Dice Used in Games  

Contents

Introduction

Table of Dice Types

Using Cards as Dice

Probability Distributions

Popular Tabletop Games and the Types of Dice Used in Each

Emulation and Fairness Techniques

List of Dice Patents (until ca. 2007)

Glossary and Acronyms

Bibliography


Introduction

I came to D&D rather late (1981) but they were still using only the five Platonic solids for dice. The dice pictured here were sold separately in the very early days, but by the time of Holmes AD&D, dice came in the box or a coupon was provided (dice free with purchase, but not physically inside the box).

''original TSR poly dice''; recent reproduction
"original TSR poly dice"; recent reproduction

As you can see, there's no d10, and the d20 has numbers 0 to 9 twice, which had to be hand-coloured in contrasting colours to use it as a d20. The owner of the d20 on the left used red and black. Later (exemplified by the modern reproduction on the right) half of the d20's numbers had a + sign. The colours were always as shown here: yellow d4, orange-red d6, green d8, blue d12 and white d20. When a second d20 was added, it was pink.

Non-cube polyhedral dice are ancient. There were tetrahedral d4 dice in Sumeria, 2600 BPE. here is a d20 from Ptolemaic-era Egypt (see [18]). From multiple views available online, it is clear the labels are arranged in alphabetical order: Α, Β, Γ, Δ, Ε around one "pole", Ζ, Η, Θ, Ι, Κ, ..., Ν, ... around the equator, Ρ, ..., Υ around the other pole. Ptolemaic-era Egypt also had d12 (rhombic dodecahedron) dice, and Romans had d20s (see [19] and [17]).

I vaguely remember gamers starting to use d10s whilst I was in college, but the common design (pentagonal trapezohedron) dates back at least to the 1904 d10 patent. Octahedral d8s with a poker-related design were used in the late 1800s.

Table of Dice Types

For now I am just giving links to the a huge, slow scroller at dicecollector.com. If you follow one of these links, you may have to use the "X" button or "Stop Loading" command because the page contains a stunningly large number of inline images.

d3 examples rock-paper-scissors (massively improved on by Eric Harshbarger's Go First dice)
d4 examples tetrahedron oldest known confirmed dice are tetrahedral d4s used in The Royal Game of Ur
d5 examples
d6 examples cube known to general public in all cultures ; historically ubiquitous with massive variation; very easy to manufacture ; 3d6 is roughly normally-distributed centred on 10.5, supporting its use for character attributes in RPGs, skill checks in GURPS, etc.
d7 examples day of the week
d8 examples octahedron
d9 examples first digit of a number (but see my Benford law dice)
d10 examples bipyramid single digits ; 2d10 (one labelled 00-99, the other 0-9) for percentile-based event outcomes in BRP, GURPS, etc. ; systems with dice-pool combat e.g. Exalted
d11 examples
d12 examples dodecahedron month/zodiac ; time of day (hour) ; Go First dice for four players (Eric harshbarger)
d13 examples sometimes simulated with playing cards
d14 examples
d15 examples
d16 examples
d17 examples
d18 examples rhombicubotahedron (w/ triangular bits rounded and convex)
d19 examples
d20 examples icosahedron event resolution in RPGs, notably D20 System ; many ancient (Rome, Ptolemaic Egypt, etc.) d20s are known. ; here is a guide to all the different number layouts.
d22 examples
d24 examples deltoidal icositetrahedron time of day (hour)
d25 examples
d26 examples letters of the (Roman) alphabet
d28 examples
d30 examples rhombic triacontahedron day of month
d32 examples
d33 examples
d34 examples
d36 examples simulate 2d6 in a single "roll"
d40 examples
d48 examples
d50 examples
d60 examples deltoidal hexecontahedron time (minutes)
d96 examples
d100 examples golf-ball-like percentile rolls for event outcomes in BRP, GURPS, etc. Lou Zocchi's Zocchihedron debuted in 1985 and has been steadily improved, but the two-d10 method remains more practical
d120 example disdyakis triacontahedron permutation of five things

Using Cards as Dice

In lieu of dice rolls, an ordinary deck of playing cards can be used to generate random numbers. Just shuffle the cards, and draw a card to get a random number. The deck can be customised for the needed dice mechanics of a game. For example, remove all face cards (but keep the aces) to get a deck with 40 cards (10 per suit). Then you can draw n cards to simulate rolling nd10 (an Ace is 1, 2-10 have face value).

This has the unique and useful property that exceptional events (critical failures, etc.) can only happen as many times as there are cards of the corresponding value. This avoids the experience of having dice roll a crit (fail or success) so often that it seems unfair, or uncertainty about dice being loaded or otherwise physically defective.


Probability Distributions

The probability distributions most relevant to dice are:

For special applications when the results need to fit some kind of power law (examples: Gibrat's law for village/town/city sizes; Zipf's law for many types of demographic data, and for vocabulary and word lists; the Gutenberg-Richter law for earthquakes) a reciprocal distribution is needed. This can be achieved by using a uniform distribution to generate the logarithm of the needed quantity, or more directly using my Benford's law dice.


