The Railgun is by far the best weapon in the game for long distances purposes.  This weapon is all-or-nothing.  I have talked about all of the weapons in this strategy guide as being very powerful, but this is by far the most devasting simply because it has the ability to drain you of 100 health/armor with a single shot, no matter where you are on the map.
Just so i don't lose your confidence as far as judgement is concerned, let me breifly explain comparable damage from other weapons.
Rocket launcher shoots quicker (less of a cool-down period) but must travel at a slow rate, often giving your opponent plenty of time to see and avoid the oncoming missle.
Lightning gun is hella-powerful, but you need to be within approx. 25 feet of your opponent, and even then you hit your opponent steadily for almost a second to achieve 100 damage points.
The plasma gun is power like the lightning gun, but like the rocket, plasma ammo travels (some would say fast, i don't know..)  And even still you need to hit about 5 or 6 plasma bullets to equal one railgun shot.
The shotgun is powerful like the railgun at close range and can shoot much more rapidly.  Which makes this weapon excellent against rail at close range.  But then again, who is going to choose the rail at close range?
As you can see, you have many choices on how to kill your opponent when they are close/mid-range.  Once they become long range targets, there is only one way to consistantly pick them off - and that's with the railgun.  As you can already tell, the railgun becomes an expert's primary weapon.  If you opponent is not good with the railgun, you can keep your distance and rail him and win every game without him even touching you (practically).  He can't even get close to you!
As with the lightning gun, the secret to aiming with the railgun is based on strafing.  Strafing left and right helps you target your opponent.  Chances are, at long distances, he is doing his best to try and rail you, so chances are you'll both be on a platform moving back and forth.  Simply let go of the mouse (for pointing purposes) and let the strafing you're doing line your opponent up, then press the mouse when he's about to 'cross' your crosshair.
That specific strategy is used 95% of the time for all railshots.  The other 5% are referred to as twitch shots, primarily because the motion your hand has to make moments before the shot is fired (sort of a twitch-like movement).  This type of a railshot is not very standard and, although at time it can be accurate, is not as consistant.  Just like Michael Jordan, quake players should aim with their wrist not their hand or arm.
Together with the rocket launcher, the railgun becomes the most important weapon in quake 3 (as well as the most popular).  It can be used to kill falling opponents before they hit the ground and run away, as it can be used to drain a healthy opponent just before you die.  There is only one mistake people make when using the railgun - forcing a shot.  Many people, when they switch to the railgun, for one reason feel they should shoot the gun at least once (they whipped it out, right? why waste time, right?) before throwing it back into the gunsack, even if the shot is at nothing in particular.  The problem with that isn't the shot itself, it's the heavy cooltime the gun needs in order to fire again, or even switch weapons!  So the result of such a move could very well be getting fired upon without being able to fire back, because you can't switch your weapon, because your railgun is still cooling down.  Don't underestimate the amount of time this gun takes to replenish itself and be ready again.
Overall, the railgun is a weapon that should be mastered by only the best.   If you're a novice, i would suggest that you learn with both the lightning gun and the rocket launcher.  The railgun is a hard weapon to use, and in the heat of the battle it's best to have a weapon that you can miss with, without such heavy, heavy repercussions.
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