Is square grid paper better than hex for fair board game movement?

[SeekerOfTruth007]

It turns out, a D&D player pointed out that charging 1.5 movement points per diagonal square on a square grided surface resolves the diagonal movement problem nicely. I now i agree with him, and a square grid is easier to print and easier to make symmetrical for fair map design.

What do you think of this?

Hex paper doesn't actually solve the diagonal movement problem at all.

[msc545]

You posit extremely interesting problems. Thank you.

For a strategy game like the one you are designing, hexes are usually more mathematically fair, while squares are usually easier and more intuitive.

The real question is:

Which kind of gameplay do you want players to feel?
Because square grids and hex grids produce VERY different battlefield psychology.

The Core Difference
Square Grid
Movement usually means:

4 directions (orthogonal)
OR
8 directions (including diagonals)
This creates:

fronts
corridors
chokepoints
directional warfare
But it also creates geometric weirdness.

Hex Grid
Every hex has:

exactly 6 equal neighbors
This creates:

smoother movement
equal distance in all directions
cleaner radius calculations
more “natural” maneuver warfare
Hexes are more mathematically elegant.

Why Squares Are Less “Fair”
On square grids:

diagonal movement breaks geometry
Example:

Moving:

1 north
1 east
…covers more physical distance than:

1 north only
Yet many games count both equally.

That creates distortion.

The Classic Problem
If diagonals cost the same as orthogonal movement:

A unit moving diagonally effectively travels:
2≈1.414\sqrt{2} \approx 1.4142​≈1.414

…times farther per move.

That means diagonal movement becomes objectively superior.

Players exploit this immediately.

Solutions Square Games Use
1. No Diagonal Movement
Examples:

early tactical RPGs
some war games
Advantages:

very fair
simple
Disadvantages:

movement feels stiff
unrealistic
blocky fronts

2. Diagonals Allowed at Same Cost
Examples:

many casual games
Advantages:

intuitive
fluid
Disadvantages:

mathematically distorted
encourages zig-zag exploitation

3. Alternating Diagonal Cost
Examples:

some tabletop systems
Diagonal costs:

1 then 2 then 1 then 2
This approximates real geometry.

Advantages:

more accurate
Disadvantages:

bookkeeping annoyance

Why Hexes Became Popular in Wargames
Hexes solve almost all of this naturally.

Every adjacent hex is:

equidistant
equally reachable
So:

movement fairness improves
artillery radii improve
line-of-sight improves
encirclement improves
That’s why serious historical war games heavily favored hexes.

BUT Squares Have HUGE Advantages
And this matters.

Squares naturally create:

urban warfare feeling
lane combat
fronts
fortifications
firing lines
This may actually fit YOUR game better.

Your mechanics already emphasize:

intercepts
defender advantage
rolling retreat
siege lines
minimum range
chokepoints
Those systems often feel stronger on square grids.

Hexes Favor Maneuver Warfare
Hexes make:

flanking easier
encirclement easier
front lines less rigid
movement smoother
This tends to create:

mobile warfare
open battlefields
operational maneuver
Very good for:

tanks
cavalry
fluid battles

Squares Favor Tactical Control
Squares make:

defensive lines cleaner
urban terrain clearer
facing more intuitive
formations easier
This tends to create:

stronger fronts
more positional tension
more deliberate pushes
Very good for:

siege warfare
infantry tactics
chokepoint gameplay

Your Current Design Actually Sounds More Square-Friendly
This is important.

Your systems:

attacks of opportunity
intercept movement
rolling retreat
siege tanks
minimum range
static defenses
…all naturally create:

front-line warfare
That often works better on squares.

Why?

Because square geometry naturally creates:

firing lanes
corridors
anchor points
defensive structures

One Very Important Issue:
Range Looks Better on Hexes
Range rings become cleaner on hexes.

Example:

“Range 2” on squares creates diamond/square weirdness
“Range 2” on hexes looks naturally circular
This matters visually and tactically.

Mortars and artillery often feel better on hex maps.

My Recommendation For YOUR Game
Honestly:

I would probably use squares.
But:

restrict diagonals carefully.
Because your game already emphasizes:

tactical positioning
fronts
defender’s advantage
siege interactions
deliberate movement
Squares reinforce those mechanics psychologically.

Best Hybrid Solution
If you use squares:

Use:
orthogonal movement only
OR
diagonals with penalties
AND

Use:
ranged attacks that can fire diagonally
This creates interesting asymmetry.

Another Option:
Offset Squares (“Pseudo-Hex”)
Some games fake hex behavior using staggered rows.

This preserves:

square readability
while reducing:

diagonal distortion
Could be worth experimenting with.

One Final Important Insight
Players usually tolerate:

geometric unfairness
more than:

movement complexity
Meaning:

simple square movement often FEELS better
even if mathematically imperfect.
That matters enormously in tabletop design.

Elegance beats precision surprisingly often.

Short Version
Hexes
Better for:

fairness
maneuver warfare
realistic movement
artillery geometry
Squares
Better for:

tactical fronts
urban combat feel
readability
chokepoints
defender advantage
For YOUR current mechanics?
I honestly think squares may fit the emotional feel of the game better.

[AI Opinion]

I get why you like the 1–2–1–2 diagonal rule on square grids; it approximates real distance pretty well and is easy to teach. 🎲

Hexes don’t “solve” diagonal movement because they remove diagonals entirely: every move is to an adjacent hex at equal cost, so distance is inherently consistent. That’s their strength.

For most board games, squares with 1.5‑cost diagonals are perfectly fair and more practical to draw and print. Hexes shine more in wargames or tactical systems where directional facing and equal adjacency really matter. Both can be fair; it’s more about the style of game you want.