You get that from a cloak you start the game with, that you will later swap out for Magicbane. The reason you’re going for the second most important intrinsic is that, as a wizard, you already have the most important one magic resistance. It also lets you physically attack floating eyes and Medusa with impunity to their gaze attacks. That means that when a dangerous wand gets picked up by a monster, as often happens, their lightning bolts or fire blasts won’t hurt you. All directional magical attacks will bounce off you and probably hit their casters. Also, it provides the second most important intrinsic in the game reflection. Unlike most strong armor, it will not make your spells more likely to fizzle, and it is not very heavy. It doesn’t really matter either way it provides excellent armor class, which means you’ll take much less damage from physical attacks. The armor won’t always be +3 it has a 50% chance of being +0 instead. Reading one of these after you’ve depleted your wand’s wishes will replenish it (once per wand) with 3 more wishes. Otherwise, the first thing you should wish for is always: If the wish came from a Wand of Wishing, and you do not have any scrolls of charging, wish for: For more general guidelines, read the wishing spoiler. This section assumes you’re a wizard with a book of identify. I suggest going to this post or to the wishing spoiler above, highlighting the exact text of the item, and pasting it into your terminal. Wishes are rare and valuable enough that you should go out of your way not to typo them. There are other ways to get wishes, but they’re all fairly unlikely. If you survive to storm the castle, there’s always a wand of wishing in one of the four towers, and never any other kind of wand in one of the towers, so when you get a wand there, it’s a wishing wand. The other place you’re likely to get a wish is in the Castle, which is around dungeon level 15-30.

Nethack wish helm of brilliance