The Tavern

rings of slaying, protection, and evasion should always be +4

rings of strength, dexterity, and intelligence should always be +5

randart rings would not be affected.

As this is an overall buff, their frequency and total ring frequency could be reduced to compensate.

at the very least +1 and +2 rings are extremely lame and should not exist

Sounds agreeable to me. Negatively enchanted and cursed examples are purely dungeon clutter. By the time the player finds one, they generally will have scrolls of remove curse on hand and will get rid of it without a second thought. If they do end up with a -2 ring of dexterity stuck to them, it's essentially just a wasted jewelry slot until remove curse is found.

+1 rings of whatever are equally uninteresting. There's something uniquely disappointing about a +1 ring of slaying.

This actualy seems like a nerf to me. Str rings an the such are underwhelming enough that a chance of getting them at +6 seems worth more to me than an increased chance of getting a useful one.

It's probably a late game nerf and an early/mid game buff (as you always use the best you can find, and the longer you play the more of them you're likely to find) I'm not sure it's overall a large enough buff that it requires lowering the number of rings you find (think of the poor octopodes!

FWIW I like there being a range of possibilities, although +1 is worth using so infrequently that it's probably worth making the same as a cursed item (like negatively enchanted ones)

A variation on this idea is already in hellcrawl. There all numerical rings have value either +3 or +6. This is pretty good, though it would probably be better to go to a single value. The variable plus creates a lot of trash items that should not exist.

Perhaps it would be worth changing +X equipment to charge with xp? So you start off with a useless ring, or perhaps even a mildly harmful -2 ring, and as you gain xp with it equipped it attunes to you and slowly reaches the maximum bonus for that ring type. A slaying ring might start as -2, for instance, and require an entire level worth of xp to go up to -1, and from there to 0, and so on. After a total of 8 levels you have a perfect +6 slaying ring that stays at +6 until you remove it, so every ring that spawns has at least the potential to be a perfect ring, but you have to invest quite a bit of gameplay with an unhelpful or actively bad slot in order to get it. Other bonus rings would probably charge faster, and might have a larger maximum plus, because they're competing with a freely swappable slot.

It would give inferior rings a reason to exist, at least, since they would be a necessary step towards a good ring. Cutting +stat rings entirely is also a perfectly viable solution.

This would be the best idea in crawl jewelry since the amulet of harm.

I do want to reduce equipment swapping but I'd suggest two changes to that idea to avoid degenerate gameplay:
1. Don't start the rings as negative
2. Instead of resetting the enchantment when the ring is removed (which just leads to the feeling of "I need to grind this ring back up to +6" if they, say, swapped it for a resistance ring), destroy it

The bad thing about +x items is that you are obliged to identify them to see if they're better than your +y and +z items of the same type. Of course, the real problem is that identification is bad, though even without identification +x has a problem of producing garbage items (worth considering here why so many rings generate anyway). Making items less swappable has the side effect of making identification even worse. As I've mentioned here before, identification is second only to food in awfulness of crawl mechanics. We should not be willing to make identification worse in exchange for reducing swapping, which is several ranks down the bad crawl mechanics shit list.

If swapping rings is your main concern, weird mechanics for rings is not the solution. Tactical ring swapping can be easily fixed by making ring swapping the same as armor swapping. I've never seen anyone swap to a stat or +defense ring for a specific encounter. My impression is that ring swapping is entirely about resistances. Perhaps, then, resistances shouldn't be available on rings that can be swapped in 1 turn? Either way you take that suggestion leads to better places, in my opinion. As for the general equipment swapping problem where you take into account frequent, total withdrawal from individual encounters to make equipment changes taking dozens of turns, I don't see a lot of this kind of thing happening in practice and to the extent that people are leaving money on the table not taking advantage of this highly optimal way of playing, it's really a problem with the ease of disengaging from encounters, retreating upstairs and to other empty spaces.

I would go with +3 and +6 rings only

The point of rings is easy swaps so let's combine KoboldLord's idea with moving slaying to amulet slot. But then we don't even need the "get better through XP" part, it can be done similar to gourmand (time-based) and even have a penalty for taking off (negative slaying, for example).

I am ambivalent about reducing ring swapping. I'm unconvinced less swapping is better, i think weapon swapping is great. I think ring swapping can be great too. On the other hand, reduced ring swapping changes some things which people advocate for, and that's fine, i'd play a branch with different ring mechanics. I suspect it would just lead to resetting a few (1-5) fights in the midgame, and I'm not sure that is a gameplay benefit.

It could be an idea with merit, and could be worth trying.

However

If ring swapping is a thing, the interface should support it better. Weapon swapping is great because it is easy. Ring swapping is awful because the interface is awful. I can run 3 different weapons on 'a', 'b', and 'w' with ease. It is much more difficult to run 3 different rings (macabre not withstanding).

To the OP: I'm a big fan of hellcrawls solve to this problem, +3 or +6. Elegant, simple, no trash items, great. An early +3 is decent. +6 is good enough to stand up to other rings. Works even better without ID.

For a while I wondered about introducing a third group of jewellery, say bracelets, that are slower to swap, and then splitting the effects between rings and bracelets. That way one wouldn't get any of the 'Remove which ring?' prompts, which is probably the worst part of jewellery swapping.

On the other hand, I'm not completely convinced that introducing additional complexity is at all desirable.

IMHO it is rare when you want to swap both rings. In most games you have a ring of protection/slaying/MR and then you inscribe it with =R. Ring swapping for Octopode is awful, I agree, I end up inscribing 7 rings with =R usually (though I suspect sometimes it might be better to remove prompt completely and just remember a couple of letters for those rings).

I use semi-fixed letters for generic rings, which is reasonably quick. Unfortunately, it can be a little error prone.

Maybe the bonus could depend on evo skill, so all rings of [str,dex,int,slay] provide the same bonus, but it's not useful unless you've trained evo. That way the awful feeling of the +1 RoS is gone and depending on the investment could encourage skill hybridization.

Evocations is already the worst skill in the game IMHO. If you want to go this way, we can use Armour for Str rings, Dodging for Dex, Spellcasting for Int and Fighting for Slay

Shield skill for Amulet of Reflection.