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 faster[[note]]specifically, it's √2, or approximately 1.414[[/note]] as 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.

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.

TheOtherWiki calls this [[ Chebyshev distance]].


* The [[ Réti Maneuver]] in TabletopGame/{{Chess}} (published in 1921, but based on a 1914 game) is a candidate for TropeMaker. The black king is able to chase white's pawn on one side of the board while simultaneously approaching his own pawn on the other. The trick is that white's pawn can only move vertically, but black's king can move diagonally.
* ''[[VideoGame/{{Civilization}} Civilization I-IV]]'': The fifth game fixed this by changing squares to hexagons.
* ''TabletopGame/DungeonsAndDragons'': 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).
* ''[[VideoGame/GalacticCivilizations Galactic Civilizations II]]''
* ''SecretOfEvermore'': Running diagonally is visibly faster.
* ''SidMeiersPirates'': 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.
* ''VideoGame/{{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.
** ''VideoGame/{{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 ''VideoGame/GoldenEye1997'' and its SpiritualSuccessor ''VideoGame/PerfectDark'' 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 ''VideoGame/HalfLife''/Source games. Spamming directional keys can get you moving slightly faster than your maximum speed, which is excusable, but you can still [[LadderPhysics 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 VideoGame/Left4Dead series only sports new ladder code for survivors; the zombie team can still climb walls 50% faster with this trick.
*** Speaking of Source, ''VideoGame/TeamFortress2'' takes the aforementioned aerial version UpToEleven, as it lets {{Rocket Jump}}ing 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.''
** ''VideoGame/{{Battlezone|1998}}'', 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 [[GoodBadBugs 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, [[BrokenBase to much rage from the veteran players]].
* Almost all {{Roguelike}}s.
** One of the earliest creatures in ''VideoGame/NetHack'', the [[MeaningfulName grid bug]], cannot take advantage of the diagonal speed boost. The "grid bug conduct" is an unofficial SelfImposedChallenge to voluntarily apply the same limitation to your character, which is much more important and potentially lethal than it sounds.
** The ''VideoGame/PokemonMysteryDungeon'' series.
** In ''VideoGame/DwarfFortress'' diagonal movement on the x-y plane takes 362/[[UsefulNotes/PowersOfTwoMinusOne 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.
** ''VideoGame/DoomTheRoguelike'' 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.
* ''VideoGame/DeadlyTowers'' 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 ''VideoGame/MarbleBlastGold''. 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 ''[[VideoGame/TecmoBowl Tecmo Super Bowl]]'' and its sequels because you don't lose speed when rushing diagonally.
* ''YoujuSenkiAD2048'' 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).
* Oddly present in ''VideoGame/{{Halo}} 3'' and ''VideoGame/HaloReach''. 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 ''VideoGame/NinjaGaiden'' for the SegaGenesis was a belt-scrolling BeatEmUp 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 ''VideoGame/{{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 ''VideoGame/HeroesOfMightAndMagic 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 ''VideoGame/{{X-COM}}'' series, time and energy costs (including terrain penalties) are multiplied by 1.5 and rounded up.
* In both ''VideoGame/PlanetSide'' games, the [[MachineCult Vanu Sovereignty's]] [[HoverTank Magrider tank]] moves significantly faster when strafing and moving forward - to the point where a Magrider can actually keep up with a [[TheEmpire Terran Republic]] [[FragileSpeedster Prowler tank]]. Aircraft in ''[=PS2=]'' likewise can fly much faster when the nose is angled down, and the vertical lift thruster is engaged.