Gaming theory: Random interval reward mechanics

Random interval (or often: Random drop) is a player reward mechanic commonly used in games. From board games utilizing shuffled cards or similar elements to the complex arrays of digital games, random interval is used to simulate spontaneous occurrences of rewards in order to add to the excitement of player efforts in the interim of gameplay.

Like many a term in gaming, it is difficult to cite an accurate source or precise definition across platforms, genres, or gaming sub-cultures for its "random drop" alternate name. I'd suggest the term came into being from the nature of the rewards and the most frequent appearance methods of these rewards; being occasional and often difficult to rationally tie to their sources with appeaing in the gaming world on the 'persons' of defeated foes or their immediate area as if 'dropped' from possession.

Cons
Can fail to be desirable by players with specific goals or those whose characters cannot effectively use the reward
Rarity of specific rewards becomes artificially greater as the list of alternate rewards increases
Often requires inventory management and liquidation efforts in order to make rewards useful
May trigger impulse control issues similar to gambling due to player market demands, wider range of reward values, and inconsistency of rewards to player efforts

Pros
Incredibly easy to design, program/implement, and expand upon
Can be a very effective means to promote player-ran/player-participant in-game markets
Excitement factor of more desirable rewards can aid in extending play duration

Commentary
Random interval rewards have a number of other instances aside of the more apparent; likely any time that there is a chance of variation in instance rewards for player efforts, they are interacting with a random interval mechanic. Some random interval systems also have a randomized chance of rewarding the player either due to sharing rewards with cooperative players or by adding a null reward option.

Random interval reward systems should very rarely (if ever) be used for progression systems as they will force players out of comparable or competitive capacity at no fault of their own efforts.

One way to think about random interval is that it's a simplified mechanic that tries to remove consideration of player specific goals and needs and offers a single system that rewards players approximately equal values of rewards for approximately equal efforts.

Gaming theory: Grinding

Grinding is the terminology in gaming that's often applied to elements of tedious, repetitive tasks the player may (in some cases, often) need to accomplish in order to maintain a minimal degree of character power level or character skill competency according to the challenges they're expected to face.
Grinding does have a degree of subjectivity to it depending on the particular tastes, expectations, and how a specific player defines what is fun in a game. In my own case, for example, I often consider nearly all combat elements to be grinding unless it directly affects the outcome of a game's storyline yet I often enjoy the  logistics and industry elements of a number of games which a lot of my friends simply cannot stand.

Cons
Unnecessary padding of game duration (though many times considered a pro, especially in subscription-model Massively Multiplayer Online games (MMOs)
Lacking entertainment value (subjective)
Emphasizes and reinforces character skill over player skill (more in commentary section below)

Pros
Aids development of reflexive player patterns (quicker player response times for common strategies)
Emphasizes and reinforces character skill over player skill (again, more in commentary section)
May be used to establish a period of learning strategies, features, etcetera with repetition of new elements

Commentary
There is both good and bad that can be said about a game that focuses more on character skill. To its benefit is how it allows for a slightly more fair playing field for casual or less experienced players, something that many MMOs will need to thrive due to their reliance on a much wider player-base. It is also a heavily criticized element of gameplay, for the same reasons, by hardcore players who often feel lacking challenge from games that implement grinding systems and which essentially handicaps development and implementation of more advanced strategies.
An important thing to keep in mind about grinding is that it tends to be more rewarding when considered as a rate equation (rewards over time) rather than a work equation (rewards over effort). This means that low-end efforts tend to pay off a lot better than high-end efforts due to lower chance of failure and a steadier but less impressive income of rewards. These sorts of efforts support the practices known as item or gold farming (randomized reward game elements have a higher output with higher numbers of  weaker opposition defeated than fewer but higher quality opposition) and is sometimes why the practice of grinding is called xp farming.