DD/Oe/BX Skills

Delving Deeper, like Oe and B/X, has lots of 1d6 skill rolls scattered throughout the rules—listen at doors, open a stuck door, detect traps. Except for the thief skills, DD's skills are pretty much the same as the early editions and other clones.

Being someone who would much rather learn a guiding principle than memorize/look up specific instances, I decided to gather all the skills together and see what I could do with them:

Listen at doors
Halflings, Elves, Dwarves: 2 in 6
Thief: 4 in 6
Everyone else: 1 in 6

Dungeon Architecture
Dwarves: 2 in 6

Find Secret Doors (takes 1 turn)
Elves, Thieves: 4 in 6
Everyone else: 2 in 6

Thiefy Stuff: Open Locks; Disarm Device; Climb sheer surface; Sleight-of-hand
Thief: 4 in 6

Stealthy movement/Hide
Halflings: “nearly invisible” “almost silent” = automatic? (B/X: 10% in underbrush, 2 in 6 w/ cover)
Thief: 4 in 6

Surprise
Thief: 4 in 6
Everyone else: 2 in 6

Open Doors
Weaklings (STR 3-6): 1 in 6
STR 7-18: 2 in 6

Evade Pursuit (Dungeon)
Everyone: 2 in 6

Distract Pursuit w/ Food
Pursued by Unintelligent Foe: 5 in 6
Pursued by Animal Foe: 3 in 6
Pursued by Intelligent Foe: 1 in 6

Distract Pursuit w/ Treasure
“Inversely proportionate”

Evade Pursuit (Wilderness) (First success to gain ground; second consecutive success to lose pursuit)
If pursuers is 4x number of evader: 4 in 6
If pursuers is 2x number of evader: 3 in 6
Everyone else: 2 in 6
Pursuers surprised: +1
Low Visibility: +1
Side with >2x Opponent’s movement: +1

Initiative
Everyone: High roll
DEX 3-6: -1
DEX 15-18: +1

Remain seated when struck in mounted combat: 5 in 6

Survive Drowning
Non-swimmers: automatic drowning
Swimmers: 5 in 6
For each heavy item retained: -1
Leather Armor: -1; Plate Armor: -4
During a storm: -1

Alright. Having them all in one place made them seem more coherent, and easier to boil down into a principle. What follows is how I plan apply them to my game. A couple notes:
1. My game uses the Adventurer, who replaces the Thief as the skilled expert in the party.
2. I'm ditching most of the mechanical differences between races. You can be an ogre, viking, or leprechaun, but if you solve problems by fighting, you're a Fighter.

DD/Oe/BX Skills
All player characters are considered generally competent and well-adapted to the campaign world. As such, it is assumed that they will succeed in any ordinary task they attempt.

When faced with a difficult task, the player should explain to the GM how the character attempts to solve it. Well-reasoned explanations should succeed.

Most tasks can be resolved without recourse to the dice. When the outcome is genuinely in doubt, the character succeeds when the player rolls a 6 on 1d6. This is a 16.67% chance of success.

If a character is in their native environment (City, Country, Wilderness, Sea, Underworld, etc.), they receive +1 to appropriate checks (hide, surprise, spot hidden, etc.). This is a 33% of success.

If a character has a 15 or greater in the most relevant attribute for a given check, they receive +1.

The GM can assess a +/-1 bonus or penalty based on significant environmental or circumstantial factors.

The Adventurer Class receives a bonus to checks relevant to their area of expertise (Communication, Craft, Knowledge, Physical, Subterfuge, Survival) based on level:
Levels 1-4 (Normal) +2
Levels 5-10 (Heroic) +3
Levels 11-12 (Superheroic) +4

A high-level Adventurer will find themselves in contexts where they are guaranteed success. They are still bound by the physics of the campaign world and the good sense of the GM.

Skill checks never apply to combat or magic.

If a character wants to have a particular incompetence—they don’t get along with horses or they can’t dance, this should be role-played, and does not need to be mechanically modeled.

More Notes
3. It's not granular at all. A +1 is a big bonus, worth working for, and significant enough that the GM should be pretty stingy with them.
4. There's no bell curve. I totally get why people like weighted results, but the percentages for this are easier for me to wrap my brain around on the fly.
5. Players might find it austere. Even if the percentages are same, it may feel better to roll d100 and feel like you have 16 chances of rolling a success instead of just one on a d6.