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# Diagonal Speed Boost

You're headed north, he's headed northeast, he suddenly turns northwest halfway to the destination, the race ends in a tie. You both traveled at identical speeds the whole way. Or at least you would have, were it not for the diagonal speed boost.

Common in square grid based games, the diagonal speed boost is when it takes the same amount of time or turns to move to a diagonal square as it does to a horizontal or vertical square. This means that diagonal movement is about 40 percent fasternote  than movement in a straight line. This allows whatever's moving on the grid to cover more ground in the same amount of time.

Not just a problem with grids; most older first-person games implement diagonal movement in a similar way: moving forward in any direction gives normal speed, while a combined sideways movement adds to the speed. It's arguably even worse, as you can change which direction you're facing to get a diagonal speed boost in any direction.

Savvy players can use this to outmaneuver and flank opponents unless there's a rule against it. The unreality of this trope is why some games use hexagonal grids, where the distance from the center of one hex to that of an adjacent hex is always the same regardless of the direction of travel.

The Other Wiki calls this Chebyshev distance.

## Examples:

• The Réti endgame study in Chess (published in 1921, but based on a 1914 game) is a candidate for Trope Maker. The white king is able to chase black's pawn on one side of the board while simultaneously approaching his own pawn on the other. The trick is that black's pawn can only move vertically, but white's king can move diagonally.
• Civilization I-IV: The fifth game fixed this by changing squares to hexagons.
• Dungeons & Dragons:
• This how it works in 4th edition. Earlier editions increased the movement cost for every other diagonal tile to 2, i.e. a diagonal move counts as 1.5 squares (making diagonal movement about +6% slower rather than +41% faster).
• 5th edition also has this, and the rules section about grid movement actually mentions that it may seem strange but you should ignore it as the grid is an approximation anyway.
• Secret of Evermore: Running diagonally is visibly faster.
• Sid Meier's Pirates!: Land battles allow diagonal movement in this manner. When combined with the flanking bonus a unit gets for attacking from the side it can allow for victory against overwhelming odds.
• Doom: Strafing and running forward at the same time is 30% faster than just moving forward or strafing - this is SR40, named so because internally your sideways acceleration will be 40 (in arbitrary units, unrelated to length units), as compared with forward/backward acceleration of 50. It is also possible for a further speed boost known as SR50, where you turn and strafe in the same direction, with "strafe on look" on. Combined with moving forward, this gives the full ~41% speed boost (but prevents you from turning), and is used in many speedruns.
• Descent took this into the third dimension. To travel fastest, combine a diagonal slide (eg, up+right) with forward thrust. This gives a 73% speed boost, not counting the afterburner added in Descent 2. Possibly justified as using several of your ship's thrusters simultaneously.
• Speed runs of GoldenEye (1997), its Spiritual Successor Perfect Dark and The World Is Not Enough pretty much require you to strafe-run everywhere.
• Quake stopped Doom-style straferunning by capping a player's running velocity (by default, to 320 units/second). However, the fix applies gradually, and only applies on the ground, meaning strafing and jumping at the same time preserves the momentum gained from strafing. You can also strafe and turn while in mid-air, speeding you up even further. Some Quake ports have a feature that will have you jump the first moment you hit the ground when you press and hold the jump key. Combining all of these, it's not surprising to see people hurtling around maps, going more than double the normal max speed, and jumping around like... rabbits. It's pretty obvious where the term "bunnyhopping" came from.
• Similar anomalies show through in the Half-Life/Source games. Spamming directional keys can get you moving slightly faster than your maximum speed, which is excusable, but you can still strafe and walk up ladders simultaneously. Custom maps have even used this as a puzzle element since you can jump from the top of a ladder with more upward velocity than your legs can provide. Even the recent Left 4 Dead series only sports new ladder code for survivors; the zombie team can still climb walls 50% faster with this trick.
• Speaking of Source, Team Fortress 2 takes the aforementioned aerial version Up to Eleven, as it lets Rocket Jumping and Sticky Jumping "airstrafe" to greatly increase distance traveled and do insane things like mid-air corkscrews that send you back faster than you started in the opposite direction.
• Battlezone, on the other hand, retains this. In fact, going forward, strafing, pitching your hovertank forward (auto-stabilizing needs to be turned off or the tank will try to level out by itself) and using the jump thrusters all at once gives much faster movement - to say nothing of a physics glitch that allows hovertanks to float high enough to be out of range for most weapons. Naturally, all versions of Battlezone 2's unofficial 1.3 patch nerfed the ability to fly, to much rage from the veteran players.