Popular Tabletop Games and the Types of Dice Used in Each

Games are listed alphabetically by their most common title. Only games that actually use dice are listed. Special dice refer to a footnote below.

The number of dice listed are the quantity needed for play, though there may be more for convenience or at the options of players. For example, Backgammon usually has two pairs of dice, one for use by each player, but only 2 are actually needed; but in Risk all five dice (3 for attacker, 2 for defender) are needed at the same time.

The d100 column has a number if the game uses percent/percentile, which can be accomplished with a true d100 e.g. the "Zoochihedron", or more typically with two d10s one of which is labeled 00-90. Numbers in the "d10" column mean that the game uses one or more single d10s; note that the original D&D had such a use but instructed players to accomplish it with the d20.

I used List Challenges' 76 Best Board Games for my initial list. At my discretion I added more dice-heavy games (particularly unique RPG systems).

game search
hits
d4d6d8d10d12d20d100 oddspecial notes
Axis & Allies 333 lots 9
Backgammon 415 2 8
Battlestar Galactica 418 1
BRP (Chaosium d100) system 307 1 3 1 1 1 yes 3 4
Call of Cthulhu 681 1 3 1 1 1 BRP
Catan 410 2
D&D (original) (694) 1 3 1 1 1 6
D&D (later, e.g. AD&D, 3rd edition) (694) 1 4 1 1 1 1 1 3 7
D20 System system 640 1 3 1 1 1 3 1 3 5
Deadlands 68.9 5 5 5 5 5 1 16
Descent: Journeys in the Dark 560 yes
Dungeon Crawl Classics 312 1 3 1 1 1 3 1 yes D20, 10
Exalted 208 30 11
Fantasy Calvinball 4.54 11 9 10 13 15 10 5 17 yes 14
Freeblades (DGS Games) 52.5 1 1 1 1 1 1 yes 13
GURPS system 1070 3 12
Life 33500 1 2
Magic: the Gathering 918 3 1 1 yes 17
Monopoly 629 2 2
Numenera (and Cypher System) 1 1 1
Pathfinder 509 1 3 1 1 1 3 D20
Risk 3980 5
Shadowrun 324 lots
Trivial Pursuit 417 1
Twilight Imperium 250 4 15
World of Darkness 1080 30 11
Yahtzee 443 5

2 : Similarly to The Game of Life and Monopoly, several other games use 1 or 2 standard d6 merly to determining the opportunit(ies) presented to the player by controlling how many steps they can move along a track. These include: Arkham Horror (original 1987 version), Dungeon!, Headache, Pictionary, Trivial Pursuit, Trouble.

3 : In most of the FRP systems that owe their existence to D&D, more dice can be useful in certain situations, and even more dice can be useful in even rarer situations. This thread on Reddit gives a good sampling of the many and varied opinions. For example, late in a game one player's character might find a frequent need to roll e.g. 5d8 for damage. The need for lots of dice is more common for the DM/GM. Since it's hard to draw the line, I've just given the numbers that seem to be the essential minimum.

4 : As described at [28], BRP can involve all the standard gaming dice, and even gives instructions for rolling odd dice like d3 or d5; however in practice all that a player will need is 3d6 to roll up characters, a weapon damage die (most always d4, d6, d8, or d10), and percentile dice for everything else. Each player would want their own d% but the whole group can share a single set of dice the others.

5 : D20 System is the present-day descendant of the original Dungeons and Dragons, which was wold to Wizards of the Coast by its original creators Arneson and Gygax. The System Reference Document (PDF here) describes how third-party modules can be designed so they fit into the material sold by Wizards of the Coast. Page 4, "dice", lists the dice needed to run a player character: d4, d6, d8, d10, d12, d20, and d100 (as either percentile or percentage).

6 : The original Dungeons and Dragons assumed only the five Platonic solids — the function of the d10 was accomplished with the d20, which was labeled 0-9 twice. Players typically got a cheap set of five Platonic solid dice, always coloured the same (yellow d4, red d6, green d8, blue d12, white d20) and used general-purpose gambling dice (e.g. borrowed from another game) for their 3d6. Later D&D sets included dice, and eventually the d20s had a + sign on one set of 0-9. The pentagonal trapezohedron d10 didn't begin to enter the D&D community until about 1980.

7 : d10 dice numbered 0-9 and a true d20 (numbered 1-20) appeared soon after D&D became a huge success. Thes use of "4d6 keep 3" began with the 3rd edition. Some other dice-related changed are mentioned here.

8 : Backgammon has a "doubling cube", which looks like a d6 labeled in powers of two (2, 4, 8, 16, 32, 64), but which is not used as a source of random chance.

9 : (The following also applies to Shadowrun):

In Axis&Allies each unit (troops, artillery, tanks, etc.) rolls a d6. You can roll for all units of identical attack value at once, or for all units at once if you have enough dice of multiple colours. The game includes 6 white and 6 black, but discussions of this question suggest that about twice that many would be a reasonable compromise between expense and convenience.

