This is not an article about how to beat Rogue. One does not beat Rogue. At most, once in a very long while, one merely survives.
The player never comes to dominate the game, like a NetHack extinctionist or a ziggurat clearer in DCSS. This @Play article explains the dynamics: in Rogue, the monsters increase in power faster than the player character. The player often has a secure advantage for a few levels, but it never lasts.
The point where monster power overtakes player power depends on how strong the player character is. It tends to fall between dungeon level 13, where Trolls appear, and level 18, where Umber hulks or Medusas appear. Somewhere in that range is the transition from the midgame, where the player has a good chance of being able to kill everything, to the endgame, where defeat is only a matter of time.
This article is about surviving that endgame. Be warned that it's written by someone who has never actually succeeded. I found the Amulet once, and then died two levels short of escaping the endgame depths.
The first vital part of surviving is to be as powerful as possible. The longer you can keep ahead of the monsters, the shorter the deadly endgame.
First, you need a good weapon. A two-handed sword is ideal, but will only be generated in a third to a half of all games, so you need a fallback plan. In V4 and V5, a long sword does 75% of the two-handed sword's damage. If you can enchant your starting mace to +3, +3, it will do about as much damage as an unenchanted two-handed sword. The long sword will be slightly better if enchanted to +2, +2.
You also need to improve your armor. Trolls can hit your starting armor class 80% of the time. Dragons will never miss. Each point of protection reduces your chance of being hit by 5%. Keeping good armor can be as hard as finding it. You may need tricks like not wearing your best armor on levels with Rust monsters/Aquators.
Experience level is important because it increases your healing rate. Once you reach XL 8 it increases rapidly, making new tactics possible. Leveling up also improves combat accuracy. Beware of wraiths. Their level-draining attack can ruin a promising game.
Maximum HP is a related factor. Its increases are highly random, varying from 1 to 10 each experience level. If the average gain is below 5, the character is unlikely to last long. The only remedy is quaffing healing potions.
High strength provides a bonus to both your accuracy and your damage. But if your strength falls below 16, you will do less damage. The potion of restore strength is one of the most valuable items.
All five of these necessities require some luck to either gain or keep. If the random number generator fails to grant one, there is nothing you can do about it. Most games are not realistically winnable. But you can never tell when the next room might have a potion of restore strength, or a sword, or a scroll of protect armor.
In those rare games where you find everything you need, you will arrive at the deep levels. There will be monsters that you can't defeat by simply trading blows. Your best strategy is to avoid them. Be ready to run. If you are injured, retreat, healing as you go, then fight again. Avoid dead ends where you could be trapped. Take the stairs as soon as you find them.
Fighting two monsters at once is risky on any level. In the depths, you need to guard against monsters sneaking up behind you while you fight or retreat from another one. Be aware of any ways they might enter rooms you have already cleared. The longer you have been away from a room, the more likely it is that a new monster was generated there.
Even exploring cautiously, you will still face deadly monsters. This is where you need your special items. A potion of haste or a wand of slow monster makes it easy to defeat dangerous foes. A wand of light prevents them from surprising you in dark rooms. Almost all items can be put to use in some way.
You have to adapt your tactics to whatever items the game provides. In later, larger roguelikes, you will eventually collect several of everything in the game. Rogue guarantees only food and the Amulet. You can almost count on finding scrolls of identify. That's all.
It's important to identify as many items as you can, so you know when to use them. Especially avoid using unidentified items that could be harmful. There's little hope for anyone who accidentally uses a wand of haste monster on a Xorn.
In the heat of battle, it is easy to forget about the life-saving item you picked up ten floors above. A good player has to mentally break out of a hopeless fight and consider other options. Try to form a habit of checking your inventory when you find yourself threatened. Resist the urge to conserve items. If you are killed, they will be just as wasted as if you used them unnecessarily.
The danger zone, at best, lasts from level 18 down to level 26 and back up, just as long as the whole game preceding it. You will not make it on your first try. You will likely scatter dozens of gravestones across the depths. Be patient. Try to get onto the high score lists or explore deeper than you have before.
I'm still waiting for someone to achieve the Gallery's first victory. But with enough games played, some bold adventurer is sure to survive the endgame and bring the fabled Amulet of Yendor up from the depths.