• Almost all Roguelikes.
• One of the earliest creatures in NetHack, the grid bug, cannot take advantage of the diagonal speed boost. The "grid bug conduct" is an unofficial Self-Imposed Challenge to voluntarily apply the same limitation to your character, which is much more important and potentially lethal than it sounds.
• The Pokémon Mystery Dungeon series.
• In Dwarf Fortress diagonal movement on the x-y plane takes 362/256 times as long as orthogonal movement, which is as close as the game engine can get to the square root of 2. Z movement, however, will just add the extra axis movement space.
• Doom, the Roguelike uses the so-called Angband metric; the distance between two points is the length of the long axis plus half the length of the short axis, rounded down. That's still a speed boost within the Moore neighbourhood used for movement (1 + 0.5 rounds down to 1), but it has consequences when determining range for weapons.
• One Way Heroics allows you to have a key, that, when held down, restricts your movement to the four diagonal directions, for those playing on a pad or with the arrow keys. Of course, you can use a numpad instead. Given that the premise revolves around outrunning an Advancing Wall of Doom, diagonal movements are extremely important and can make the difference between "phew, barely escaped the autoscroll, onward for another few hundred kilometers!" and "gods dammit, Yet Another Stupid Death!"
• Deadly Towers plays this straight in the first place, but there is also an item (called the Hyper Shoes) that increases your move speed...but only if you're moving diagonally.
• Occurs in Marble Blast Gold. Hold down two direction keys at once and the marble will travel faster than normal. This is sometimes needed to beat the gold times.
• "Zig-zagging" is the best way to run in the open field in Tecmo Super Bowl and its sequels because you don't lose speed when rushing diagonally.
• Youju Senki AD 2048 has an odd variation: moving one space diagonally is considered the same as moving one space vertically or horizontally (counted as one space when moving or shooting), but the characters cannot move like this if the spaces next to them are occupied by enemies or obstructions (to put it simply, if you can't move there without diagonal movement, you can't move there period). However, this limitation does not affect attacks (meaning that even if a character can't move diagonally into a space, they can still shoot that space if they're in range).
• Halo: Oddly present in Halo 3 and Halo: Reach. Picking up a turret normally causes you to move slower, but moving diagonally negates that speed decrease entirely.
• Gunrox, an online turn-based, grid-based, squad-based tactics game, has this. Making use of it is an easy way to gain the advantage over an inexperienced player.
• The prototype Ninja Gaiden for the Sega Genesis was a belt-scrolling Beat 'em Up where Ryu could only move diagonally unless hemmed in by the top or bottom. This was likely a bug which would have been corrected had it received a final release.
• In Minecraft, minecarts travel diagonally over curved rails. If you place rails on two adjacent diagonals, you get a zig-zagged track, which you can travel over as if it were a straight diagonal. This results in a speed boost.
• In the Heroes of Might and Magic IV-VI combat screen, diagonal movement takes 1.5 times the amount of movement points for horizontal and vertical movement. (The first three games used a hexagonal combat grid.) But there's no extra cost for moving diagonally on the overland map, like in most TBS games.
• Similarly, in tactical combat of XCOM series, time and energy costs (including terrain penalties) are multiplied by 1.5 and rounded up.
• In both PlanetSide games, the Vanu Sovereignty's Magrider tank moves significantly faster when strafing and moving forward - to the point where a Magrider can actually keep up with a Terran Republic Prowler tank. Aircraft in PS2 likewise can fly much faster when the nose is angled down, and the vertical lift thruster is engaged.
• In the X-Universe series, the player use the (player-exclusive) strafing thrusters to give them a small speed boost while using the main engines. Strafing speed is generally much slower than most Space Fighters, but on the slow-as-molasses Space Trucker transports, it can make a world of difference. However, in practice it is rarely used outside of combat since for travel it is far faster to just turn on the autopilot and engage the Singularity Engine Time Accelerator to speed up the game. In X Rebirth, the Albion Skunk has very powerful strafe thrusters which are handy for maneuvering without using the shield-sapping Nitro Boost.
• Undertale applies this not just to moving around areas, but also the Bullet Hell attack-dodging interface. This can take a little getting used to if you frequently play scrolling shooters, most of which avert this trope.
• A feature of Blood Bowl, which is played on a pitch divided up into squares, where moving diagonally costs no more points of movement that moving straight forwards. Because movement in open squares is one of the few actions that doesn't risk ending your turn, understanding how to move your players efficiently is a key skill.

http://tvtropes.org/pmwiki/pmwiki.php/Main/DiagonalSpeedBoost