History MediaNotes / Dice

Dice[[note]]"Dice" is a plural; the proper singular form is "die". The word "dice" is however quite commonly also used for a single die, not least because unlike "die" it cannot be confused with a common English verb that [[NeverSayDie the squeamish find uncomfortable to use]].[[/note]] are ubiquitous low-tech [[UsefulNotes/RandomNumberGenerator randomness generators]] that have been in continuous use as [[GameplayRandomization gaming aids]] for well over ''[[OlderThanDirt four thousand years]].'' Their basic design exploits the inherent imprecision of human movement (of the hand rolling the dice) and various isohedral symmetries (most commonly, those of a cube) to produce a uniform distribution of random numbers, which, in turn, can produce near-normal (a.k.a. "bell curve") distributions by rolling many dice at once and summing up the results.

Lastly, many games come with custom dice, although these are usually just re-skins of regular dice with non-numeric faces rather than truly unorthodox shapes. Perhaps the most iconic of these are the "UsefulNotes/{{Fudge}} dice", denoted as '''dF''', which are regular d6s that have plus, minus, and blank faces (two of each) instead of numbers on them.

|| '''2d6''' ||Bell-curve between 2 and 12, skewed towards 7 ||''Monopoly'', Craps, ''TabletopGame/{{Catan}}'', UsefulNotes/PoweredByTheApocalypse ||

|| '''4dF''' ||Bell-curve between −4 and +4, skewed towards 0[[note]]stochastically equivalent to a 4d3−8[[/note]] ||''UsefulNotes/{{FUDGE}}'', ''UsefulNotes/{{Fate}}'', and the latter's many offshoots ||

* '''d4''' (tetrahedron): The only common die that cannot actually roll or land with one side up. Instead, you usually toss it in the air and after it lands, read the number written either near the vertex or near the face opposite to it, depending on design.
* '''d6''' (cube): Easily the most common type, often synonymous with the word "dice" itself.
* '''d8''' (octahedron)

* '''d12''' (dodecahedron)
* '''d20''' (icosahedron)

The dice notation has long become one of the symbols of gaming and of role-playing games in particular, especially ever since Creator/WizardsOfTheCoast had trademarked their UsefulNotes/D20System.

|| '''1d20''' ||Uniform (flat) between 1 and 20 ||UsefulNotes/D20System, ''Dungeons & Dragons'', ''TabletopGame/{{Numenera}}''

|| '''[=NdXkP=]''' ||"Roll N X-sided dice, keep the P highest values, and sum up the results" || 4d6k3 ||

Dice are commonly used in BoardGames to generate random numbers within a certain range in order to [[GameplayRandomization randomize]], for instance, [[RollAndMove how far a player token moves]] on its turn in ''TabletopGame/{{Monopoly}}'' or which tile generates resources in ''TabletopGame/SettlersOfCatan''. Games may also exploit non-uniform roll distributions to make certain outcomes more likely than others: when rolling 2d6, for example, a total of 7 is six times more probable than a 2 or a 12.

|| '''2d6''' ||Bell-curve between 2 and 12, skewed towards 7 ||''Monopoly'', Craps, ''Settlers of Catan'', UsefulNotes/PoweredByTheApocalypse ||

Dice[[note]]"Dice" is a plural; the proper singular form is "die". The word "dice" is however quite commonly also used for a single die, not least because unlike "die" it cannot be confused with a common English verb that [[NeverSayDie many people find uncomfortable to use]].[[/note]] are ubiquitous low-tech [[UsefulNotes/RandomNumberGenerator randomness generators]] that have been in continuous use as [[GameplayRandomization gaming aids]] for well over four ''thousand'' years. Their basic design exploits the inherent imprecision of human movement (of the hand rolling the dice) and various isohedral symmetries (most commonly, those of a cube) to produce a uniform distribution of random numbers, which, in turn, can produce near-normal (a.k.a. "bell curve") distributions by rolling many dice at once and summing up the results.

|| '''2d6''' ||Bell-curve between 2 and 12, skewed towards 7 ||''Monopoly'', ''Settlers of Catan'', UsefulNotes/PoweredByTheApocalypse ||

* ''TabletopGame/UnknownArmies'' often represents mystical shenanigans by allowing or forcing a player to "invert" their d% roll (by swapping the tens and the ones), which has the effect of either saving or screwing a roll, with probability nearly independent to that of making the roll in the first place (basically, its a reroll that doesn't require actually rerolling the dice).

* The German RPG ''TabletopGame/NewHongKongStory'' uses roll-under for opposed rolls in a clever way: when a character is hit in combat (but not {{critical|Hit}}ly), they can roll to evade or to parry (only in melee). Rolling under your own skill lets you half the incoming damage, while rolling under the attacker's roll lets you avoid it completely. Finally, if you crit on a parry roll, you evade all incoming damage ''and'' inflict a small but unblockable amount of damage back on the attacker.

Less common shapes include d2 (also known as "coin flip"; easily emulated by rolling any common die and reading odd results as 1 and even ones as 2), d3 (usually emulated by rolling 1d6, halving the result, and rounding it up), and the so-called "percentile dice" or '''d100''' (also noted as "d%" or "d00"). While the last one is technically available as a physical non-fair die (see [[https://en.wikipedia.org/wiki/Zocchihedron Zocchihedron]]), it is most commonly emulated by rolling 2d10 and reading one die as units and the other as tens. The (cardinally) largest perfectly numerically balanced fair die possible is the d120 or [[http://thedicelab.com/d120.html disdyakis triacontahedron]].

