(This is a train-of-thought posting, where no proper research was conducted. Surely a myriad of illuminaries have arrived at the same conclusions before. Please point sources my way, thank you!)
In recent games I have been fortunate enough to introduce several new players to the hobby of roleplaying games. Frankly, they are my favorite group to fish for. As much as I like the expertise of a commited and focused group of players tackling a demanding adventure, the delightful ingenuity from someone new to the medium is charming. They bring their own Appendix N of related media, minus past experience RPG baggage.
All of this to say that when playing Old School games with these neophyte players (B/X via OSE as of late), I see a lot of confusion about what rolls to make. And if they need to roll high or low!
Many systems have tried simplifying and streamlining things since. From new OSR inspired games that use roll-under ability score for all, to many other variants. Knave (everything's a save!), Black Hack (only players roll!), Macchiato Monsters (all is a risk die!)
This post from 2009 (!) suggests using the Swords & Wizardry unified single Saving Throw (ST) for general task resolution.
BUT, I much prefer keeping things seprarate. The d20 to avoid and inflict danger (ST and combat). And a d6 for general task resolution. Since bonuses/maluses in WhiteBox are just up to plus/minus 1, let's use a simple d6. Target number is 5+.🦄
Having a relevant Background can give you a +1 to the task. And players can pour gold and weeks/months of downtime to gain new ones! 🦄🦄 So combined with a positive ability score maximally a player can stack a +2 to a roll.
Now some important caveats: keep rolling scarce, and avoid it in most cases in lieu of common sense. "Yes, you were a Butcher (background) and brought the Basilisk's carcass to the keep, so you are able to extract its eyes." OR "No, you cannot read or understand the runes in this archway since you don't know that area".
The outcome of this roll is not a binary YES/NO. Instead, since we are playing a TTRPG and there is a human brain running the fiction, I lay out chances and possible outcomes BEFORE any rolling is done. And this can be a YES/NO or YES/YES WITH CONSEQUENCES or YES/NO WITH CONSEQUENCES or whatever.
To the consequences. Everything is for grabs. Attack the character sheet. Most obvious...
1. Time. Task succeeds, but you are slow. Random encounter checks, timer, timer, timer.
2. Equipment. You force the door open with the crowbar, which ends up bent and useless in the process.
3. Future risk. You jump the chasm, but the bridge is damaged for your return.
🦄 With this I would reverse the usual Open Doors, Listening at Doors, Find Traps, etc. from the 2-in-6 to this 5+ to have equal odds, but a "roll-higher" instead.
🦄🦄 There are plenty of such d100 tables, from WHFRPG, to for instance Black Pudding, Shadow of the Demon Lord, etc. They inform setting and tone. As the effect is mild, there is no real risk of having less useful Backgrounds, as players have to come with interesting applications in each situation that comes up during play.