I made a post about this on my blog a while back, that I feel like I should expand upon, that most random chance in O/AD&D does not rely on PC stats or abilities. I feel like this is an important thing to write, as this style was very quickly forgotten as early as 1981, when Moldvay’s Basic book put in a paragraph titled “There’s always a chance” where it advised players to roll under a character’s stat to determine probability

This advice is nowhere in AD&D 1e, and in fact the opposite is given where the GM is told to grab a handful of dice and just make up a probability that seems fair.

 

Perception is based on character stats. One character with a high WIS will have a much better chance of succeeding than one with low WIS, and the former might always be helpless against hidden traps.

X-in-6 is standard for all characters, and doesn’t rely on their build 

 

Roll under stat probabilities would become a standard resolution mechanic in AD&D 2e, which evolved into 3e’s skill and save system