Kill them all!
Henzell says...
  1. If you are invisible, monsters won't shoot ranged attacks at you unless they can see you, or can guess where you are. Monsters get a random fuzz to their aiming point, which might be inaccurate in the first place.
  2. Monsters can guess your position when you are invisible if they knew your position before and you are still within two spaces, if you are in water, or if they are adjacent to you and make a roll based on their intelligence (usually 1 chance in 3). The chance is higher if they are smarter.
  3. Beams shot at you by monsters who can't see you (even if they can sense you) have their accuracy cut in half. Monsters trying to melee you without see invisible and who have correctly guessed your location have their accuracy reduced by 35%.
  4. If you are invisible, and don't have see invisible, you receive -5 to hit (same as amulet of inaccuracy). If you are attacking a monster you cannot see, you receive -6 to hit. (These stack, of course). Your accuracy is no longer reduced when invisible with no SInv in 0.18+.
  5. Fleeing monsters always know which way is away from you whether they can sense you or not.

Information based on master branch and the great LearnDB.
© Dungeon Crawl Stone Soup, 2010.