Lastly, many games come with custom dice, although these are usually just re-skins of regular dice with non-numeric faces rather than truly unorthodox shapes. Perhaps the most iconic of these are the "TabletopGame/{{Fudge}} dice", denoted as '''dF''', which are regular d6s that have plus, minus, and blank faces (two of each) instead of numbers on them.

|| '''4dF''' ||Bell-curve between −4 and +4, skewed towards 0[[note]]stochastically equivalent to a 4d3−8[[/note]] ||''TabletopGame/{{FUDGE}}'', ''Fate'', and the latter's many offshoots ||

|| '''2d6''' ||Bell-curve between 2 and 12, skewed towards 7 ||''Monopoly'', ''Settlers of Catan'', TabletopGame/PoweredByTheApocalypse ||

* ''TabletopGame/DungeonsAndDragonsFifthEdition'' has streamlined the older editions' plethora of situational 1d20 modifiers into the Advantage/Disadvantage mechanic, where the player rolls 2d20 and keeps the highest or the lowest result, respectively. Statistically, this is the equivalent of shifting the mean by ±3.325[[note]]from 10.5 to 13.825 and 7.175, respectively[[/note]] and the median, from 10 and 11 to 6 and 15, respectively.[[note]]The modes are trivial: respectively, 20 and 1.[[/note]]

|| '''3d6''' ||Bell-curve between 3 and 18, skewed towards 10 and 11[[note]]10.5, to be exact[[/note]] ||''TabletopGame/{{GURPS}}'', ''TabletopGame/DragonAge'', [[HonestRollsCharacter Statgen]] in ''[[TabletopGame/OriginalDungeonsAndDragons OD&D]]''[[note]]the newest editions instead suggest 4d6k3 (see below) to randomly generate stats, which produces a slanted bell curve skewed towards 12 (mean, median) and 13 (mode)[[/note]] ||

* ''TabletopGame/DungeonsAndDragonsFifthEdition'' has streamlined the older editions' plethora of situational 1d20 modifiers into the Advantage/Disadvantage mechanic, where the player rolls 2d20 and keeps the highest or the lowest result, respectively. Statistically, this is the equivalent of shifting the mean by ±3.325[[note]]from 10.5 to 13.825 and 7.175, respectively[[/note]] and the median, from 10 and 11 to 6 and 15, respectively[[note]]the modes are trivial: 20 and 1, respectively[[/note]].

* ''TabletopGame/DungeonsAndDragonsFifthEdition'' has streamlined the older editions' plethora of situational 1d20 modifiers into the Advantage/Disadvantage mechanic, where the player rolls 2d20 and keeps the highest or the lowest result, respectively. Statistically, this is the equivalent of shifting the mean by ±3.325[[note]]to 13.825 and 7.175, respectively[[/note]] and the median to 6 and 15, respectively[[note]]the modes are trivial: 20 and 1, respectively[[/note]].

* ''TabletopGame/DungeonsAndDragonsFifthEdition'' has streamlined the older editions' plethora of situational 1d20 modifiers into the Advantage/Disadvantage mechanic, where the player rolls 2d20 and keeps the highest or the lowest result, respectively. Statistically, this is the equivalent of shifting the mean by ±3.325[[note]]to 13.825 and 7.175, respectively[[/note]] and the median to 6 and 15, respectively[[note]]the modes are trivial: 20 and 1, respectively[[/note]].

* ''TabletopGame/DungeonsAndDragonsFifthEdition'' has streamlined the older editions' plethora of flat modifiers into the Advantage/Disadvantage mechanic, where the player rolls 2d20 and keeps the highest or the lowest result, respectively. Statistically, this is the equivalent of shifting the mean by &plusminus;3.325[[note]]to 13.825 and 7.175, respectively[[/note]] and the median to 6 and 15, respectively[[note]]the modes are trivial: 20 and 1, respectively[[/note]].

* 1d20: The core mechanic of the UsefulNotes/D20System and later editions of ''D&D'' involves this, as does the (unrelated) one of ''TabletopGame/{{Numenera}}''.
* 2d6: ''Monopoly'', ''Settlers of Catan'', and every game TabletopGame/PoweredByTheApocalypse.
* 3d6: The core mechanics in TabletopGame/{{GURPS}} and the [[TabletopGame/DragonAge AGE system]], as well as [[HonestRollsCharacter statgen]] in ''OD&D''.
* 4dF[[note]]stochastically equivalent to a 4d3−8[[/note]]: The core mechanic in the original ''TabletopGame/{{FUDGE}}'', its successor ''FATE'', and every game based on the latter's many editions.

A slightly modified roll-over can be used for '''opposed rolls''', where another player's roll replaces the target number -- in other words, the player with the highest total wins. Although opposed rolls can be based on roll-under, too, they usually require additional tricks to factor in the contestants' skill levels. An opposed roll can involve multiple players (for instance, everyone at the table usually rolls for ActionInitiative at the same time), and they don't even have to all roll the same (number of) dice, depending on the system. Some game systems (e.g. ''TabletopGame/{{Sorcerer}}'') don't have unopposed rolls at all and instead frame inanimate and even intangible obstacles as if they were hostile {{NPC}}s.

Dice are commonly used in BoardGames to generate random numbers within a certain range in order to [[GameplayRandomization randomize]], for instance, how far a player token moves on its turn in ''TabletopGame/{{Monopoly}}'' or which tile generates resources in ''TabletopGame/SettlersOfCatan''. Games may also exploit non-uniform roll distributions to make certain outcomes more likely than others: when rolling 2d6, for example, a total of 7 is six times more probable than a 2 or a 12.

* In addition to the standard dice set of a d4, d6, d8, d10, percentile die, d12 and d20, ''TabletopGame/DungeonCrawlClassics'', enhanced rolls are accomplished with "Zocchi dice", a set of non-standard dice originally created for use in wargaming. ''DCC'''s official set alone adds to the standard set with a d3, d4, d5, d7, d14, d16, d24 and a d30.