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 faster^[1] 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.

The Other Wiki calls this Chebyshev distance.

Examples of Diagonal Speed Boost include:

• Chess: Averted for the bishop since it can't turn while moving so it takes two turns to get to a position that the rook could reach in one (although it can be vice versa in other situations). Played straight for the king.
  • This fact becomes important in several chess problems.
  • This fact is critical for the proper use of the king in pretty much all endgames. Which makes it critical for playing the game well, period.
• Civilization I-IV: The fifth game fixed this by changing squares to hexagons.
• Dungeons & Dragons: Played straight in 4th edition. Mostly averted in earlier editions by increasing 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).
• Galactic Civilizations II
• 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 you move at ~40 units/tic. It is also possible for a further speed boost known as SR50 (~50 u/t), where you look and strafe in the same direction, with "strafe on look" on. Combined with moving forward, this gives the full ~41% speed boost, 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 Golden Eye 1997 and its Spiritual Successor Perfect Dark 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 do 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 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 an engine 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 take flying out, 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.
• 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.
• The online RPG program MapTool is variable; the GM can choose the movement metric, which lets one play the trope straight, avert it, or outright invert it (the "No Diagonals" metric, which forces movement along straight axes). It also lets you use hexes instead, just avoiding the whole issue altogether.
• The first Diablo averted this trope, and managed to replace it with invulnerability to most damage when moving horizontally. Most commonly used to dodge missiles like arrows and fireballs, it could also be used to walk safely through a firewall or lightning (chain or otherwise) spell. On the Diablo Strategy Forum, we called it "Happy Feet."
• 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).
• Oddly present in Halo 3 and Reach. Picking up a turret causes you to move slower, but moving diagonally is slightly faster than walking straight ahead.
• Some Racing Games have an unintentional technique called "snaking" in which zig-zagging left and right across a straightaway causes the vehicle to move faster than if it just went in a straight line. This is due to to how these games give out boosts for drifting in certain ways. The Mario Kart series and F-Zero GX are examples of games with snaking.
• An odd variation in Sonic Labyrinth is that Sonic walks slighty faster if he moves to the left or to the right.
• 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.

1. ↑ specifically, it's √2, or approximately 1.414