"4E, as an anti-4E guy" (Session Two)

[N0Man]

[/list]
If you compare the values directly instead of rounding off first, 3E comes out even further ahead. For example, in your 6x+4y case, you list it as a tie, but 8 is a much better approximation of 7.21 than 6 is.

If your goal is to get the closest to 8, then yes, 7 is closer to 8 than 6 is, but that's not really the goal now is it?

If you were actually making the mathematical calculations, you would certainly not round up from 7.21 to 8, you would round down to 7. Both of them are 1 off. The fact that one is 1.21 off and the other is .79 off is inconsequential, unless you play a form of D&D where you use fractional squares.

In the end, does it really matter? I've already said that mathematically that 3E has a very slight advantage, but it's an advantage that can be overstated and it's not even universal. Just as 4E underestimates distances the closer to a true diagonal you go (when X=Y, or is close), 3E overestimates distances at sharper angles (where X > 2Y, or X < 1/2Y).

Both systems can be off, the differences aren't that big of a deal. Use what you want, but honestly the passion for such a small difference is not really rational. That's why I said I think a lot of it is psychological bias, not a rational bias.

1:1 is close enough, easy to explain to new players, easy to eyeball, and makes for speedier play for many average players, as well as new players.

1-2-1 is slightly closer on average, but can be wrong too. It isn't going to really break much to use if that's what your group wants to do. It's easy enough to implement.

However, just like any houserule, I would strongly urge a DM to really consider about what feels comfortable to a group, and don't make a houserule out of what YOU think makes more sense. Consider that sometimes there are good and compelling reasons that a game is designed the way it is. Any houserule that adds complexity (even if it's minor complexity) or tedium to a game should be agreed on by the group, not just dictated by an inflexible and opinionated DM.

And along those same lines, consider the effect a houserule has on new players that you might bring into the game.

 

[Herremann the Wise]

• 6x + 1y = 6.08. 3E = 6. 4E = 6. Tie.
• 6x + 2y = 6.32. 3E = 7. 4E = 6. 4E wins (by 1)
• 6x + 3y = 6.71. 3E = 7. 4E = 6. 3E wins (by 1).
• 6x + 4y = 7.21. 3E = 8. 4E = 6. Tie. (Both are 1 off of the closest integer).
• 6x + 5y = 7.81. 3E = 8. 4E = 6. 3E wins (4E off by 2).
• 6x + 5y = 8.49. 3E = 9. 4E = 6. 3E wins (3E is off by 1, 4E off by 2).

3E's 1-2-1 math is not the landslide of realism that some of the 1:1 critics seem to argue. I think whole debate is largely psychological and is weighted by how highly some people value realistic and consistent math (even if it only wins by a small lead).

Your list indicates to me that the 1-2-1 method is equal or best in all cases except one. The big psychological issue for me is the following.

The issue I have with the 1-1-1 is if you organise the grid to move diagonally "25ft.", it takes 5 squares of movement. If however, you align the grid at 45 degrees to that, it now will take you 7 squares of movement (see attached pdf). To me, this is a huge discrepancy that breaks down the robustness of the game. We play with minis and battlemap and judge cover and movement etc. fairly accurately. While 1-1-1 does make things easier to adjudicate mechanically, it is just one more thing that makes you scratch your head and wonder why all the streamlining and simplification.

To me, 1-2-1 strikes the nice balance of ease of use while at least attempting to mirror some measure of mathematical realism. This pretty much defines how we like to play the game. However, I can understand how others who play a more beer-and-pretzels style game, or one that does not worry too much about simulation would find 1-1-1 good enough.

Best Regards
Herremann the Wise

 

[Herremann the Wise]

If your goal is to get the closest to 8, then yes, 7 is closer to 8 than 6 is, but that's not really the goal now is it?

If you were actually making the mathematical calculations, you would certainly not round up from 7.21 to 8, you would round down to 7. Both of them are 1 off. The fact that one is 1.21 off and the other is .79 off is inconsequential, unless you play a form of D&D where you use fractional squares.

On the one hand, your mathematical rigour is out of order but on the other, you could just as easily apply your argument of "who cares?". If what you set out to do was say, "this is the mathematical reality", which one is closer?, then in that situation, the 1-2-1 method approximates it better than 1-1-1.

In the end, does it really matter?

