I prefer 1-in-6 chance checks, sometimes modified by your attributes: a +1 STR would translate to a 2-in-6 chance, while a negative means it’s impossible for you, or else you must roll 2d6 and only succeed if both dice come up 1. If you’re benevolent, let them roll without a penalty.
Why? Because some of the actions are not inherently difficult or easy depending on your own physical or mental traits. The difficulty of finding a trap is about the same for everyone regardless of their stats; high intelligence doesn’t necessarily make you better at finding traps, so INT 10 and INT 18 and INT 6 have the same 1-in-6 chance of finding the trap.
Yes, sure, some have an easier time doing so, but it’s certainly due more to experience and knowledge than to intrinsic intelligence values, or simply due to good luck (i.e., chance). And this is where the flexibility of OSR comes in: Can you give me a good reason why, on this occasion, your character should have a better chance of finding a trap? Maybe you have already found another trap in the same area, you are using some useful tool, or you remember reading or hearing stories about this place. For this time, you have a chance of 2-in-6 or even 3-in-6.
A base chance of 1-in-6 gives a 16 or 17 percent chance, which neither is too high nor too low. It’s unlikely but possible, as it should be. See, a group of 3 characters will have a 50-50 chance of success if all 3 make the roll, which I allow if it makes sense, but sometimes only one person can roll. If it was easy, then what would be the point? Just tell the story and avoid rolls. Decide the result by only speaking and move on (which sometimes might be the right way to do it).
However, if an action becomes harder or easier due to a character’s innate traits, then their range of success is modified by their attributes (as explained on the first paragraph). Why not roll 3d6 in those cases, since those traits are based on a 3d6 roll? Because I firmly stand that we shouldn’t make a different rule when your traits alter the result than when they don’t. Let’s use the same system for both cases, when your stats are relevant and when they are not. (Later I talk against D20 system using the same rule but it’s not a contradiction; here we use the same rule for tests, D20 uses the same rule for everything).
1d20 is basically the same as 3d6, albeit more elegant; in both cases you roll under your traits, so it only makes sense when the difficulty depends on your stats and not on the action itself, which means we should not use these (pro tip: use whatever you like, I’m just saying.)
Games like Into the Odd rely on d20 rolls under your traits; it’s ugly but at least the game is quick and easy. ItO is based on quick and easy. In that sense, this is the right choice.
Other games, such as DCC, call for a d20 roll against a difficulty set by the referee, and a high score is needed. Depending on the game and circumstances, the result can be modified positively or negatively by the character’s attributes or the tools used. It is the same principle as the 1d6 system, but in the 1d6 system it is very easy to modify without having to think whether this action is of a standard difficulty, or higher, or lower. And if we take into account that the standard difficulty is 10, it is actually very easy to succeed in about half of the attempts, and if more than two characters can roll, success is almost guaranteed, although in the case of DCC, if you are not trained in an occupation or profession related to the task, you don’t roll 1d20 but 1d10 instead. It makes sense but it adds more complexity.
In the d20 system (where this last mechanic comes from) all the rules are the same, so finding traps, climbing, attacking an enemy or seducing an NPC, don’t feel like different actions to the player.