Quote from: RobMuadib;512436Oh was thinking in the about cutting down on rolling Whispering Vault deserves a mention as it had all character/player only rolls. Pretty cool game.
 
Also, some discussion of problems related to opposed rolls, because of effectively doubling variance. Was reading about people complaining about FATE,think it was Dresden files, where because of the granular trait range versus the effective 8dF variance, you get some huge variation of results in combat.

Have gone back through and added some notes, though not done as yet. Thanks again! BTW, found that Space 1889 ('88 release) used some target number type stuff too (just in combat) -stumbled across it looking up a Shadowrun 1e review in Dragon to see if they'd mentioned a release date.
 
Not overly familiar with Whispering Vault, though I've seen the player rolls idea - I think Icons has all player rolls as well [d6-d6]; a thread roundabout here somewhere on ICONS suggested rolling 1d for both PC and NPC for opposed rolls as a fix.
I'm surprised that there's a problem though, actually. I'd have thought an (effectively) 8d3 roll would be a very tight bell-curve of results, though I've never sat down and crunched the relative probabilities.

Quote from: Bloody Stupid Johnson;512680Have gone back through and added some notes, though not done as yet. Thanks again! BTW, found that Space 1889 ('88 release) used some target number type stuff too (just in combat) -stumbled across it looking up a Shadowrun 1e review in Dragon to see if they'd mentioned a release date.
 
Not overly familiar with Whispering Vault, though I've seen the player rolls idea - I think Icons has all player rolls as well [d6-d6]; a thread roundabout here somewhere on ICONS suggested rolling 1d for both PC and NPC for opposed rolls as a fix.
I'm surprised that there's a problem though, actually. I'd have thought an (effectively) 8d3 roll would be a very tight bell-curve of results, though I've never sat down and crunched the relative probabilities.

It's not just the potential variance, its the variance plus FUDGE/FATES tight/granular trait/results scale... Because +/- 4 is extreme result for general rolls, doubling the variance makes it more common, so you have the potential for 'blow outs' relative to the scale. it's easy to go 'off the chart' because of the doubled range of results from opposed rolls. Most often comes up as gotcha's in combat. Just something to pay attention too in designing.

Quote from: Bloody Stupid Johnson;507383This is only an incomplete listing which I’ll go back to later and add to (maybe), but please feel free to suggest anything I’ve missed and I’ll add it here.
 
Ars Magica: ?

Ars magica has one of the most flavorful and innovative magic systems. Its primary 'schools' are Hermetic, Hedge magic (wizardry outside of hermetic tradition), and witchcraft (via Infernal powers).

an extensive overview of system can be found at  http://en.wikipedia.org/wiki/Ars_Magica (lot of innovative bits in that game.)

QuoteThe focus of the game is the magic system. There are 15 Arts divided into 5 Techniques and 10 Forms. The Techniques are what one does and the Forms are the objects one does it to or with. This is sometimes called a "Verb/Noun" magic-system. The Arts are named in Latin.

The Techniques are named after the corresponding first-person singular present tense indicative mood Latin verb.

    Creo is the technique that lets the Magus create from nothingness, or make something a more "perfect" examplar of its kind; this includes healing as healed bodies are "more perfect" than wounded bodies.
    Intellego lets the Magus perceive or understand.
    Muto lets the Magus change the basic characteristics of something, giving something capabilities not naturally associated with its kind.
    Perdo lets the Magus destroy, deteriorate, make something age and other similar effects - essentially, making something a worse example of its kind.
    Rego lets the Magus control or manipulate something without affecting its basic characteristics.

The Forms are named after the corresponding singular accusative Latin noun.

