When it comes to playing games, be they traditional or electronic, there are few terms more loaded than "random chance." The reason why is simple: most players want to feel like they have some degree of control over whether they win or lose. That's why games that depend entirely on chance, like the Luck-Based Mission, are generally considered bad game design: a game where everything is determined at random and presents the player with no meaningful choices isn't much of a game at all.
On the other hand, random chance is a very important element of game design. The vast majority of games have some form of "randomizer" element — be it dice, cards, or a Random Number Generator — designed to introduce some level of unpredictability to the proceedings. Randomizers prevent every play session from being exactly alike, prevent situations where only the "best" or most experienced player ever wins, and helps the game maintain a decent degree of challenge when replayed.
One especially common way in which randomizers are used to keep gameplay fresh is the way most Role-Playing Games handle combat. In most tabletop RPGs, the strength and efficacy of an attack is determined by a roll of the dice. In most turn-based Video Game RPGs, a random number generator determines whether or not the attack will land, while another determines the exact number of Hit Points' worth of damage it will deal. Games such as these have a Random Damage System — a combat system in which the damage inflicted by an attack varies randomly, to one degree or another.
Keep in mind that "Random Damage System" rarely means completely random — a system in which every attack does a completely arbitrary amount of damage would make every fight nothing more than a game of chance. Most Random Damage Systems assign a range of possible damage amounts to an attack or weapon, and select numbers randomly from that range. For example, your Infinity +1 Sword may have a range of 9000-9999 Damage Points, and each strike from that sword deals a random number between 9000 and 9999. The range assigned to the attack may be fairly small, producing a fairly reliable attack whose efficacy doesn't fluctuate all that much. The range could also be huge, which produces an attack that could score a massive amount of damage, or next to none at all.
The above is a fairly simple example; it doesn't take other potential variables into account, such as how much defense the enemy has, and if the attack's damage values vary wildly on one terrain, but only a little on another. Even so, it illustrates the core tenet of the Random Damage System: the amount of damage an attack deals isn't fixed or completely predictable, but it isn't necessarily completely random.
Contrast Fixed Damage Attack, which is an attack that always produces the same amount of damage regardless of context, and Percent Damage Attack, which produces damage equal to a certain percentage of the enemy's current Hit Points. See also Situational Damage Attack, an attack in which the damage dealt varies according to non-random variables.
