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.)
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 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 because it gives a 16 or 17 percent chance, which is not too high but not too low either. It’s unlikely but possible, as it should. 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.
However, if an action becomes harder or easier due to the character’s innate traits, then their range of success is modified by their attributes, so 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.
1d20 is basically the same as 3d6, 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 (disclaimer: 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.
Other games, such as DCC, call for a d20 roll against a difficulty set by the referee, and a high score is sought. Depending on the 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 award without having to think if this action is of a standard difficulty or higher or lower. And if we take into account that the standard difficulty is, say, 12, 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.
Not to mention, too, that the d20 system (where this mechanic comes from) is that all the rules are the same, so climbing, hitting or seducing don’t feel like different actions to the player.
And this, the 1-in-6 checks, is the main reason I like LotFP’s system more than others. It’s not the only reason but it’s the main reason.