On it's own? Not really, it's not a dealbreaker and is easily enough houseruled. The big picture is however that for those of us that like a certain style of play - with a degree of simulation - there are numerous instances where the rules are out of kilter with that style. In that regard, I suppose the 1-2-1 issue is the symbolic figurehead and representative for that entire banner of simulationist issues. So yes, in terms of the big picture for players like me, it does matter.

Best Regards
Herremann the Wise

 

[N0Man]

You're missing the point. I said multiple times that the closer to a 45 degree angle, the less accurate 4E becomes, so in the literal 'corner case', it is off noticeably. I'm not arguing that 4E is more mathematical, but rather than it's not mathematically inferior to such a degree that it matters much in the majority of the cases.

Both are simplifications. Both have places where they are stronger at. Should I create a PDF in response to show this too?

You can spin that 3E is equally accurate, equally wrong, or superior in the majority of the cases, and it's true.

I could also spin that 3E only is superior in 3 out of the 6 scenarios, and it's also true.

You could argue that the worst offender is 4E being off by 2 squares, which is 1 more square in error than 3E ever has, which is also true.

I could respond that in the diagonal examples, that the average size of error for 4E was only 0.5 greater than that of 3E, which is also true (0.5 vs 1.0).

See, I understand how all of this work. You don't have to draw me a picture, or explain the math on it. I understand. As difficult as it is for some to believe, I can be proficient in math and still be ok with choosing one flawed arbitrary approximation over another slightly less flawed arbitrary approximation for the reason of simplicity.

And again, if your group decides they want to play 3E style, that's fine. But the point remains is that over the course of many diagonals of varying angles, on average, it's just not that great of a benefit to bother with 1-2-1. Just don't make the classic DM mistake of "my houserules that introduce complexity are more realistic" at the expense of the fun of your players or future players down the road.

If 45 degree angles occur so commonly in your world that you want to houserule the old 3E rule back in, you might want to consider rotating your entire world 45 degrees. Doing this would make all your angles closer in 4E again.

 

[Zinovia]

You could always use a hex grid, as others have suggested. It's what our group chose to do, although that was in part due to already owning a large Chessex battle mat with a hex grid. I like it better for intuitively seeing facing and flanking, and for the lack of problems with diagonal movement. Also fire hexes > fire cubes in my book.

Because spell areas aren't always intuitive on a hex grid, I made some templates, with bursts being round (hexagonal) and blasts being cones. You can find the hex templates here. Although it seems not many people use hex maps, but they work well for our group.

 

[aboyd]

I use hex maps in my 3.5 game. Thanks for the templates.

 

[Jhaelen]

I never realized there was a problem with the 1-1-1 movement. I guess it's because the mathematical error hardly matters if you're looking at relatively short distances. Since 4E actively encourages combat encounters to start close to the action, it becomes a non-issue.

As someone who has also played DDM 1.0 and 2.0 I can say that I definitely prefer 1-1-1 over 1-2-1. It solves a lot more problems than it causes (if any).

 

[Nikosandros]

It makes nearest or closer than less obvious. You eyeball that differently than in normal life.

Exactly. You look at the battlemat and your geometric intuition tells you something, but the rules say something different.

 

[ExploderWizard]

I have thought a lot about the 1-1-1 vs the 1-2-1 issue and have come to the conclusion that I don't need to use either to play D&D even if I still want to use minis.

Thinking outside the grid works wonders. Any game rules that make square occupation important enough to worry about can get tossed. Two melee fighters that want to lock shields and defend a 5' passage side to side is fine with me. I have always hated the 5' imaginary bubble more than the diagonal rules anyhow.

I like sometimes having a grid for easy eyeballing distances but it isn't something that I want the action to conform to or depend on. I can even accept a character ending a move straddling 2 or more squares . If the grid isn't integrated within the rules then movement feels more natural and less like a board game.

 

[Storminator]

The true beauty of 1-1-1 is that it requires NO explanation. None.

Try this: take a person that's never played any RPG before. Put their mini on the grid. Tell them the can move 6 squares. See if they come up with 1-2-1-2 on their own.

I've recently done this with half a dozen players. Everyone has done 1-1-1. Compare to the many, many games I've seen where long time, experienced gamers have botched the 1-2-1-2 rules...

1-1-1 is just a superior rule.

PS