Hex vs Square

[Duringar]

Just curious as to why GURPS uses hex maps as opposed to square. I've not yet found a reason in the rules. I could be glossing over it.
Looking for an "offical" answer/reason.

Thank you in advance.

[Varyon]

Originally Posted by Duringar

Just curious as to why GURPS uses hex maps as opposed to square. I've not yet found a reason in the rules. I could be glossing over it.
Looking for an "offical" answer/reason.

Thank you in advance.

I'd imagine that the true answer is that, way back when Steve Jackson was designing what would eventually become GURPS (looking at Wikipedia, looks like the earliest precursor was Melee, which shortly thereafter evolved into The Fantasy Trip), he weighed the pro's and con's of hexes vs squares, and decided he preferred hexes. You'd need to ask Steve himself why he had this preference.

[whswhs]

The big difference between hexes and squares, geometrically, is that a square is surrounded by eight other squares. Four of them are at its sides; the other four are beyond its corners. If the distance to a side square is 1, the distance to a corner square is ~1.4. Dealing with that takes calculation. Or if you simplify to counting, you can either count "one" for the side square and "two" for going on to the corner square, which is too much, or just count "one" for skipping directly to the corner square, which is too little. Either way, movement is distorted.

With a hex, however, there are six nearest neighbors, and all of them are the same distance. You can handle ranges and movement by counting with significantly less error. I believe that's a major reason that many wargames have used hex grids, since long before the earliest edition of D&D.

[Varyon]

Originally Posted by whswhs

The big difference between hexes and squares, geometrically, is that a square is surrounded by eight other squares. Four of them are at its sides; the other four are beyond its corners. If the distance to a side square is 1, the distance to a corner square is ~1.4. Dealing with that takes calculation. Or if you simplify to counting, you can either count "one" for the side square and "two" for going on to the corner square, which is too much, or just count "one" for skipping directly to the corner square, which is too little. Either way, movement is distorted.

The solution DnD opted for, which works decently well (although I still prefer hexes), is to treat the first diagonal movement in a turn as 1 square, the second as 2 squares, the third as 1 square, and so forth, alternating - in other words, it rounded 2^0.5 to 1.5 and further rounded total movement in a turn down. So, for a character with a movement rate of 30 feet - 6 squares - you could move 6 times forward, backward, or sideways, or up to 4 times diagonally, in either case moving 30 feet (well, technically that last option would be around 28.28 feet, but that's close enough - around 6% under par - given the resolution involved). You could also mix and match, which you could use to go a little further than 30 feet if you only moved diagonally once, but this wouldn't be an egregious boost to movement rate - you're looking at moving roughly 32.5 feet, or around +8% to movement rate (technically, closer to 32.07 feet, or around +7% to movement rate).

At least it's not like Goldeneye 007 for Nintendo 64, where strafing and running forward at the same time let you indeed move diagonally at x2^0.5 velocity compared to doing either alone.

[Michael Thayne]

While hexes have a certain mathematical elegance, I do wonder if they're a bit overrated. Hexes are probably better for "two combatants circling each other", but they won't align neatly with the walls of artificial structures (or even city streets), and can be awkward for large fights that feature (or at least start out with) two lines of combatants that can't really "circle". For GURPS though I do wonder about the effect on facing. You might need to redo traits like Peripheral Vision and Tunnel Vision, for example. The other option is to dispense with a grid and just use a ruler to figure range—to use GURPS's facing rules as written you'd want to use figures with circular bases that can be marked at 60° intervals.

[Varyon]

Originally Posted by Michael Thayne

While hexes have a certain mathematical elegance, I do wonder if they're a bit overrated. Hexes are probably better for "two combatants circling each other", but they won't align neatly with the walls of artificial structures (or even city streets), and can be awkward for large fights that feature (or at least start out with) two lines of combatants that can't really "circle". For GURPS though I do wonder about the effect on facing. You might need to redo traits like Peripheral Vision and Tunnel Vision, for example. The other option is to dispense with a grid and just use a ruler to figure range—to use GURPS's facing rules as written you'd want to use figures with circular bases that can be marked at 60° intervals.

One thing I've considered - mostly as a joke, but it could certainly be workable - is to have the buildings, rooms, roads, etc in a setting designed for GURPS actually follow the hex grid. Hex-shaped rooms, roads that meet at 60-degree angles, etc. If you design everything with the hex-grid in mind (like when designing maps in at least the original StarCraft, IIRC), everything will line up without issues.

[Curmudgeon]

Originally Posted by Michael Thayne

<snip>
For GURPS though I do wonder about the effect on facing. You might need to redo traits like Peripheral Vision and Tunnel Vision, for example. The other option is to dispense with a grid and just use a ruler to figure range—to use GURPS's facing rules as written you'd want to use figures with circular bases that can be marked at 60° intervals.

But GURPS facing rules use 60° intervals because that is the interval between hex sides. Most games that use facing and don't use hexes use 90° intervals, either parallel to a square grid, i.e. left front, right front, right rear, left rear, or rotated 45° to give front, right side, rear, left side. In truly freeform movement, you could make facing exact, i.e. if you want to turn 82°, you turn exactly 82°, though you may need a protractor to regulate facing.

They're unlikely to be "over-rated." If you want a grid that doesn't leave inaccessible gaps between points, there are only a few options: triangles, squares (and rectangles), and hexes. The benefits of a particular choice are independent of the game they're used for.

Most designers have come to the conclusion that for wargames and wargame-like boardgames, hexes tend to be the optimal choice. As mentioned in my earlier post, most designers go not only with a hex grid, but specifically with a SPI hex grid.

[ericthered]

Originally Posted by Michael Thayne

While hexes have a certain mathematical elegance, I do wonder if they're a bit overrated. Hexes are probably better for "two combatants circling each other", but they won't align neatly with the walls of artificial structures (or even city streets), and can be awkward for large fights that feature (or at least start out with) two lines of combatants that can't really "circle". For GURPS though I do wonder about the effect on facing. You might need to redo traits like Peripheral Vision and Tunnel Vision, for example. The other option is to dispense with a grid and just use a ruler to figure range—to use GURPS's facing rules as written you'd want to use figures with circular bases that can be marked at 60° intervals.

This is my default mode, I always forget most people play with hexes. Another "gotcha" is that radius 2 areas are a bit more efficient when not playing with hexes.

Originally Posted by Curmudgeon

They're unlikely to be "over-rated." If you want a grid that doesn't leave inaccessible gaps between points, there are only a few options: triangles, squares (and rectangles), and hexes. The benefits of a particular choice are independent of the game they're used for.

Technically you can do a pentagon grid, though that has enough oddities that no one seriously considers it.



I suspect that "hexes are overrated" comment really means "grids that don't line up with neatly with floorplans are overrated.

[Polydamas]

Originally Posted by Michael Thayne

Hexes are probably better for "two combatants circling each other", but they won't align neatly with the walls of artificial structures (or even city streets)

If you look at the plans of homes, workplaces, and forts before the 19th century, the angles are almost never right. Anything between 70 degrees and 110 degrees was usually 'good enough'. Street plans are even more irregular (and forced later buildings to fit onto not-rectangular plots defined by the first not-rectangular building built on them).

[Stormcrow]

Originally Posted by Michael Thayne

they won't align neatly with the walls of artificial structures (or even city streets),

They're not supposed to. GURPS hexes don't get laid down first and then walls built next. They're meant to be an overlay over whatever is there, and then partial hexes are treated as full hexes. Hexes are supposed to abstract battlefields into playable areas, not measure buildings.