D&D Basic Rulebook (1981) p. B8
Open Locks may only be tried once per lock. The thief may not “try again” on a difficult lock until until he or she has gained another level of experience.
What if we generalize this to one retry per level per lock. So, if a second-level thief had tried to pick a lock when they were first-level, they’d get a second try now that they were second-level as per the rule. When faced with a locked they hadn’t tried before, however, they’d get two attempts.
The down side is that each attempt takes more time. I don’t recall the amount of time required being specified, so let’s go with the default “1 turn” (i.e. 10 minutes) for each attempt. If that seems excessive to you... Well, you don’t need me to tell you to use whatever you want. I will say that based on my admittedly amateur attempts, I’m not sure that is unrealistic.
This means that, given unlimited time, a second-level thief’s overall chance of opening a lock is (2 tries at 20% each) 36%. For a third-level thief it is (3 tries at 25% each) 57.8%.
This, of course, is a boost for thieves. Some, however, will say that thieves can use every boost they can get. Unfortunately, it is a boost that pays off much more for higher level thieves—who need the boost less—than for lower level thieves.
Given the low chances at low levels, I’m tempted to allow unlimited retries. The time trade-off remains. After each failure, the party must ask: Is it worth standing around for another 10 minutes to give the thief another try?
Well, “unlimited” is perhaps too much. A cumulative penalty for each try after the first seems reasonable.