10 : A comment here claims, "Dungeon Crawl Classics's die chain uses d3, d4, d5, d6, d7, d8, d10, d12, d14, d16, d20, d24, and d30". The unusual dice are used for the same sorts of things, but offer more granularity. For example, a level-1 thief rolls 1d3 for Luck, L2 Thief rolls 1d4, L3 Thief rolls 1d5, etc.; and similarly for the Warrior's attack modifier (which is randomised per each attack).

DCC, from Goodman Games, is at attempt by Joseph Goodman to restore the design simplicity, "look and feel", sense of delight and inspiration by Appendix N, and above all a return to the original D&D balance between gameplaying, narration, and simulation (see GNS theory). Goodman had a passion for "funky dice" and considered it a part of the wonder experienced by players new to D&D in the late 1970's [27]. DCC began as modules for the D&D-descended D20 System, with the first module using the funky dice appearing in 2006.[24]

11 : Exalted, World of Darkness, and all other games from White Wolf use a d10-based "dice pool" resolution mechanic for everything. You determine how many dice to roll based on attributes/skills and applicable penalties, etc.; you roll all the dice at once, and anything 8 or higher is worth 1 "success"; the result of the dice roll is simply the number of successes, which directly determines the resulting amount of damage. Earlier editions involved multiple dice-rolls per attack attempt, later editions do it all in a single roll and have limits that reduce the need for quite so many dice. Game shops sell 10d10 sets; a player could do with one set, but players typically buy two or three. Here is a representative set of opinions.

12 : 3d6 is really all you need for any campaign in a GURPS system. Some players might have a second set so they can have one set they roll for skill tests and another for combat, but even that is viewed by some as excessive. Some representative opinions are at [25].

13 : Freeblades uses: d4, d6, d8, d10 (but not percentile), d12, d14, d16, d20, d24, and d30.

14 : Numbers shown are representative ("The most important part of the rules is having lots of dice."), higher numbers better. MS Paint Adventure's CDDC [22] was made for Fantasy Calvinball.

15 : Combat in Twilight Imperium can be streamlined by pre-colouring a large number of d10s dedicated to each possible combat value. For example, a cruiser with no bonus/malus has a combat value of 7; it would use dice that have the numbers 7, 8, 9, 0 painted in red. This thread on BoardGameGeek includes some representative opinions.

16 : The original Deadlands seems to need lots of dice, though I haven't found much about it as it's a less widely-known game. this has one relevant comment. Deadlands has also been adapted to use other dice mechanics, such as D20 and GURPS, but these adapted versions lose much of the appeal of the original.

17 : Magic: the Gathering players often use a d20 as a life counter. Called a "spindown d20", the numbers are arranged in numerical order so it's easy to find the next number as you count down. Some players use a d6 as a randomising agent when deciding at which creature to direct a spell, or to keep track of an attribute of a creature whose attribute varies. For example, there is a special d8 marked 1/2 through 8/9 to keep track of the power and toughness of a Tarmogoyf. I have also seen d10s in MTG sets (but unsure if they serve any different type of purpose).

Fundamental Differences in Action Resolution Mechanics

Among the games that use a dice-driven system for resolving actions (like combat), variants have arisen in an attempt to use dice in a way that more realistically reflects the probabilities of success/failure in a wide variety of attempted actions.

To illustrate the problem, imagine that a character with STR 8 (a fair bit less than typical strength) engages in a pushing contest with a character of STR 18 (the strongest human possible, i.e. an Olympic gold-medalist weighlifter). Their STR difference is 10, and in the real world the outcome would be certain. Nevertheless, the D20 System would give the strong character a +10 strength bonus as compared to the weakling, and ask them both to roll a d20: if the weaker character's roll exceeds the opponent's roll by 11 or more, the weaker character wins!

Similarly, pit both players against an equal challenge: Suppose a given door's Break DC is such that the strong character needs to roll a 5 or above to break it, so their odds of success are 75%; but the weakling would have to roll a 15 or above, which is still a 25% chance of success at the same task. Most games would allow them to try again, and both characters would have a comparable chance of success if the weak character makes 4 or 5 attempts. This seems contrary to real-world intuition.

Modified systems attempt to deal with this by using different dice distributions, e.g. 2d10 or 3d6 instead of d20; and altering how the success threashold is computed. If the first example (pushing contest) were done with 3d6 rolls and the same threshold (weaker player must exceed stronger player by 10 or more), the odds of success for the weak player would be much lower and arguably more realistic.

Smaller differences are evident in e.g. Numenera, which uses a D20-like difficulty check but has the GM announce the DC (difficulty class) to the player(s) rather than keeping it secret. The players then know how hard a challenge they are up against and roll their own d20 to find the result. In most games descended from D&D, in which the DM/GM effectively keeps most of the probabilities secret, players can experience a sense of unfair treatment; Numenera's unusual mechanic addresses this.


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