Invis works best at range.  The ideal 1v1 offensive use is poison needles at full screen.  Do this:

  1. Invis
  2. Retreat to range, nearly fullscreen
  3. Open fire
  4. If foe steps towards you or fires at you, then he knows your position.  Move to break his lock.
  5. Once foe is no longer tracking, reestablish range and resume fire
  6. If foe wanders off-screen or out of view, shout to pull him back.

Documentation claims monsters detect player invis better within a 2-tile radius.  I seem to observe that they're still good at 3 tiles.  More range seems to be better.  This might merely be due to the improved odds of random guessing at close range.

Monsters have no actual intelligence.  They lock you, move to a noise, follow their pack, return to bound position, or wander aimlessly.  Thus aimless wandering reveals lock is lost, and shouting pulls them back into view.