    Animal is used for animals. Since bacteria were unknown in medieval times, illnesses are evil spirits, which come under Vim.
    Auram is used for anything that has to do with the air, including lightning. Weather phenomena such as rain and hail may be covered by Auram or Aquam.
    Aquam is used for water, or any other liquid. This includes ice in the 5th edition; In 4th edition, Ice was Terram, since it is a solid.
    Corpus (the incorrect declension Corporem was used in older editions) is used for the human body.
    Herbam is used for plants and fungi, and their products - cotton, wood, flour, etc.
    Ignem is used for fire, and fire's basic effects of light and heat.
    Imaginem deals with images, sounds, and other senses, though humans' ability to perceive them is part of Mentem.
    Mentem deals with intelligence and the mind, such as human or ghosts. The minds of animals are not affected by Mentem but by Animal.
    Terram stands for earth and minerals, or any other non-living solid.
    Vim has to do with pure magic; many spells to ban or control demons and other supernatural beings also belong to this Art, as such beings often have a form that expresses magically.

Quote from: Bloody Stupid Johnson;496045Attribute scores may be used directly in game mechanics or may have secondary “modifiers” which are used by the game mechanics – compare e.g. GURPS (roll under stat on 3d6) or White Wolf (roll dice equal to the stat) and D&D 3E (Strength score of 13 = +1 modifier on Strength rolls on d20). In some games modifiers are used only during character generation (i.e. Dragon Warriors) and so do not take up character sheet real estate, though break points may still exist. Dragon Warriors is also interesting in having basically two varieties of modifiers; though not named explicitly stats can give a larger 'primary' modifier, or a smaller 'secondary' modifier, depending on how strongly they influence a derived attribute. Most derived attributes are affected by one primary and one secondary modifier.
 

Oh yeah, was gonna talk about Minor/secondary modifiers a bit. Like in Runequest some versions of BRP. You have category modifiers for certain skills, which give a bonus based on your basic attributes. Like combat skills might have a primary modifer based on STR (+1/per point overunder 10) and Dex and secondary for SIZ (+1/2pts over 10/under etc). Because it's percentile, these are relatively small influence.

Another thing to consider is how fewer important attributes can lead to serious min/maxing especially in GURPS. while systems like Silhouette, or Paragon HDL and Interlock, with 10 or more attributes and stat+skill pairings reduce this problem. It also circumvents 'dump statting' somewhat. Especially if you have like reflexes/agility/dexterity  So one might affect your initiative speed, the next your dodging ability, and the last to hit with ranged weapons. So you can't focus on stat for max effectiveness and dump the others as much. All of this contributes to feel of system, and kinds of characters it produces. (i.e. gurps talented amateurs, while RQ's its all about skill specialization and experience/training is more important)

(getting more into elaboration and effects of system types, but useful to consider ramifications of your mechanic choices.)

Quote from: RobMuadib;512751It's not just the potential variance, its the variance plus FUDGE/FATES tight/granular trait/results scale... Because +/- 4 is extreme result for general rolls, doubling the variance makes it more common, so you have the potential for 'blow outs' relative to the scale. it's easy to go 'off the chart' because of the doubled range of results from opposed rolls. Most often comes up as gotcha's in combat. Just something to pay attention too in designing.

Checked into this some more and indeed you are correct.
Used an online dice calculator at www.anydice.com (there are no doubt others around - Troll, etc. - just found this one lying around).
 
4dF distribution (using 4d3-8, since each dF equates to d3-2)

 
 
8dF distribution (8d3-16)
 

 
 
In the first post on attributes I've added further discussion on balance and # attributes - although I'd contend that the problem with GURPS is GURPS-specific (i.e. some of the stats suck, at least for some settings) rather than fundamental to low numbers of stats. IMHO, a high numbers of stats come with their own possible problems (getting a high attribute requires less trade-offs since you can spread the cost around. I'm open to being convinced though (and would link to any interesting discussion, irrespective of my own opinion).

Quote from: RobMuadib;512752Ars magica has one of the most flavorful and innovative magic systems. Its primary 'schools' are Hermetic, Hedge magic (wizardry outside of hermetic tradition), and witchcraft (via Infernal powers).
 
an extensive overview of system can be found at http://en.wikipedia.org/wiki/Ars_Magica (lot of innovative bits in that game.)

Thanks for that - comprehensive. I'm familiar with the system - at least in outline - though I only touched on it briefly in post #84 in a single line or so.
With the post you quoted I was looking largely at types of magic; so Hermetic, Hedge and Witchcraft here (adding). I vaguely recall that there were a set of inviolate rules of magic in Ars Magica which each of the non-hermetic schools can break just one law of (e.g. affecting spheres above the lunar, or immortal souls) which I thought was a great idea, but can't recall any specific details of. It may have been in a supplement I browsed rather than the core rules.

