Analogous to, and in contrast with, fighting ability, the concept of thieving ability usually refers to a discrete subset of "skills" typically only available to thieves, and the probability of their success. In the first edition Player’s Handbook it is referred to when describing the limitations of the multi-class thief (pp. 16 and 33), indicating the reduced capability of the assassin in the same regard (pp. 28-29), the monk (pp. 30-31), and the limitations on the bard (pp. 117-118). By contrast, the Dungeon Master’s Guide uses thieving ability in the sense of thief experience level when referring to life energy level drain (p. 119). A rendering of Conan as an Advanced Dungeons & Dragons character, authored by Gygax and published in Dragon #36 (April, 1980, pp. 10-11), makes use of both terms in the wider and narrower senses, also noting that his exceptional ability to move silently and hide in shadows (which Conan can naturally accomplish as though a tenth and fourth level thief, respectively) allows him to surprise opponents fifty percent of the time. So, as with fighting ability, the term appears to be employed loosely, but can be usefully applied to the collection of ten abilities that differentiate the thief class from the other three.
It is worth considering that there are a number of objections to the thief class, these often being rooted in, or deriving legitimacy from, the fact that the thief was not included in the original three booklets that composed the Dungeons & Dragons adventure game, but was introduced only afterwards with the Greyhawk supplement. These run from at best perceiving the class as superfluous to requirements, to at worst as a usurper of activities that ought to lie in the domain of the fighter. In fact, though, as soon as one steps away from the simple abstract dichotomy of the fighter and the magician, the result is intrusion or surpassing of a sort. Moreover, and as Robert Fisher pointed out to me several years ago by ways of his writings on the subject, thief abilities are not just colourfully named skills, but frequently duplicate spell effects, such as silence, invisibility, knock, find traps, and spider climb. The fighter class lost nothing in this regard, even if the perception was created that they could not be stealthy or search for traps. Indeed, it seems to me that the quartet of classes, fighter, magician, cleric, and thief, are fundamental to the identity of the game in a way that the subclasses and, even the races, are not.
Whilst objections on the grounds of aesthetics or misunderstandings have little weight, a more substantial criticism of the thief class is its relative weakness in comparison to the other three. As has been demonstrated elsewhere, the starting fighting ability and progression of the thief has varied across editions, and even the relatively speedy level advancement that he enjoys will not serve to make him the equal of the fighter nor often that of the cleric. Much like the magician and cleric, then, we must look to the special abilities of the class in order to seek justification for its inclusion. Unfortunately, the probabilities of success for most thief abilities start out exceedingly low and then rise rapidly until almost certain by around twelfth level in the original and classic versions of the game. For the first edition of Advanced Dungeons & Dragons, the starting probabilities were slightly increased and then the rate of advancement reduced by a relatively more significant amount, so that by the same point several abilities compared very unfavourably with earlier versions. With second edition an entirely new approach was taken making use of point allocation so that the player determined the probabilities within certain defined limits.
The benefit of this approach was that a single ability might start at around forty percent, higher if racial and dexterity modifiers were favourable, and be increased by up to fifteen percent at each level. The obvious problem with this was that the abilities of any given thief were unpredictable, depending on what the player had decided to specialise in (or not, as the case might be) and relatively less useful abilities were sacrificed in favour of high scores in more desirable ones. Less obviously, the allocation of points substantially increased character creation time, most importantly for non-player characters, and required an entire extra statistic line for each individual entry. This may seem like a small price to pay for a resolution to the problem of the underpowered thief, but it is more of a redistribution of power than it is an actual solution to the underlying issue, which is that the class starts out with very limited usefulness and then rapidly rises in capability in uneven steps, much like the non-advanced fighter does with regard to fighting ability. A comparison of the various approaches taken to thief abilities in different editions and versions can be downloaded in pdf format here.
However, there is one major difference between the first edition version of the thief and all of the others, and that is the seeming lack of a limit on the number of times a thief can try some abilities. In the case of move silently, hide in shadows, and climb walls there are obvious immediate repercussions for failure, but none that prevent further attempts under the same conditions, assuming life still remains of course! The asterisks in the Greyhawk supplement indicate that only hear noise may be retried, but the actual note only refers to pick pockets, so it could conceivably be an editing error (pp. 11-12). The rules for Advanced Dungeons & Dragons put no absolute limit on the number of times that characters may listen, nor seemingly on the number of times they may attempt to open doors, or search for secret doors (DMG, pp. 60 & 97). In particular they contrast with Greyhawk by explicitly allowing repeated attempts at picking a pocket (DMG, p. 19). On the other hand, more than one attempt to open a lock is prohibited and restricted to one attempt per thief (PHB, p. 28). More significant is the time consumed for each attempt, as this increases the probability of being interrupted by wandering monsters.
For my Silver Blade campaign the concept of thieving ability has suggested a different approach to the problem. Many tasks are rated by thieving ability (or thief level), so certain secret doors can only be found by a third level thief, for example, and the same applies to hearing noises, opening locks, as well as finding and disabling traps. In some cases no ability check would be required, in others repeated checks permitted, though obviously the dice roll must be hidden from the players so that they remain uncertain as to whether they have failed or there is simply nothing to be found. The probability used is a base thirty percent plus five percent per level, though it can be adjusted if the situation requires. With regard to stealth, lightly or unencumbered parties have an increased three-in-six probability of achieving success, medium encumbered parties two-in-six, and heavily encumbered parties a reduced one-in-six chance. A magically silenced party, silently moving and lightly armoured thief, elf, scout or ranger would thus have a four-in-six probability of surprising enemies. I remain in two minds as to whether to follow the example of Conan in forgoing the move silently roll in favour of overall increased surprise.