# D&D 4ENon-Euclidean Geometry in 4E?

#### Jeff Wilder

##### First Post
On Sunday, we mentioned -- just mentioned -- the 1-1-1-1 rule to the most tactically-minded player in our group. His immediate response was, "That's really going to screw things up, tactically." I don't think he actually minds the idea, because he knows he'd be more able and more willing to exploit 1-1-1-1 than would either of his DMs, but he noticed immediately. Literally within a second of hearing the change.

#### Reaper Steve

##### Explorer
ainatan said:

Man, it's gonna be hard to be a defender in this game...

I am coming to terms with the 1:1 movement.
What I have realized is that it's not the counting so much, but the fact that movement, especially charges, doesn't have to be in a straight line.
Using the above pic, if the charging model were one square forward, it could go around the middle model to attack one behind it (also one square closer) using either the 1-2-1-2 method or the 1:1 method.
It's not the counting... it's that a model can move around another one without that one being able to respond... at least in 3.5 and previous. This has always bugged me... a guy in front should be able to intercept a dude that's trying to go past.... hence the whole purpose of the offensive line in football.
Something tells me that 4E will grant defenders in specific--and maybe any model in general (to a lesser degree?) the ability to move out of turn to intercept another model trying to pass.

Such an intercept mechanic would make most of this discussion moot... there would be no reason to 'swing wide' if the defender could get to you anyways.
I hope this is in store... It's about time!

#### hong

##### WotC's bitch
Reaper Steve said:
I am coming to terms with the 1:1 movement.
What I have realized is that it's not the counting so much, but the fact that movement, especially charges, doesn't have to be in a straight line.
Using the above pic, if the charging model were one square forward, it could go around the middle model to attack one behind it (also one square closer) using either the 1-2-1-2 method or the 1:1 method.
It's not the counting... it's that a model can move around another one without that one being able to respond... at least in 3.5 and previous. This has always bugged me... a guy in front should be able to intercept a dude that's trying to go past.... hence the whole purpose of the offensive line in football.
Something tells me that 4E will grant defenders in specific--and maybe any model in general (to a lesser degree?) the ability to move out of turn to intercept another model trying to pass.

Such an intercept mechanic would make most of this discussion moot... there would be no reason to 'swing wide' if the defender could get to you anyways.
I hope this is in store... It's about time!
As I mentioned in the other thread, this behaviour is similar to what's seen in the Civilization games, which have had 1-1-1 diagonals for ~15 years. Another quirk of those games is if you have a frigate exploring, it's best to move in a diagonal zigzag pattern to uncover the most squares per round.

Is it quirky? Yes, especially if you're used to 1-2-1 diagonals. Does it mean things are broken? Not really, once you get used to it.

#### HeinorNY

##### First Post
Reaper Steve said:
Using the above pic, if the charging model were one square forward, it could go around the middle model to attack one behind it (also one square closer) using either the 1-2-1-2 method or the 1:1 method.
Yes, but if the dots were aligned diagonally, in 1-2-1-2 the outcome would still be the same.
That's called consistency.

#### fnwc

##### Explorer
Arkhandus said:
OH! And tables/charts! Lots of 'em! Like even further back in the day!
If you want a system with a lot of charts, you can look no further than Rolemaster. There's a chart for everything.

Hit a monster? Chart. Ordering ale at a tavern? Chart. Taking a dump? Chart.

Player: "I rolled a 12..."

GM: "Uh oh, diarrhea! You've clogged the toilet! Roll for the overflow..."

Player: "..."

#### glass

##### (he, him)
UngeheuerLich said:
Chess uses that symetrie for hundreds of years now, and nobody I know ever complained about a chess board beeing round. (Ok, in chess you actually do exploit that rule sometimes)
People keep mentioning chess, but it is utterly irrelevant because you never measure distances in chess -pieces either move one square or all of them.

glass.

#### Benimoto

##### First Post
Lackhand said:
Lies and calumny! 5 foot steps are an explicit exception to every rule; so they remain here.
10 foot reach, similarly has the corner-filling hack in both systems.

All this solves is the counting aspect
The 1-2-1-2 diagonal system and the 2 for straight, 3 for diagonal system still aren't exactly mathematically equivalent. Try this: in both systems, move a creature with a speed of 20 feet 3 squares on the diagonal. Or move a normal human, speed 30, one square diagonal and 5 straight in both systems. You'll find that to make the two systems equivalent, you have to give 1 extra movement point to creatures in the 2/3 system to make up for the "free" first diagonal the 1-2-1-2 system gives them.

So a creature with a speed of 30 feet would have an equivalent movement rate of 7, and a spell with radius 20 would be radius 5. So not only is the 5 feet = 1 square = 2 movement somewhat unintuitive, but there's not even a single step conversion from movement rates to speed in feet.

#### Lackhand

##### First Post
Benimoto said:
The 1-2-1-2 diagonal system and the 2 for straight, 3 for diagonal system still aren't exactly mathematically equivalent. Try this: in both systems, move a creature with a speed of 20 feet 3 squares on the diagonal. Or move a normal human, speed 30, one square diagonal and 5 straight in both systems. You'll find that to make the two systems equivalent, you have to give 1 extra movement point to creatures in the 2/3 system to make up for the "free" first diagonal the 1-2-1-2 system gives them.

So a creature with a speed of 30 feet would have an equivalent movement rate of 7, and a spell with radius 20 would be radius 5. So not only is the 5 feet = 1 square = 2 movement somewhat unintuitive, but there's not even a single step conversion from movement rates to speed in feet.
But it does work. Worth it or not, your call, but it seems easy enough to do, and easier than 1-2-1-2 (to me). But, sure, not worthy of the core game, fair enough.

That said, I have no problem with saying "diagonals just cost more" and denying the 20 footer that extra step. Why not? He hasn't the movement to complete it. Not by a lot (1.2132 feet); but that's not the point. Which side of that boundary you want to fall, permissive or not, is a personal choice. It's okay if the two don't map onto each other.

#### Nom

##### First Post
One benefit of 1-2-1 is that the key movement axes are de-emphasised a little, compared to hex or diagonals. When you are off the key axes, there is a set of "shortest path" that forms a rhomboid. The further away, larger the movement allowance, and closer to the midpoint between the axes the bigger the rhomboid. 1-2-1 has this effect too, but the narrower error angle and more circular shape reduces how visible it is.

Terrain affects this too. Most D&D battle maps don't have more than 5-10 spaces of clear terrain. In contrast, space games commonly have wide-open maps, which emphasises the rhombus.

Compared to 1-2-1, a 1-1-1 system puts more focus on the diagonal axes rather than the orthogonal axes. A creature moving along a diagonal axes can move "furthest" but is most limited in choice of paths. A creature moving along an orthongal axes has greater choice of paths but total movement distance is more limited.

My expectation is that a 1-1-1 system compared to the current system is that it will make movement more fluid - in that it is slightly easier to move around and through obstacles - and put more focus on diagonals for blocking. For those who watch carefully, this will probably feel slightly less realistic and slightly more mobile than 3.5, which is probably why they chose it.

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