Thought of a more detailed/realistic system. Millennium's end sticks out in my mind, as it used a fairly complicated non-ablative invidual body location wound based system.

It used 'Trauma Levels' and had a detailed damage table (though not on the order Phoenix Command's ultra hardcore system. Which has great big scary damage tables by ultra-fine body location and shot direction etc.) Paraphrasing...

QuoteMilleniums end uses a non-ablative damage system that rates individual wounds on a one to twenty five scale of severity. The scale operates in units called trauma levels with a TL of 1 least damaging, 25 most. Wound of TL over 25 is instantly fatal.  TL's are not added together unless 2 or more wounds occur in same body zone. So a character may survive several near-fatal wounds at once.  TL indicates severity of wound, but nothing about its effects. Wound effects include impairment, unconsciousness, blood loss, broken bones and shock.  

The delivered damage (DD) of an attack is determined prior to use of Damage Table(DT). DD is then plugged into Damage Table. DD = base damage of weapon (Fixed for firearms based on bullet type), Minus armor at location, then multiplied by a location modifier (1.6 for head, 0.8 for arms/legs, 0.6 for hands feat.) (and possibly a mass modifier, usually 1.0). This gives your final Trauma Level.

All wounds cause Impairment based on TL and damage type (concussive, impact, puncture, cut burn, and Hydrostatic Shock (ballistic injuries), with effects of impairment logically based on Wound area.(which are percentile modifiers, so vary quite widely, and are finely detailed.)

There is chance of stunning based TL/Body zone, and modified by damage type. This gives a stun chance modifier, which is subtracted from percentile Con roll, with very large penalties for big hits/sensitive locations.

Blood loss, most wound bleed. Check for serious Blood Loss after each wound, compare trauma level by body zone, modified for Damage type. This gives blood loss rate, amount of time will pass in minutes, before character loses one unit of blood. With 4 units lost meaning death. (for humans, one unit = 2pints (useful info for vampire's grabbing roadkill I guess). Blood loss = auto shock, and gives a decline rate modifier for eventually fatal wounds.

There is also the chance for Broken bones or severed limb (Consult limb loss sub-table!). Shock leaves you stunned (also caused by TL 20 or higher, left untreated, shock leads to death).

Eventual fatal injury is shown as an E result on Damage table, as determined from TL and damage location. This gives decline rate, which gets progressively shorter, until TL passes 26. at which point they die.

So as you see, damage determination in this system is slightly less excruciating than actually getting shot. Generally, major concerns of Damage are Impairment, Incapacitation and Eventually Fatal/Deadly damage. Hit point systems just attach this to absolute numbers (0 hp's, -10 hp's), while detailed systems can require a painful amount of effect determination.

FEEL OF COMBAT
Oh yeah another thing that bear's mentioning with the more abstract systems with increasing hit points is how normal threats (i.e. falling) become trivial (the old saw about high level fighters being able to jump off a cliff and get up and fight with no ill effects.) So you have to add kludges like the massive damage rules etc.

Another thing is the overall speed and feel of combat. Does it resolve quickly, or does it end up like D&D combat with everyone hacking on each other for several rounds, etc. You should design it for the effect you want out of combat. Do you end up with lots of corpses in a gritty system, do people cut and run after getting wounded. Does everyone just get knocked out and roughed up like in Super Heroic systems. Each type of system works better for some things than others.

The more heroic the game system, the less lasting effects of damage there should be, and the more of a beating character's can take. While gritty systems can end up with lots of dead character's, often to the extent that combat is effectively MORE deadly than real life, lots of people die every time there is combat, instead of people getting wounded, fleeing combat and dying without medical attention. Indeed, because most game systems don't include any morale systems, lots of fight are to the death, while in real life, people cut and run if possible.

