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.

1. 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 game's mechanics.

• The player accepts penalties in areas that hamper his character's in game effectiveness least.

  • The player makes tool and equipment choices that give the most benefit as measured by the game's mechanics.

1. Example: The Fighter chooses the most possible Strength and Constitution, and accepts that his Intelligence or Wisdom scores will be suboptimal.

2. 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).

2. 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.

It began with going into a "Dungeon" (the areas underneath a fortress) during the development of the game Dungeons and Dragons.

According to Gary Gygax (in an interview with Dungeon #112), the first dungeon crawl¹ was part of a wargame in which the invading force entered the enemy's castle through a former escape tunnel dug from the fortress's dungeon. The group had so much fun with this scenario that it was repeated over and over with increasingly complex dungeons until the wargame aspect of the game was dropped in favor of exploring the dungeon.

Origin in Publication: the dungeon is where Underground adventures take place

The dungeon as a place to conduct an underworld adventure is spelled out in the opening paragraphs of Volume III of the Original Publication of Dungeons and Dragons Wilderness and Underworld Adventures on page 3. (© COPYRIGHT 1974 • TACTICAL STUDIES RULES, by Gary Gygax and Dave Arneson).

THE UNDERWORLD
Before it is possible to conduct a campaign of adventures in the mazey dungeons, it is necessary for the referee to sit down with pencil in hand and draw these labyrinths on graph paper. Unquestionably this will require a great deal of time and effort and imagination. The dungeons should look something like the example given below, with numerous levels which sprawl in all directions, not necessarily stack neatly above each other in a straight line.

Why Dungeons and Dragons?

The "Dungeons and Dragons" game was going to be called "The Fantasy Game" as far back as 1971. The founders of TSR had difficulty in selling the game initially. Gary Gygax had been working in game rules and fan magazine publishing since about 1965. He and his early partners (Arneson, Kaye and Blume) doubtless knew how important a title/name/brand was in getting a product to market, even the small market of miniatures and wargames enthusiasts. It was renamed in 1973. The game rules (cf. above) indicate that "dungeon" had become standard jargon during the game's development.

• Note: Alliteration is an old tool in publishing, witness how headlines get written in newspapers and gossip magazines in the golden era of print media.

Dave Arneson was up in St. Paul and not with me when I wrote down two single-word lists of possible titles for the game. I did ask my player group which they liked, also queried my family. My youngest daughter Cindy, was adamant that I must use "Dungeons & Dragons." As a number of others were in agreement with that choice, and I liked the alliteration, that's what I went with when I took the mss. I had written to the printer in early December 1973. ~ Gary Gygax

Two Meanings of "Dungeon" in the game's context

By the time of the game's first publishing run, dungeon had two connotations in this new sense:

1. the generic setting for an underworld adventure and is below ground, dark, and dangerous

2. the D&D campaign/setting run by a given person.

   The second usage is probably as old as the playtests Arneson's playing group, and later Gygax undertook (early 1970's) in the adventures under Arneson's Blackmoor castle.

This jargon (unique to a small community of gamers) is seen in the TSR newsletter The Strategic Review #6 (Volume II No. 1, Feb 1976) on page 7 in one of E. Gary Gygax' articles:

DunDraCon I: Update

Some of the misleading advertising has been clarified in regard to the “Fritz Leiber” dungeon that has been advertised. The truth of the matter is that there exists a sprawling palace, complete with underground, that has been constructed/ populated by a friend of Mr. Leiber’s, with his aid and direction. It is said to contain hazards and treasures drawn from his stories. Fritz has also agreed to attend for a couple of hours, at least, on one of the two days. (We have been told the preceding facts, and have accepted them in good faith.)

The jargon had apparently become so ingrained -- among the people playing in the settings Arneson (Blackmoor) and Gygax (Greyhawk) used to playtest original adventure milieus -- that the authors saw no need to explain why they used "dungeon" as opposed to something else.

In an interview with theonering.net Gygax said that his initial vision was that this game would be for gamers. It took a little while for the TSR team to see, and capitalize on, its broader appeal. When the initial set of rules was published, it was a case of "gamers publishing for gamers (and we all speak in the same jargon so we don't need to explain it)."

Personal Experience: the second usage had spread, and was present as far back as 1975, when I first began to play Dungeons and Dragons. We would ask one another "whose dungeon are we playing in?" to decide who would be the referee/dungeon master for the next session. It obviously preceded our experience -- we lived in Virginia and the game spread from the Wisconsin-Chicago area (in our case, through a game store where a friend bought the first boxed set any of us had seen). There was no internet to spread memes or jargon at the speed that they now spread.

Per @Lexible's comment on this not always translating well into other languages, like the French edition called Donjons et Dragons ... from the Wiktionary etymology article.

The word "dungeon" comes from Old French donjon (also spelled dongeon), which in its earliest usage meant a keep, the main tower of a castle. The first recorded instance of the word in English was near the beginning of the 14th century when it held the same meaning as donjon. In French the term donjon still refers to a "keep", and the term oubliette is a more appropriate translation of English "dungeon". Donjon is therefore a false friend to "dungeon" (for instance, the game "Dungeons & Dragons" is titled "Donjons et Dragons" in its French editions).

Another example is Brazilian Portuguese, Caverna do Dragão (i.e. "Cave of the Dragon," or "the Dragon's Cave"), which doesn't include a cognate of "dungeon." Crossing languages barriers often leads to idiomatic rather than literal translations.

¹Per @RobertF a dungeon crawl has developed into a standard gaming model where a band of diverse adventurers (wizard, fighter, elf, dwarf, ranger, etc.) battle monsters in an underground setting, including a final boss monster -- a literary template being the Mines of Moria from J. R. R. Tolkien's The Fellowship of the Ring.