I'm thinking of doing a study/paper/educational-piece about different dice rolling systems in RPGs and other games. I've played RPGs in the past but it's been years so I wanted to be sure I knew the common terms and see if you all could briefly describe some of the common (or uncommon) systems for using dice. What'd I'd really love to know are examples of specific games, rolls, and the contexts in which those rolls are used. For example, in such-and-such-game you make this kind of roll for combat.

What I know of so far are

  • Target Rolls: Roll some number of dice and sum them attempting to make or break some target. You may also add or subtract some value to the dice roll. I believe I've seen instances of people dropping low or high rolls from the set as well.

  • Dice Pools: Roll some number of dice and treat each dice individually. You might check to see if some number of the pool are at or above a target value.

I'm sure I'm missing something and I know I'm missing specific games and contexts to associated with these types of rolls. I also know that this is a very broad question. I'm not looking for a comprehensive list, just some common examples and maybe some more exotic examples as well.

(Paper Clarification) The goal of the paper isn't to survey the dice systems but to discuss the mathematics of dice/dice systems in general. These systems will act as real-world examples to help motivate the math.

  • 1
    \$\begingroup\$ The discussion in this question may be of interest: rpg.stackexchange.com/questions/15971/… \$\endgroup\$
    – Soulrift
    Jan 8, 2013 at 22:18
  • 3
    \$\begingroup\$ Here's how I would research this. Find a dice-roller program under ongoing development and improvement → look at the rolls available; find its user forums → read about the missing roll types that users want (and have wanted in the older posts about previous versions) for their games. You'll get a more complete answer and a better "in the trenches" look at current terminology than here. And I don't often say that elsewhere would give better answers! (This is how I learned about a lot of odd roll types during the heyday of Google Wave and the development of dice bits for it.) \$\endgroup\$ Jan 8, 2013 at 22:30
  • 1
    \$\begingroup\$ That's not quite fair CatLord, this sounds like more of a voluntary thing, and he's asking for help with research. Besides his motivations, it's a good question anyway. \$\endgroup\$
    – user5834
    Jan 9, 2013 at 1:22
  • 2
    \$\begingroup\$ This threatens to be a list question as there are 100k different dice rolling methods out there. If anyone thinks they can answer this without resorting to a list do; otherwise we may need to close this. \$\endgroup\$
    – mxyzplk
    Jan 9, 2013 at 2:49
  • 2
    \$\begingroup\$ Sorry about the list question thing. I'm used to Theoretical CS where we have a tag for big-list questions and these types of questions are allowed. \$\endgroup\$ Jan 10, 2013 at 2:14

3 Answers 3


Dice Pools

Where in a variable number of dice are used, the number determined by some attribute or combination. Usually, only one kind of die is used.

Roll and Total

The dice in the pool are all totaled before reading, then compared to a target nuber set by difficulty. WEG's d6 system is the best known, but also several other games used similar, including Space:1889 and BTRC's EABA. Axiomatically roll-high.

Roll and Keep

A number are rolled based upon one stat, and a number totaled based upon a different stat. Best known example is L5R, but other games have used the mechanic; EABA uses a roll based upon skill, keep is best 3 in almost all cases, but a trait allows keeping a fourth in some cases. Almost every game using it is roll-high.

Roll, read best only

The dice pool is assembled, rolled, and a single die is read, and compared to a target number. A shocking number of variations on this exist. Savage Worlds is usually 2 dice rolled, 1 being a d6, the other by stat or skill; maximum counts as maximum plus another die. Chronica Feudalis is Skill and tool dice, possibly also a die from an advantage, read best.

Orcworld and Silhouette (Jovian Chronicles, Tribe 8) both have multiples count as more than the face but read as if a single die. In Silhouette, only 6's do that, so a roll of 3 6's is an 8, but a 6 and 3 5's is a 6. In Orcworld, 3 6's is an 8, but 3 5's and a 6 is a 7 (5+2).

Best Two and...

Cortex Plus (Marvel, Smallville) uses 3 or more dice, with the best two roll dice being totaled, and the largest remaining die (number of sides, not roll result) being how much effect was done.

Count Successes

Each die is individually checked against a target number.

Vampire: the Masquerade: in the original appearance, the difficulty set a target number, and the number of dice which exceeded that TN was the quality of the result. Shadowrun also used this model.

World of Darkness in general moved to a fixed TN - tho it varied being either 6, 7, or 8, with difficulty being the number of successes that got ignored.

