
OOXOO
OOOOO
XXXXX
OOOOO

XOOOX
OOOXO
OOXOO
OXOOO
XOOOO

In both situations, there is a single person facing a line of people who are spaced five feet apart, about 10ft away from him. In the first example, he can't pass at all. In the second example, he can pass through with hardly any movement penalty (I am ignoring AoOs for this example). In order to completely block movement with the diagonal line, it is necessary to set it up like this:

XOOOX
OOOXX
OOXXO
OXXOO
XXOOO

In other words, you practically need twice as many people to secure a diagonal line as you need to secure a vertical or horizontal line.

Really, I know this has very little to do with the change from 1,2,1,2 counting and diagonal=1 counting, but it rubs me the wrong way. However, in a hex grid this situation is not present (or at least a lot more minor), which I think is a decent enough argument for using that system. I suppose Manhattan Geometry has the opposite problem (people supposedly ten feet apart can block movement in a diagonal, but not on a horizontal or vertical), but I prefer options that make it easier to defend, rather than harder, so I would prefer that to the 4E system.