Minimization and Maximization for Optimization
Min-max (minmax) comes from using mathematics to solve optimization problems. An example is finding the maximum area for a given perimeter.
- As applied to RPG's (the example will be D&D 5e) min-max addresses
how to best assign ability points, equipment, and skills to get the
most power or effectiveness within the game as reflected in the
Example: The Fighter chooses the most possible Strength
and Constitution, and accepts that his Intelligence or Wisdom scores
will be suboptimal.
The point buy system (you don't get to start with all 18's) in Basic
Rules, page 8, is a good illustration of this. It shows the
difference between the min/max 27 point buy of 15/15/15/8/8/8 versus
the "median" approach of 13/13/13/12/12/12.
- The former has a number
of +2 bonuses, and some -1 penalties, whereas the latter has a
collection of +1 bonuses.
- When the character then applies racial
bonuses, some of those values with increase to +3 in the former, and
+2 in the latter).
- An analogue from regular life: budget your monthly paycheck/income.
Depending on what your needs, desires or goals are, you spend money
where you wish to maximize a goal (such as a either the nicer car or
the nicer apartment) and accept a sacrifice in another area (the not
as nice apartment or car) so that you get the most out of the
limited dollars you have in your budget based on what is most
important to you. (In this example, assume that you are buying a car
with a loan that has a monthly payment).
Thanks to Lucas' suggestion to amplify ...
In systems where characters can add to their base abilities as levels progress, the decision to keep "pumping" a given score, be it Strength, Intelligence, etc, toward it's maximum permissible value to accrue more bonus points (additions to die rolls or ability to set higher DC's for spells) is a form of optimization. If you apply this to the 15 15 15 8 8 8 example above, the player would keep boosting Strength to 17 or 18 or 20 while still not improving upon the sub optimal scores. While this may help the party, in their need for the best fighter they can hope to have by their side, it is a form of optimization in the min/max style.
If the minmax approach is taken as an end in and of itself by one player in a group, it can cause conflict at the gaming table. The GNS theory (Gamist, Narrativist, Simulationist) and the experience of many RPG players suggest that focusing exclusively on mechanics driven optimization is incompatible with the other core elements of role playing.
Full Disclosure: Since 1e, I most often boost Dexterity on any character since it has an impact on initiative, armor class, dodging, and missile weapon use. While an agile cleric or wizard may or may not make sense, I assess the game's system and try to give my player the better chance to act before the monsters, or to not be hit. This is a deliberate choice. It is informed somewhat by books, cartoons, movies and other stories where the main character is just missed by that arrow, narrowly dodges a blow, ducks under the swinging cleaver, barely gets under the closing door/gate that is descending, just catches the swinging vine, etc. In RPG's, the characters are the heroes of the story as it comes to life during the serial sessions of play.
@Trinidad's point on possible confusion in terms is worth adding as a footnote. *In mathematics there are at least two uses of the term: one is regarding to linear programming that may apply to RPG's usage, while the other is related to decision theory that is most applicable to multiplayer game strategy.
The Load (Warning: TV Tropes)
Basically they are someone that is just a 'load' that gets dragged around by the hero, but either doesn't really do anything productive most of the time and the hero has to spend time that they could use saving the world protecting this load from harm.