Please forgive me if this post covers old ground that I've written about before - as long as I'm here (p. 19 of the DMG), I feel it's best to be comprehensive.
Before getting into the individual abilities, let me address an overarching issue related to rolling dice for thieves' skills. For those who don't know, the original rules relied on a pass/fail mechanic: you wished to "hide in shadows," you rolled a die. If you succeeded, you disappeared; and if you failed, you didn't. I'll talk more about hiding in shadows later.
Let's start with this quote from Gygax:
"Roll of the dice for any thief function must be kept absolutely secret, so the
thief (or similar character) does not know the results."
This remarkable, firmly made statement is never properly explained in the original books. Presumedly, thieves "can't know" if they've succeeded in hiding in shadows or moving silently, since they can't see themselves. This doesn't quite work, however, since pickpockets will obviously know whether they've picked a pocket, while a wall climber will know if the wall was climbed. However, it does say "ANY" thief function, which means it applies to opening locks, hearing noise, reading languages and — here's the kicker — finding & removing traps.
Now, this last is a thinking problem. Let's say that I'm holding the roll secret as your DM. You check for traps and I say you don't see any. Aha! You know that might mean there are no traps, or that you didn't find them. For you, there's no way of knowing which. Of course, you know that if you're a much higher level thief, there are probably no traps ... but since there's always some possibility of the die roll failing, you can never really know, not even if you're 17th level (where the thief table stops).
Okay, let's say there is a trap and you detected it. You try to remove it and I roll the dice. You ask, "Did I remove the trap?" and I answer, "You don't know." See, the die roll must be kept secret. You're not meant to know if you succeeded. You're just supposed to trust to your luck. Period.
On the surface, this sounds like a great mechanic. It's really not bad ... the first time you encounter it. The tenth time, or the hundredth time, the mechanic gets pretty frustrating. Since it applies to every thieving ability, very soon it becomes the core reason that players don't want to play thieves — because if you play a thief according to the original rules, this mechanic is all you have.
Supposedly, the low amount of experience you need to go up a level compensates for this frustration. Except it doesn't. Eventually, you learn to hate the thieving skills, ceasing to rely on them except when absolutely necessary. Eventually, you'll settle into the hear noise and open locks skills, which you'll overuse, because are the options in your skillset that won't bite you in the ass if they fail.
Pass/fail mechanics suck. The exception is any rule that lets you try to pass repeatedly until you do, such as attempting to hit with a weapon, where you can make the attempt every round. When you get one chance at something, however ... well, the pass/fail option better really, really matter, because when it is applied to stupid bullshit stuff like can you pick a pocket, and do it without being noticed and sparking the 95th chase of a thief through the streets of a town by the guard that's taken place in your world (in my early days, seemed like this was happening every session), then the mechanic just sucks.
It is not made better by keeping the mechanic a secret. Imagine fighting a whole combat where every hit you make is a secret, but every hit the enemy makes is fully revealed. Sound like fun? Yes, yes, I know that some of you right now are pausing and saying, hey! That really sounds ... accurate or realistic or cool. You might even try it ... and I'd lay money that the first time, it would feel workable.
The tenth time, not so much.
Too many times game designers come up with mechanics they think really work ... because they don't have to spend hundreds of hours at the fucking forge, watching a green bar so you can strike the blade properly, until your eyes bleed.
A pickpocket in the real world gets to know precisely whose pockets can be picked and how hard it is to get something they've seen once out of a pocket they've identified. It isn't a die roll. It isn't even a 99 in 100 roll. It is so close to certain that it's possible to do it for months at a time without being caught. The balance is not "can the pocket be picked" but is that particular pocket worth the effort? Since most pockets aren't with certainty, the pickpocket floats around areas of tourists, because tourists have lots of money and they usually carry it on themselves. Pickpockets also frequent areas where people use cash to pay for gambling and hookers, so there's no record of where they've spent or lost their money, or how much they're earning. Anyone who looks comfortable and at ease in such places are left alone; pickpockets target the uncertain, the uncomfortable, the ones that are nervous and sweating ... because they have money and they're not part of the local criminalized community. There's a lot that goes into the practice. Additionally, when a pickpocket gets caught, it isn't by failing to pick a pocket. There's always a strategy for that, when it so very rarely occurs, such as making the pull near a place where the dupe can be pushed into an alley or either clubbing or stabbing the dupe before they can cry out for help. No, a pickpocket gets pinched because someone else who knows how pickpockets work is watching. They see the pull. The dupe never does.
