Below are the details of what rings have been added, removed, and changed.

NOTE: ring combos will be discussed in a separate doc to avoid spoilers for those who want to figure them out themselves.

Ring Stacking:
    Any in-game ring description that includes "Can stack" indicates that wearing that ring with
    others that affect the same kind of thing(i.e. both heart rings, both rang rings, both light 
    rings, etc) will produce a stronger effect(often stronger than just both added together).

    The only stackings that are worth going into more detail on are the Joy rings and rings that
    modify attack/defense. Those are described below.

    Joy Rings:
        The Red/Green/Blue Joy Rings each stack with Gold Joy Ring to provide x4 of that item.
        Red Joy Ring + Gold Joy Ring + Discovery Ring makes for quite fast rupee farming.

    Attack/Defense:
        The way attack and defense are calculated has been tuned to avoid making ring stacking too busted.

        When calculating damage dealt, the sum of the multipliers are added together first, then 
        multiplied by the sword's base damage, and then any +- modifiers are added to the result.
        The final value is rounded down, and is capped to a minimum of 1/4 heart damage.
        Examples:
            Red Ring        = +100%
            Red Curse Ring  = +100%
            Gold Ring       = +100% (assuming we have less than 4 hearts)
            Green Ring      = +75%
            Power Ring L-3  = +3

            Master Sword    = 5 base damage
                Total = 5*(1 + (1 + 1 + 1 + 0.75)) + 3 = 26.75 = 26 damage

            Noble Sword     = 3 base damage
                Total = 3*(1 + (1 + 1 + 1 + 0.75)) + 3 = 17.25 = 17 damage

            Wooden Sword    = 2 base damage
                Total = 2*(1 + (1 + 1 + 1 + 0.75)) + 3 = 12.25 = 12 damage
        
        When calculating damage taken, the +- modifiers are first added to the base damage, which
        is then multiplied by the sum of the multipliers. The final value is rounded down, and is
        then capped to a minimum of 1/8 heart damage. Additionally, the armor percentage is capped
        to 5/8, or 62.5% reduction.

        Examples:
            NOTE: 1 point of damage == 1/8 of a heart
     
            Gold Ring        = -25%
            Green Ring       = -37.5%
            Armor Ring L-1   = -1

            Cheep Cheep      = 4 base damage
                Total = max(1, (4 - 1)*max(0.375, (1 - 0.25 - 0.375)))  = 1.125 = 1 damage

            Blue Darknut     = 8 base damage
                Total = max(1, (8 - 1)*max(0.375, (1 - 0.25 - 0.375)))  = 2.625 = 2 damage

            Ganon Trident    = 12 base damage
                Total = max(1, (12 - 1)*max(0.375, (1 - 0.25 - 0.375))) = 4.125 = 3 damage

            Ganon (Contact?) = 16 base damage
                Total = max(1, (16 - 1)*max(0.375, (1 - 0.25 - 0.375))) = 5.625 = 5 damage


Removed rings:
    Whimsical Ring:
        Repurposed for Gold Ring.
        We can all agree this thing is useless. No one will miss it.

    Protection Ring:
        Repurposed for Fairy's Ring.
        Also pretty useless since hardly anything will hit you for more than a heart, and even if it does you also have defense rings.

    Dbl. Edged Ring:
        Repurposed for Blue Curse Ring.
        Would be too powerful with the other damage modifier rings being able to stack now.

    Snowshoe Ring:
        Repurposed for Haste Ring.
        The effect has been combined into the Hiker's Ring, so this ring is no longer necessary.

    Gold Luck Ring:
        Repurposed for Alchemy Ring.
        The 50% fall damage effect has been moved to the Blue Luck Ring, so this ring is no longer needed.

    Whisp Ring:
        Repurposed for GB Color Ring.
        Whisp nulling effect has been moved to Red Holy Ring.

    Cursed Ring:
        Converted into Red Curse Ring
        No one will miss this thing, and if they do they can use both new curse rings instead.

    Quicksand Ring:
        Upgraded into Hiker's Ring(quicksand effect remains intact.)

