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For those that actually get the William James reference, I'm not suggesting that playing VO is religious, just about as fun as surfing down a new wave of powder at 9,000 feet. There are so many different types of PvP situations and combat in VO that I felt impelled to write about a few of them:
1. The Duel
Also known as 1v1, duels can happen any place at any time. When you see another pilot staring you down at 1,000m and you know it's on, that's when a duel happens. Duels can be official or unofficial, and the official ones will get you ranked on the main website using the same rating system as chess tournaments. Unofficial ones can carry just as much clout, however, since the userbase is sufficiently small that you will very quickly build up a word of mouth reputation whether you like it or not. There is an unspoken code of ettiquete that goes along with dueling; hail before you begin, never run from a fight that you started, never interrupt another duel in progress, and certain weapons are off limits. It's like a 17th century gentleman's club, and Sedina b8 is the garden.
2. The Chance Encounter
Sometimes two ships pass in the night and they happen to be mortal enemies belonging to warring clans, or the subject of personal Vendettas, or the predator and prey in that shady buisiness of space piracy. The only warning you get may be the sound of incoming weapons fire. The playing field is wide open, chases can run across systems, around stations, into and away from the Strike Force protesting the clash of violence. Trickery and deception are essential here, as most often fighting by the rules will only get you killed.
3. The Furball
Two groups of players battling for dominance in a massive killfest, the sector doesn't really matter as much as the chaotic ballet taking place and the stories that will be told about it afterwards. Tactics are complex and varied, and having a good leader is essential. Communication between group members can be with text or with voice, but in the best furballs it's not even necessary; you just know where you're supposed to be and count on your teammates. These battles can stretch long into the night until one side has exhausted their supply of credits, focus, or energy.
4. The Station Conquest
Bombers primed with chaos swarms warping in at vectors precalculated to take them on an optimal trajectory toward their target. Streaking in they hit and run, dodging the turrets and the enemy fighters. If you are playing defense then it's a rush to keep your station's defenses healthy and pick off incoming bombers whenever you get the chance. This form of combat is a contest of wills as much as anything else as it can go on for hours and involve morphing alliances of guilds and players. Once the station's defenses drop there are two minutes of frenzied dogfighting outside the station before the first person to dock takes control. Even then it's not over as the station will be in a severely weakened state and will need to be guarded while its defenses recharge. Stations will change hands two, three, even four times before a victor is decided. These battles are important because it's only at the conquerable stations that one can manufacture the components necessary to craft a pilotable capital ship.
5. The Organized Event
Impromptu or planned events often take place, and these will pit pilots against each other in unusual circumstances and rules. Some examples include the weekly nation war where survival tactics are key as the last team standing wins, armed tube races, "bus" wars involving the least lethal weapons and ships, capture the flag... players getting together and having fun, caring less about who wins or loses and enjoying the lighter side of combat.
edit: e.g. here's a video to show what I'm mean:
These are just a few scenarios I wanted to illustrate, I'm sure as you play you will find many more.