Arrowflight used a roll-low variation: stat dice for skill or less each, with difficulty modifying the skill.

Fantasy Flight

Mixed pool; grab skill dice by skill, stat dice for stat, difficulty dice for difficulty, etc. Roll them, and read the two-axis results. Successes are cancelled by failure results, advantages/boons are cancelled by threats/banes. You succeed or fail based upon successes, and for attacks, add the number of successes to the damage; the advantages represent side effects. It's possible to fail but have a strong pile of advantage left which results in favorable outcomes. Conversely, it's possible to succeed and have lots of thread/bane results that mean bad things happened to you even tho' you succeeded.

Additional symbols (Sigmar's Comet, Chaos Star in Warhammer; Triumph and Despair in Star Wars) indicate even stronger side effects, but also count as a success.

One Ring

Base is a d12. Each level of skill is an addition d6. Roll and total for TN+ to succeed. Quality is determined by how many 6's rolled 6's, but only if you succeeded does quality matter.

Dice by Difficulty

The difficulty sets the die roll. Almost always, it's been roll and total, then try to hit under a target number. Harder tasks get more dice.

The Fantasy Trip, Traveller T4, and Traveller T5 all use d6's by difficulty.

Alternity is a d20 + another die by difficulty, for skill or less on the total. It ranges from -1d20 to +1d20, then increases by additional d20's.

Fixed Roll systems

Many systems have a set roll of a certain number of dice for almost all rolls.

Roll and add skill

Usually, a target number is set, a roll is made, a modifier from abilities is added, and the total compared.

  • D20 system uses 1d20 + Stat Mod + Skill
  • Interlock (Cyberpunk, Mekton) uses 1d10
  • MegaTraveller uses 2d6+(asset1)+(asset2) with an asset being either a skill's level or 1/5 of an attribute's level.
  • early D&D editions used this for combat rolls. 1d20, add modifiers, beat TN by target armor class and your level.

Roll skill or less

Many games use a fixed roll for a target number or less. Almost all use a target based upon a skill or ability, and adjust the target number for the difficulty.

  • GURPS - 3d6 for skill or less
  • Chaosium - d100 for skill or less
  • FASA Star Trek RPG - d10 for skill or less on "routine actions", d100 for other actions.
  • AD&D and Cyclopedia D&D Proficiencies are 1d20 for skill or less.

Generally, lower rolls are better. Variations exist. Some do crits on doubles, rather than some low fraction of adjusted skill. Warhammer FRP 1E and 2E do this (It's in a supplement for 1E).

High but under

Some use a fixed die, rolling equal to or less than a target number to succeed, but the quality of success is how high the successful die was. Pendragon is one such game. AD&D 2E's Psionics Handbook used a similar mode for Psionics.

Just roll, but spend stats to reroll

A few games you simply roll. The number of dice is fixed, but you can reroll if you fail if you have the stats. One such is the Dying Earth RPG.

Modifications due to rolls

Open Ending

Open ending, also called exploding, is a not uncommon technique. When a particular roll result occurs, additional rolls are made and counted.

  • Whole Second Roll when total is X
    • Rolemaster and derivatives: the trigger condition results in a reroll and add or reroll and subtract. In the case of Rolemaster, a 96-100 on d100 results in reroll and add, and is recursive, so rolls in excess of 500 have occurred in my limited Rolemaster and Spacemaster experience. Certain rolls in RM and SM are "double open ended" - on a low enough roll, roll another d100 and subtract, continuing to go lower with further 96-100 results.
    • Tunnels and Trolls has two different fixed rolls with open ending
      DARO - When the dice show doubles on a saving roll, roll 2d6 again and add them to the total. This recurses, so I've encountered rolls as high as 55.
      TARO - When an attribute throw (on 3d6) is made, if all three dice match, reroll them all and add to the total. This being only in newer editions (5.5 onward), my experience is less, but I've seen throws into the high 50's.
  • Add a die when total is X
    • Decipher's Star Trek and Lord of the Rings - On a natural 12, roll 1d6 and add. This one is not recursive. It applies to attribute generation and to task rolls.
    • Palladium Games - on an attribute generation roll, some open ending is allowed. For a specified 2d6 attribute, on a natural 12, a 3rd d6 is added. For a specified 3d6 attribute, a 16, 17, or 18 allows adding a fourth die, and if the fourth die is a 6, a fifth die may be added. This has a quirk - a 16 result can only occur when the attribute roll specified for the race is not 3d6; attributes specified as 4d6 or 5d6 get no rerolls.
  • Individual dice reroll and add - in many dice pool systems, and in several roll and keep games, the individual die rolling a maximum result rolls again.
    • Prime Directive - each die that rolls a 6 counts 5 plus a reroll. Note that only one "die" is counted, but given that the rerolls count as part of the rerolled die, a single "die" can hit 50+
    • Savage Worlds - An Ace (Maximum on a given die) counts its full value plus the reroll. The best of the 1-3 dice rolled is the result.
  • Special success gets additional dice for successes
    • In World of Darkness, games, each die rolling a 10 may allow a reroll. It counts as a success, and the additional dice are checked for successes.
    • Burning Wheel and derivatives - 6's on the d6 pools may open end in certain circumstances (certain attribute throws, and when fate artha is spent to do so), with further 6's automatically triggering further rerolls. Every rolled die is checked for successes separately.
  • Reroll at bonus
    • Ars Magica's Stress Rolls - on a 1 on 1d10, roll again with a x2 multiplier; this recurses. I've seen rolls into the high hundreds this way. (As an aside, a 10 on the initial roll is 0. No result of 1 is possible, and a 10 can only happen on a roll of 1 with a reroll of 5.)
    • D&D 3E - There is an option that a Natural 20 that fails may be rerolled at 1d20+10; this may also be allowed to recurse, so a natural 20 on the second roll generates a total at 1d20+20. This allows for spectacularly high rolls.