These realities surrounding the practice obliterate the pass/fail structure. It doesn't make sense. Similar arguments can be made about hiding in shadows and moving silently. If I'm far enough away from you, I'm always "moving silently" in relation to you. It always matters how near to you I want to be; and details like what surface I'm walking over or what I'm wearing, how much light exists and most importantly, who's listening and what are they doing? We train people to pick their moment, pick their equipment and pick their target ... so it isn't a chance thing. With enough experience and enough time to prepare, slipping up to a person silently is automatic ... unless the target has their own training and has made their own preparations. Any flat method for calculating this that doesn't recognize these conditional issues is a dumb, ill-considered mechanic. A single die roll that applies to ALL situations is idiocy in the extreme.
Sneaking up on a person or past them is a combination of many factors — the use of silence and shadows being only two of them. There's no practical game rule for treating silence and hiding as different skills; you never do one without attempting to do the other, and by insisting that a roll is made for both in all circumstances only assures that full likely success is a very tiny number. The chance of a 1st level thief in AD&D, without dexterity or racial bonuses, succeeding at BOTH hiding in shadows and moving silently is 10% of 15% ... or 1.5%. The best you can do at 1st level is to be a halfling thief with an 18 dexterity: this gives you a 35% chance of 35% to succeed in both: 12.25%. You literally have a 1 in 8 chance of slipping up on a guard at 1st level, if you're the best thief possible. And, of course, if you fail at either roll, you'll be seen or you'll be heard. You're set up to fail.
And remember: you're not supposed to know if you succeeded at either. That information is kept secret from you, until it's too late.
Similar arguments to these apply to other abilities. Opening locks is not a matter of "can you succeed?" but "how long does it take?" If you understand locks, and you have the proper tools, a success roll is meaningless. Also, just for funsies, locks don't exist in a pre-17th century world. And those in the 17th century were laughably easy to break. The locks were large, so they made noise while they were opened. Not because they were notoriously hard to break.
Gygax included his thief ability comments in the DMG because, as he said, they would "prevent abuse of these activities." He clearly believed that the thief being able to automatically perform thieving abilities would overreach the game: as though climbing a wall or reading a language compared with casting a spell. What is the issue with a thief being able to read a magic scroll, exactly? Aren't there other players who can do that automatically? How does this sort of thing break the game?
I haven't yet discussed "hear noise." Until I puzzled it through, this used to be the bane of my existence as a DM. Players were constantly pausing to hear noise, calling it out like 5e players call out perception checks. Naturally, players always want more information; they want more warning of things that are coming ... and a particular kind of DM doesn't want to give that warning. They're convinced that the best possible sort of tension is built out of the players no knowing what's coming next.
I circumvent the problem by telling players that if they can hear something with hear noise (I call it "heightened senses") then I'll say so without my having to be asked. Moreover, I like the players to know what's ahead. Knowing is much more worrisome than not knowing ... a truth that Hitchcock taught the world 80 years ago. Watching the gasoline creep across the street in The Birds, and then the fellow with the match, and then the fire, is far more interesting than having no idea that there's anything to worry about. If the players know there's a powerful demon behind a door, waiting for them, whenever the players are ready to push on through and engage it, that is MUCH more interesting in game terms than opening an apparently harmless door and finding a demon behind it.
The sad truth is that a great many DMs don't have very much idea of what tension is, or how its built, and so they think information is a bad thing. They don't watch enough good movies, or they watch too many of a certain kind of movie, and they don't investigate and study storytelling as a subject. For these reasons, they subvert possibilities in their gaming by adopting mechanics deliberately designed to keep players in the dark, when in fact knowing that there IS a trap, and that it's not deactivated is much more compelling than knowing nothing.
The thieves' abilities, understood right, played right, are a means of pouring exposition into the players' hands, by ensuring that the thief sees things, learns things and hears things, in a hundred different circumstances, enabling us to fuel the game's momentum. Why would we want to keep the thief from going places and getting details about the scenery we want the players to have?