The single most helpful thing that can happen to a nethack character is getting to make a wish. In nethack, a wish means you get to type in the name of an item, and that item will be added to your inventory. If you know what to wish for, a single wish will approximately halve your chances of not winning.
How to get a wish
The main way you’ll get your first wish it by finding a magic lamp. Your first job is to find a lamp. Lamps aren’t all that uncommon, and about 20% of them are magic. Your second job is to find out whether your lamp is magic. Do this by casting identify, or, alternatively, try dropping it in a store (or, if it’s already in a store, try picking it up). If the price is more than 30 gold, it’s magic. Buy it if you have to. Now your job is to bless your magic lamp.
You do that by finding out whether it’s blessed or cursed already. If it’s cursed, you have to remove the curse; you can do that mainly by dipping it in holy water or wielding it while reading a noncursed scroll of remove curse. If it’s uncursed, you need to dip it in holy water to bless it. You get holy water by dropping uncursed water in a chaotic altar and praying there.
Once you have a blessed magic lamp, #rub it over and over. Eventually a djinn will come out, and will give you a wish 80% of the time.
You can also get wishes by finding a throne – a “\” – and #sitting on it over and over until it vanishes. Make sure to drop all your gold first; the only negative effect of sitting on thrones to speak of is to remove all your gold. One of the random positive effects is to grant you a wish.
The other place you’re likely to get a wish is in the Castle, which is around dungeon level 15-30. It’s tough to miss. 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.
There are other ways to get wishes, but they’re all fairly unlikely. If you’re interested, read this.
How to wish
Wishes are rare and valuable enough that you should go out of your way not to typo them. 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. BE CAREFUL. Think before every keystroke. Do not accidentally touch the keyboard.
What to wish for
If the wish came from a Wand of Wishing, and you do not have any scrolls of charging, wish for:
2 blessed scrolls of charging
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:
blessed +3 silver dragon scale mail
The armor won’t always be +3; it has a 50% chance of being +0 instead. It doesn’t really matter; either way it provides excellent armor class, which means you’ll take much less damage from physical attacks. Unlike most strong armor, it will not make your spells more likely to fizzle, and it is not very heavy. Also, it provides the second most important intrinsic in the game; reflection. All directional magical attacks will bounce off you and probably hit their casters. 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. It also lets you physically attack floating eyes and Medusa with impunity to their gaze attacks. 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. You get that from a cloak you start the game with, that you will later swap out for Magicbane.
What you spend your second wish on depends on whether you have two or more unique artifacts. When you do, your wishes for more unique artifacts can fail; you do not want to take that risk. You almost certainly have Magicbane by the time you get your second wish, so it comes down to whether you’ve found a second random artifact lying around or finished the quest.
It’s quite likely that your second wish comes from the wand of wishing in the castle, which will be after you’ve completed the wizard Quest, which gives you an artifact. Do not delay completing the quest so that you can wish for an artifact. The Quest artifact is worth getting early, and artifact wishes are not _that_ much more important than normal ones.
If you have only one or zero artifacts in your inventory when it’s time for your second wish, wish for:
blessed Master Key of Thievery
(Don’t wish for it if you’re low on health; it will do 2-20 damage to you when you first touch it and every time you pick it up.) Just having it in your inventory gives you the ability to choose your destination whenever you teleport, making it a very attractive proposition to eat leprechaun, nymph, or tengu corpses, all of which will make you automatically teleport every once in a while. It reduces all physical damage you take by half. Last, every time you #apply it to unlock a door or chest (which always succeeds), it will tell you a “rumor” about the game. As long as the key remains blessed, the rumor will always be true.
Any remaining wishes you’re lucky enough to make, in order:
blessed fireproof +2 pair of speed boots– unless you already have speed boots. They let you take 1.6 more turns than normal. Technically, they slow the rest of the game down.
blessed amulet of life saving– unless you already have one. If you die while wearing one of these, it uses up the amulet, restores you to full health, and cancels all status ailments (which otherwise might just kill you again immediately)
blessed bag of holding– unless you have a bag of holding already (which is quite likely). These quadruple the amount of stuff you can carry around with you, which is likely to be a concern by the time you get this many wishes, if you do.
uncursed magic marker– If you have no scrolls of charging, the first thing you do is write one of those. When the marker is used up, you can recharge it with that. Then you use this to write scrolls of enchant armor. You use them to get all your armor up to +4 or +5 (going beyond that can destroy the armor). Only write on blessed scrolls of blank paper; you can make scrolls blank by dipping them in fountains, then dropping them, then picking them back up. You can make them blessed by dipping them en masse into holy water. You get holy water by dropping potions of water on chaotic altars and then #pray ing there. You get water by dipping useless potions in fountains.
blessed rustproof +3 gauntlets of power– unless you already have some, you have gauntlets of dexterity, or you have a +2 or +3 ring of increase damage. These will hinder your spell casting, but increase your strength to 25, making you do more damage and letting you carry more. If you need to cast the more difficult spells, you can always take off your gloves.
blessed greased rustproof +3 helm of brilliance– unless you already have one, or you have an elven leather helm or cornuthaum. These are the helmets that wizards want to wear; all others hinder spell casting.
blessed fireproof +3 T-shirt– unless you already have a shirt. You can wear shirts under other armor, and enchant them up. They’re worth wishing for because they don’t occur randomly very often.
blessed ring of levitation– unless you have one already, or have a pair of levitation boots (which you probably will. You’ll need this to get across some areas of the game that are flooded or covered in lava.
uncursed magic marker– yes, a second one, and even a third one, if it takes that many to get all your armor up to at least +4.
blessed ring of slow digestion– unless you already have one
blessed ring of polymorph control– if you don’t already have one, and you do have a spell or wand of polymorph, and you have a lot of useful but expendable rings and amulets. Take off your armor, polymorph yourself into a Xorn, and eat all your rings of increase damage, increase accuracy, invisibility, polymorph control, protection, searching, see invisibile, stealth, and teleport control. Also eat any amulets of magical breathing. Each of these has a 1/3 of permenantly granting you the benefit of the ring / amulet without you having to wear it. Your xorn-ness will wear off after a little while, and you can put your armor back on. You might notice that Xorns can only eat some of the rings listed above – it’s the ones that were described as some kind of metal before you identified them. You can also polymorph into a Gelatinous Cube as well to eat more rings – the organic ones – if you want/need to.
blessed amulet of life saving -Any remaining wishes you get should be spent on these. You can never have too many.