|(for those uninitiated, that's Hanna-Barbera's "Ricochet Rabbit")|
In Basic D&D, searching and listening are critical activities, and the odds of characters finding hidden treasure, secret doors, or gathering clues about the number and variety of lurking monsters prior to an encounter with them can depend heavily on these in-character activities.
Of course the usual system for determining if a thief's Listen check is successful or if a magic-user notices a revolving wall panel is to roll a six-sider, a result of 1 (or possibly 1-2) being successful, higher results being failures.
The problem with this is that if the player rolls a failure, then she knows it and has out-of-character incentive to have her character spend extra time checking an area for things she might have missed the first time when normally she might pass that area by (meta-gaming).
The simple fix is to have the DM roll the check behind a screen or out of the players' line of sight, but that robs the players of the chance to chuck small pieces of plastic around.
A solution we use when playing B/X is hidden target numbers. I do almost all of my dice-rolling in the open, but when players want to listen or search I throw a hidden D6. The players then get to roll their own dice in an effort to match the (still hidden) number I rolled. For those pesky elves, thieves, and dwarves (who succeed on a 1-2 in the rules) I just treat the target number and anything one point lower as a success.
|From the artists at Jinx.com (and on sale there)|
It's not a perfect solution ... clever players now watch to see if their roles generate a range of numbers and may spend extra time in a location until the dice produce a spread of results that they like, but at least it keeps the dice (and agency) in their hands while maintaining a sense of the unknown.
I'd be interested in hearing other ways that people have solved this dilemma at their tables.