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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.

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The discussion in this question may be of interest: rpg.stackexchange.com/questions/15971/… –  Soulrift Jan 8 '13 at 22:18
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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.) –  SevenSidedDie Jan 8 '13 at 22:30
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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. –  shatterspike1 Jan 9 '13 at 1:22
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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. –  mxyzplk Jan 9 '13 at 2:49
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Dice programs are quite common now—lots of roleplaying is done online now, what with groups growing up and moving apart but still wanting to play together, and lone gamers who don't have any fellow gamers in even extended driving distance. –  SevenSidedDie Jan 9 '13 at 2:58
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closed as not constructive by mxyzplk Jan 9 '13 at 16:04

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3 Answers

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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.

Dice Substitutions

Several games use other methods to replace dice.

Cards

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

Sometimes they can add additional aspects besides just the normal modes.

Rock-Scissors-Paper

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.

Wierd use

Fiasco uses the dice on the table for varios 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.

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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.

FUDGE/FATE

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

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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. –  YogoZuno Jan 9 '13 at 0:51
    
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. –  GMJoe Jan 9 '13 at 3:36
    
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. –  YogoZuno Jan 9 '13 at 8:13
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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.

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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. –  Logan Mayfield Jan 8 '13 at 21:57
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