[aidenn0]

FWIW, I strongly prefer square grids for tabletop games.

Hexagonal grids give you precise measurements in exactly 6 directions.

If you approximate sqrt(2) as 1.5 then square grids give you pretty darn accurate measurements in 8 directions, including 2 pairs of directions that are orthogonal, which is good for rectangular features like buildings.

Furthermore the distance between two points can be quickly calculated with (long-side + 1/2 short-side), which is doable in your head, unlike the distance calculation on a hex grid.

Lastly, if you divide the circle into a large number of slices and calculate the average error for path distance using hex or squares, among those slices, the average error (compared to pythogorean) is smaller with squares (obviously for small multiples of 6 and small multiples of 8 respectively, one or the other will be preferred).

[SAI_Peregrinus]

I like octagonal grids. Sure, you have to have your game in hyperbolic space, but you can have accurate movement in 8 directions. Your players will just have to deal with parallel lines diverging, there being unique things like pseudocycles, horocycles, circles with a circumference that grows exponentially with increasing radius, etc. Sadly such geometry isn't supported by any tabletop software I'm familiar with, and crocheting a game board of sufficient size takes a very long time.

[dri_ft]

I haven't been able to play hyperbolic tabletop games since I lost my hyperbolic table in my last move. YMMV.

[jere]

A HyperRogue fan? If not definitely check it out. I don't see why that kind of program couldn't be adapted for digital tabletop games.

[pdkl95]

Hyperbolica devlog: https://www.youtube.com/playlist?list=PLh9DXIT3m6N4qJK9GKQB3...

[SAI_Peregrinus]

I'm definitely a HyperRogue fan.

The biggest issue with adapting it to multiplayer (tabletop) games would be splitting the party. If the party splits, finding a path back together (without just backtracking) can become effectively impossible. Visualizing the spatial relationship between widely spaced points in hyperbolic space is also really hard.

[dragonwriter]

> Hexagonal grids give you precise measurements in exactly 6 directions.

Square grids give you precise measurements in exactly 4.

> If you approximate sqrt(2) as 1.5 then square grids give you pretty darn accurate measurements in 8 directions, including 2 pairs of directions that are orthogonal

If you approximate sqrt(3) as 1.75, then hex grids give you pretty darn accurate measurements in 12 directions, including 3 pairs of directions that are orthogonal.

(If square grids have an advantage here, it's that the quantum of measurement the same on each axis of each orthogonal pair, 1 on one axis and 1.5 on the other; whereas each orthogonal pair on a hex grids has one axis with quantum 1 and one with quantum 1.75.)

> Furthermore the distance between two points can be quickly calculated with (long-side + 1/2 short-side), which is doable in your head, unlike the distance calculation on a hex grid.

The equivalent loose approximation on a hex grid would seem to be long direction minus 1/4 short direction, which doesn't seem any harder.

[aidenn0]

> The equivalent loose approximation on a hex grid would seem to be long direction minus 1/4 short direction, which doesn't seem any harder.

As promised in a sibling comment I would work it out on paper. By my path, using the 7/4 approximation for sqrt(3), the ratio between X and Y directions is 12:21 which is much harder to do in your head than the 3:2 that a square grid gives you. However, a simpler approximation of (5:3) with acceptably low error came out.

Math (see diagram below)

Normalizing your 1.75 approximation to 7 "units" then the sides of the hexagon are of length 7, the distance from center to corner is length 7, and the distance from center to side is 6. This gives a distance from A to other points as:

B: 12 (Center -> Side -> Center)

C: 12 (Center -> Side -> Center)

D: 21 (Center -> Corner -> Corner -> Center)

Given that the actual value of A->D is ~20.784 that suggests approximating A->D = 20 alowing us to reduce as follows:

B: 3

C: 3

D: 5

This has a ~3.7% error in the horizontal direction.

       ______            ______      
      /      \          /      \     
    /    B     \______/          \___
    \          /      \          /   
      \      /          \      /     
        ----      C       ----       
      /      \          /      \     
    /    A     \______/    D     \___
    \          /      \          /   
      \      /          \      /     
        ----              ----       
      /      \          /      \     
    /          \______/          \___
    \          /      \          /   
      \      /          \      /     
        ----              ----

[dragonwriter]

> As promised in a sibling comment I would work it out on paper. By my path, using the 7/4 approximation for sqrt(3), the ratio between X and Y directions is 12:21

Well, yes, 4:7 is 12:21.

But I think 4:7 is a lot easier to do in your head than 12:21 (3:5 is a little easier, at the expense of being less accurate); not sure why you did all that work to make it more complicated when you started with a fraction that gave you the ratio in its simplest form.

[aidenn0]

I haven't seen the 1.75 approximation; I'll have to work that out on paper later.

[rendall]

No need. I got you fams

sqrt(3) = 1.73205080757

https://duckduckgo.com/?q=sqrt+3&ia=calculator

[aidenn0]

I wasn't planning on working out sqrt(3) on paper, but rather the claimed approximation from GP's post. See my sibling comment for details when I did.

[rendall]

I prefer Penrose tiling for all tabletop games. Sure, the number of directions for each tile vary, but distances are incalculable

[arrow7000]

I like

[jghn]

I always found the hex grid useful in Battletech as your facing has an impact on where you get hit and having 6 sides provides more potential combinations of facing.

[aidenn0]

I find 8 facing directions (4 sides, 4 corners) to be sufficient, but I suppose a hexagon gives you 12 (6 sides, 6 corners).

[grawprog]

>FWIW, I strongly prefer square grids for tabletop games.

I agree mostly, though i prefer hex grids for war games and square grids for rpgs/roguelikes.

Hex grids allow for more units in a given encounter, plus, i'm likely biased as the first tabletop war game i ever played was battle masters which used a huge hex grid map and a card draw system for movement with some 'cool skull dice' for battles and big plastic figures on bases with flags for units. There was like 6-7 unique unit types for each side, including a special unique unit for each army with special abilities. You got to build an awesome plastic tower units could occupy, it was basically orcs vs humans like the first warcraft. My 8-9 year old self was pretty stoked.

Also, for some reason i remember there was an elven shortsword item card that had this description

'Light as a moonbeam, sharp as a tiger's claw'

That's really stuck in my head as the definitive description of elvish/elfish(for you pedantic Tolkien fans) weapons.

Just seems fitting.

[rrobukef]

On the other hand, for movement along the 8 directions the distance is 41% short, for movement along the 4 main directions, the taxicab distance is 41% longer than the actual distance.

For a hexagonal grid, the distance is approximated by counting the number of cells of the shortest path. This has <10% relative error (IIRC) from the actual distance.

[alisonkisk]

If you take diagonals to be 1.5, then distances are <10% high.

The half-short-side heuristic (sqrt(aa + bb) ~= a + b/2) makes taxicab very close to correct for non-square distance as well.

[rrobukef]

But only if you move multiple cells in one turn. If movement is restricted to one cell each turn, your field distorts.

The same happens when you split your movements: For example: player A moves 6 each turn; player B moves 2 thrice in a turn. Conclusion: A outruns player B at speed (4,4)/turn vs (3,3)/turn. (For A d(4,4)=6; B has d(1,1)=1.5)

[aidenn0]

Yes, hex grids are better when the number of cells moved per turn is very small.

Handling multiple moves in a single turn is easy either by doubling the movement points you get (then N/S/E/W is 2 points, diagonal is 3), or informally by treating every other diagonal move as costing 2 points.

[aidenn0]

Diagonal moves equal to horizontal/vertical moves is horrible. I don't remember which D&D suggested that, but "circles" being square is just terrible.