Minimum Roll counts nothing

Several games count 1 as 0. Several others specify a natural minimum roll fails, or has side effects.

  • Cortex Plus System games - in this keep best 2 dice system, a 1 not only counts as a 0, but also triggers a side effect, even if the 1's are not the best dice.
  • Tunnels and Trolls - on a Saving Roll of 2d6, a [1][2] or [1][3] on the 2d6 fails, even if the attribute alone would be sufficient to meet the target number.
  • MegaTraveller - A natural 2 that fails is a fumble; a natural 2 that succeeds is unaffected
  • d6 System - Most d6 system games have a "wild die". If the wild die is a 1, and the pool fails, it's a fumble; if the pool total would succeed, the highest die in the pool is lost and the 1 counts as a 0


In several games, a "cap" applies in certain circumstances, meaning that dice that roll in excess of the cap are either read as the cap or read as 0.

  • WEG's Star Wars game has used both capping modes.
    • Under 1st edition with the Rules Companion, when scaling applies, dice are capped on the disadvantaged side of a roll. For example, a starfighter firing at a capital ship has its dice capped at 5 for dodging and range changes, but the fighter's weapons are capped at 5's to damage a capital ship. Any individual die in excess of the cap counts nothing. A character firing at a starship, the to hit is unaffected, but the damage dice cap at 2's while the ship's hull is not capped. This edition has no wild die.
    • Under 2nd edition (but not revised & expanded), the caps are lower, but count as the cap when exceeded. So a starfighter firing at a capital ship, the dodge roll caps at 2, with 3-6 counting as 2, but the damage roll the starfighter's damage caps at 3 while the ship's hull isn't capped.
  • Several heartbreakers have used a fixed roll capped by a skill value in opposed resolution. Most of these are relatively unknown.
  • Quite a few games cap results of modified throws. AD&D 1E, for example, caps attribute throws at 18 for most player-character races, despite positive modifiers.
  • Most games have a "floor" on modified damage rolls - some set the floor at 1, and almost all the rest at 0 - mostly because the concept of "negative damage" is almost nonsensical.

Dice Substitutions

Several games use other methods to replace dice.


Cards can be used as direct dice replacements in all of the above modes.

Sometimes they can add additional aspects besides just the normal modes. The most important is that card draws have memory effect - if you drew a 2-heart, you cannot draw a 2-heart again until a shuffle, so the odds change through play. The net effect is to reduce the randomness.


A number of games replace dice rolls with Rock-Scissors-Paper. The mechanics of Masquerade (Live Action WoD) are very similar to those of the Dying Earth, but using RSP in-place of the die roll, and spending attributes to reroll.

Point Pools

Some games use point pools in lieu of dice. Want to succeed? Spend enough points on it. Some use pools figured by action, and spent on "attack" and "defense" sides; others the pools refresh less, say, per scene or per session, so you ration more carefully.

Weird use

Fiasco uses the dice on the table for various table lookups at key points in the game.

Dark Realms uses non-linear results - roll, look up on the table, find the result points. The table isn't linear; high rolls are not universally good nor bad. And, given that what a particular roll means varies by the difficulty, no particular number is good nor bad.