    Pegasus Ring:
        Upgraded into Mystic Ring(Pegasus effect remains intact.)

    Friendship Ring:
        Upgraded into Vasu's Ring.

    Rupee/Hundredth/Slayers/Sign Ring:
        Upgraded into Green/Blue/Red/Gold Color Ring.


New rings:
    Gold Ring:
        Gives +50% sword damage and -25% damage taken.
        If you have less than 4 hearts, these double to 100% and -50%.

    Haste Ring:
        Movement speed increased.
        Works by bumping the movement speed on the current tile to the next fastest.
        Speed-on-stairs -> Speed-on-grass
        Speed-on-vines  -> Speed-on-grass
        Speed-on-ladder -> Speed-on-grass
        Speed-on-grass  -> Normal-speed
        Normal-speed    -> Pegasus-speed-on-grass

    Vasu's Ring:
        Open the ring list from anywhere by clicking the Ring Box in your inventory.

    Fairy's Ring:
        Revives you if you die, but breaks and is removed from your ring list.
        Only activates if you die without a potion.
        Replacement rings can be gotten as a tier 0 drop.

    Hiker's Ring:
        Movement unaffected by ice/quicksand.
        No speed penalty while moving on stairs/grass/vines.

    Mystic Ring:
        Lengthens Pegasus seed and Scent seed effects.
        Super Slingshot fires 5 seeds.
        Seed Shooter can have 5 seeds onscreen at once, and the bounces are doubled.
        Ember seeds burn much faster.
        Scent seeds deal +2 damage.

    Curse Power Ring:
        Adds 100% more base attack, but your hearts are constantly capped to 4.

    Curse Armor Ring:
        All damage you received and deal is reduced to 1/4 heart(Sword L-1).
        Other armor/power rings are ignored while this is equipped.

    Alchemy Ring:
        If you attempt to use a seed/bomb/bombchu while you have none, one will be crafted from rupees.
        Cost per item is:
            * Seed:     2 Rupees
            * Bomb:     5 Rupees
            * Bombchu:  50 Rupees

    Green Color Ring:
        This is the Rupee Ring, except it changes your color to green.
        Sounds useless, but can combine with another color ring to blend the colors.

    Blue Color Ring:
        This is the Hundredth Ring, except it changes your color to blue.
        Can combine with another color ring to blend the colors.

    Red Color Ring:
        This is the Slayers Ring, except it changes your color to red.
        Can combine with another color ring to blend the colors.

    Gold Color Ring:
        This is the Sign Ring, except it changes your color to gold.
        Can combine with another color ring to blend the colors.

    GB Color Ring:
        Switches the game to GBC mode(i.e. uses darker color palette and advance shop closes.)


Modified rings:
    Unless stated otherwise, assume any unmentioned effects from the base game are still present.

    Power/Armor Rings L-1/2/3:
        Each tier increases the buff by 1 without increasing the debuff.
        This means wearing a L-3 of each doesn't cancel each other out.

    Green Ring:
        25% more damage dealt and 12.5% less damage taken than the original Green Ring.

    Fist/Experts Ring:
        Works with only 1 item slot empty instead of requiring both.

    Blast Ring:
        Increases blast radius by 2x

    GBA Time/Nature Ring:
        Increases invulnerability timer by 60%

    Steadfast Ring:
        Enemies contacting your shield will not knock you back.

    Bomber's Ring:
        Up to 4 bombs can be set at once.

    Green/Blue/Red Luck Ring:
        Provides a 30% chance to reduce damage from a hit to 0.

    Green/Blue/Red Holy Ring:
        Provides immunity to electricity/zora fire/whisp jinxes
        Reduces damage taken by 25%

    Roc's Ring:
        Increased jump height

    Discovery Ring:
        Increases chance for random item drops to occur.
        Equates to roughly 2x increased liklihood.

    Octo/Moblin/Like Like/Subrosian/First Gen Ring:
        Does not prevent usage of any items.
        Works during cutscenes.

    Victory Ring:
        Upgrades your sword and shield level.
        1 -> 2   and 2 -> 3
        Does not go past Master Sword
