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From Wikipedia, "orthogonality" is a term that "in mathematics, describes the relation of two lines at right angles to one another".
Or in the realm of computer programming, it refers to "a relatively small set of primitive constructs that can be combined in a relatively small number of ways to build the control and data structures of the language".
I'd like to introduce the concept of "Roguelike Item Orthogonality", since I see it as vital to taking roguelike game design beyond grinding, hack-n-slash dungeon crawlers into a world of chess-like strategic gameplay. With this phrase, I'd like to refer to a school of game design in which a small pool of items have multiple interactions with the beings in the game rather than just one single purpose. More importantly, those multiple interactions should be logical progressions from one another. OK, enough of the lofty ludological airs...
Here's an example from one of the greatest roguelike games ever created, Mystery Dungeon: Shiren the Wanderer...
One of the myriad amazing examples of tightly-coupled monster and item designs in Shiren the Wanderer is the Rice Changer monster and riceballs (Mmmmm Onigiri! :)
Quoting from the now-lost Shiren wetpaint wiki, "The Rice Changer casts a spell that changes a random item in your inventory into a Big Riceball. It is weak to thrown Rice Ball attacks." This means it has a special attack of changing one of your inventory items into a riceball, which is usually annoying but sometimes welcomed when you're starving.
But there's more, and here is where item orthogonality fits in -- Rice Changers can often be insta-killed with a thrown riceball, which is a clever way to gain levels in the infamous Fey's Final Puzzle dungeon. Yin, meet Yang.
In my own roguelike game, Voyage to Farland, I've tried to add more depth to the gameplay to distinguish it from a dungeon crawler & other games that rely on grinding. One example is the Vial item. From the in-game description, it's "a cursed vial that when thrown, can capture a monster's soul!"
But you should always remember that in Voyage to Farland, your hero character is just another monster, albeit a cute one whose movements you can control. So normally, you'd throw a Vial at a monster to "capture its soul" or essence. Later, if you drink the essence, you’ll turn into the monster until you move to the next dungeon floor or explicitly revert to human form.
There could be several reasons you might want to change into one of the game's monsters -- some monsters have pretty powerful ranged attacks that can be useful, e.g. the Nosferatu’s "Evil Eye" attack, the ViperBeetle's "Spin & Toss" attack or the SparkDroid’s "Lightning" attack. When you become a monster, you can also take advantage of its inate abilities -- a Ghost can pass through walls freely, and the GrayLady can move at double speed compared to other monsters.
This aspect of the game is borrowed from Shiren the Wanderer’s "monster meat" gameplay mechanic and it's interesting enough to merit a dedicated dungeon for learning how to use the item wisely. The specialty dungeon is called The Vial Trial and you can get to it by clearing certain events on the Thatched Hamlet floor.
But the ability to turn into a monster isn't enough in designing a complex roguelike game. For me, item orthogonality is very important -- all "good" items should have some potential disadvantages, and all "bad" items should have some beneficial uses occasionally. It keeps the game interesting and adds yet another layer of replayability to the already compelling gameplay that procedural environment generation brings to a video game.
A Vial is great for throwing, morphing into a monster and then throwing down. Yet there are monsters in the game who delight in picking up stray items and tossing them at the hero. The Catapult family (felines on mobile mini-catapults!?) does just that. If it's standing on a sword, it'll lob it at the hero doing damage. If it's standing on a medicinal herb, it will toss the herb at you, which you'll feel compelled to ingest, maybe saving you from death in a tricky situation.
And here's where the subtle twist in item design comes into play -- if the Catapult runs across a vial, it will toss the Vial at the hero. Perhaps the Vial contains the essence of a Wraith (level 3 Ghost). If so, you'll morph into a Wraith and you can pass into a nearby wall and attack any monsters that come near you. Their attacks can't affect you, but yours will do high damage to them! Cool, huh?
But if the Vial was empty when tossed, that's another story... Your essence will be trapped for a few turns and any nearby monsters can approach and pound on you. Just pray that your level was high enough to withstand the onslaught, or it may be YASD (Yet Another Stupid Death) and back to the starting village.
One of the Dwarf Fortress taglines is "Losing is fun!" and most roguelike gurus appreciate that fact. It's part of the draw of these games. They're not for the faint of heart, but for those of us willing to learn from our mistakes and grow from them, roguelike games are extremely rewarding.
So in summary, "Use the Vial, Luke. Use the Vial." Just don't leave one lying around near a Catapult when you're playing Voyage to Farland.