For someone looking for dice mechanics, John Kim has described them far better than I can. Worth reading is the PDF book "Design Patterns of Successful Role-Playing Games" on that website. In terms of specific mechanics that I can give examples of:

  • Unknown Armies uses percentile dice, and has a mechanic on certain rolls known as flip-flopping. On rolls that are allowed to be flip-flopped, you could roll a 75, and flip-flop the digits to a 57. You can only flip-flop rolls with certain skills (you have one skill called your obsession skill that can always be flip-flopped) or in certain circumstances.
  • New World of Darkness uses a dice pools of d10s, but also allows you to re-roll any 10s you roll for additional successes. This allows for even very low dice pools to theoretically get large amounts of successes.
  • Don't Rest Your Head uses an unusual variant of dice pools with d6s in that low rolls (1s, 2s, and 3s) are successes, but high rolls dictate the outcome of the scene. This only works because you roll all your dice pools together when making a roll. It leads to situations where you succeed because you rolled more successes than the GM, but the GM had higher die rolls, so you end up with a sort of pyrrhic victory.

I hope that these are sufficient examples, and there's far more written on the specifics of dice rolling on the linked website.

  • \$\begingroup\$ I'd +1 this for that link if I had the rep. That site definitely looks like the kind of resource I've been looking for. \$\endgroup\$ Jan 8, 2013 at 21:57

Here's a few systems. There are generally a few variations amongst each and I've tried to note a few.

D&D (from Basic to Next)

Roll a d20, aim to get lower (usually AD&D 2E and before) or higher than a target number.

White Wolf Storyteller

Roll a number of ten sided dice based on an Attribute+Ability. Each dice that hits the target number is counted as a success. A number of successes are required to succeed. Variations include 1s subtracting successes and more 1s than successes causing a Botch, fixed and variable target numbers for each dice. 10s have different effects in the different variants. Some (Exalted) give you a flat 2 successes and others (New World of Darkness) let you keep rerolling 10s and adding successes.

AEG Roll and Keep

Roll a number of ten sided dice based on Attribute+Ability, Keep a number of dice equal to your Attribute. Add up the kept dice and try to get over the target number. It is possible to Raise (increase) the target number to get more effects, but if you miss the new target number then you fail entirely. 10s explode, meaning you get to roll again and add the new result to the total for that dice (repeating for each 10).

Percentile (Chaosium Basic Role Playing)

Roll 2d10, counting one dice as the tens and the other as the units aiming to roll higher or lower than a target number (normally your skill).

Feng Shui

Roll 1 positive d6 and 1 negative d6. Add them together and compare to a target number.


Roll 4 6-sided dice that each have 2 + symbols, 2 - symbols and 2 blank symbols. Start with your skill level and move it up 1 per +, down 1 per - and ignore blanks.

Fantasy Flight Games (Warhammer Fantasy Roleplaying and the Star Wars Roleplaying Game)

Create a dice pool of dice with varying numbers of sides and symbols. You succeed if you get more Hammers than Swords, get benefits if you get more Eagles than Skulls, get complications if you get more Skulls than Eagles and get weird effects from Chaos Stars and Sigmar's Comets. Success/failure and benefits/complications can happen independently of each other in this system.

Deadlands/Savage Worlds/Cortex

Your level of skill or attribute determine the type and number of dice you get to roll, aiming to beat a target number.

White Wolf Mind's Eye Theater

Play Rock/Paper/Scissors

  • \$\begingroup\$ About the only one I can see you missed is the original Deadlands mechanic - Dice Pool, constructed by using attribute for size of die rolled and skill for number of dice, exploding dice, totalled to try and hit a target. \$\endgroup\$
    – YogoZuno
    Jan 9, 2013 at 0:51
  • \$\begingroup\$ You forgot the explosions in Feng Shui! The relatively small die size makes Sixes fairly common, and each time you roll one, you roll that positive or negative die again and total them up. This leads to a potentially infinite scale of values with a strong bias towards zero. \$\endgroup\$
    – GMJoe
    Jan 9, 2013 at 3:36
  • \$\begingroup\$ Well, if you want to be complete with explosions, Deadlands dice also explode. The Rolemaster d100 system was open-ended as well, as was the original Star Wars d6 system. \$\endgroup\$
    – YogoZuno
    Jan 9, 2013 at 8:13

Not the answer you're looking for? Browse other questions tagged .