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.
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.
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.
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, 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  or  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.
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.
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.
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.