Ignoring diagonal movement cost?

[Jon_Dahl]

Measuring Distance

Diagonals

When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on.

I was just thinking...
So far in my games I have ignored this rule totally. Diagonal movement and "normal" movement are the same. However since we have lots of smart guys here in Enworld, could someone give me a solid reason why I should implement this rule?

 

[Vegepygmy]

The only reason to use it is that it is more accurate / realistic. If you don't care about those things, don't worry about it.

 

[Shin Okada]

FYI, 4e has totally removed the said rule. But as a result, 4e has changed the area templates, too. Basically, everything (including fireball) are squares. If you ignore diagonal movement rule, I recommend to use square areas, too.

 

[Herzog]

You could also use a hex-map

 

[GunbladeKnight]

Main reason? a^2 + b^2 = c^2 + 2*a*b*cos(C), where C is the angle between sides a and b. Simply put, if you ignore the rule while on a grid, you could actually move FARTHER than what you're supposed to.

 

[AdmundfortGeographer]

You could use it fine as long as you change diagonal reach rules and change circular area spells to squares. Otherwise, it's a fine rule.

 

[Hassassin]

Ignoring the rule makes movement along diagonals 50% faster. I'm sure there's an encounter or two in some published adventures that will be easier or more difficult because of this. Think about a large square room, where you enter from a corner and enemies with bows and cover are at the opposite corner.

 

[Jackinthegreen]

Put simpler than Gunblade, a square's diagonal is ~1.414 times longer than the sides.

If you want to go with Pythagoras then it's a^2 + b^2 = c^2, which is how we get the above number. Each square has a side of 1, squaring that is still 1, adding them together results in 2, and then take the square root of that for v/2, (one of these days I'll find the proper square root character) approximated with 1.414.

The standard 3.x rules are such because the actual distance is greater and the designers felt using the fact would work alright. 4.0 ignores this to streamline things, and makes adjustments appropriate.

 

[kitcik]

Dang it lost my whole post.

I will break it down to a short bit:
For the first square, the rule and no rule are the same - 0% difference.
For two squares, the rule and no rule differ by 33% (you pay 10 instead of 15).
For the third square, the difference is only 25% (15 vs 20).
People rarely move more diagonal in one round.
On average, I would say about 15% difference, not 50%.

On that note, up to you.

 

[GunbladeKnight]

Put simpler than Gunblade, a square's diagonal is ~1.414 times longer than the sides.

Round it up to 1.5, so every 2 squares of movement = 2*1.5 = 3 squares.

If you want to go with Pythagoras then it's a^2 + b^2 = c^2, which is how we get the above number.

Fun fact: Pythagorean formula is a shortened law of cosines. Since Cos(C) of a 90 degree angle = 0, it becomes a^2 +b^2 = c^2 + 2*a*b*0, so you just drop it to a^2 + b^2 = c^2. It's not important to this discussion, but may prove useful to remembering it.