Another thing is on Impairment, in real life, people can be wounded and not really notice any significant effects of the wound due to adrenaline, unless a bone is broken, the body part is mangled outright. In some famous cases of suspects on PCP, they can take over a dozen gunshots to the torso and not even be slowed down. (In reality people only drop immediately if they take major damage to the CNS (Brain, spine, neck), or the heart is directly damaged) People can be shot without realizing it. While at the same time they can drop for purely psychological reasons, or die of shock from a shot to the foot.

Most often impairment is used in RPG's so people can be beat down and rendered ineffective, the death spiral, instead of just eventually dying. Incapacitation is used to make for an effective end to combat, without necessarily people dying, especially in Heroic/Super Heroic realities.  Needless to say there is HUGE amount of variation in combat systems.

Quote from: RobMuadib;512932FEEL OF COMBAT
Oh yeah another thing that bear's mentioning with the more abstract systems with increasing hit points is how normal threats (i.e. falling) become trivial (the old saw about high level fighters being able to jump off a cliff and get up and fight with no ill effects.) So you have to add kludges like the massive damage rules etc.
 
Another thing is the overall speed and feel of combat. Does it resolve quickly, or does it end up like D&D combat with everyone hacking on each other for several rounds, etc. You should design it for the effect you want out of combat. Do you end up with lots of corpses in a gritty system, do people cut and run after getting wounded. Does everyone just get knocked out and roughed up like in Super Heroic systems. Each type of system works better for some things than others.
 
The more heroic the game system, the less lasting effects of damage there should be, and the more of a beating character's can take. While gritty systems can end up with lots of dead character's, often to the extent that combat is effectively MORE deadly than real life, lots of people die every time there is combat, instead of people getting wounded, fleeing combat and dying without medical attention. Indeed, because most game systems don't include any morale systems, lots of fight are to the death, while in real life, people cut and run if possible.
 
Another thing is on Impairment, in real life, people can be wounded and not really notice any significant effects of the wound due to adrenaline, unless a bone is broken, the body part is mangled outright. In some famous cases of suspects on PCP, they can take over a dozen gunshots to the torso and not even be slowed down. (In reality people only drop immediately if they take major damage to the CNS (Brain, spine, neck), or the heart is directly damaged) People can be shot without realizing it. While at the same time they can drop for purely psychological reasons, or die of shock from a shot to the foot.
 
Most often impairment is used in RPG's so people can be beat down and rendered ineffective, the death spiral, instead of just eventually dying. Incapacitation is used to make for an effective end to combat, without necessarily people dying, especially in Heroic/Super Heroic realities. Needless to say there is HUGE amount of variation in combat systems.

Nice - I've quoted this up into the combat section here.

Quote from: Bloody Stupid Johnson;497762.

Quote from: RobMuadib;512287Oh yeah, more discussion of open-ending mechanics is probably warranted. Main way to get around flat die-distributions, give remote chance of success, etc. Lots of variations common. (ars magica's stress die, roll d10,on a 1, roll again and double result, keep doubling, a 0 on it is a botch) All die open-end/explode, single die can open-end explode (star wars), etc. DC heroes used an open-ending 2d10 roll compared to your chart, roll again and add on doubles.

OK attempting this topic...
 
The most merciful thing in the world, I think, is the inability of the inferior roleplayer to correlate all MetaScapeII's contents. We live on a placid island of roleplaying ignorance in the midst of black seas of infinite levels, and it was not meant that we should voyage far. The booklets, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of roleplaying, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.
-from thread "Metascape: Pretentious Much?" on TBP
 
 
Many games allow 'open-endedness' in results. This can be seen, perhaps, as a case of the more general question of how to deal with PCs attempting very difficult or virtually impossible actions, which should have a very low chance of success (if any). Rolling up can also have an impact on 'margin of success' and so effect. In a take-highest dice pool system, open-ending is also useful to fix the issue that the highest result on a single die is the most common result e.g. reducing chance of ties.
Sometimes rolling up is desired as a way of letting characters 'push their luck', so that a rollup is something a player may take but with risks - as in DC Heroes where a double-1 rolling up causes the action to fail.
Systems where higher is better on rolls often have ways of directly converting a roll into effect, so that rolling up /an increase in the raw dice roll can be used. In roll-under systems there's sometimes an extra roll, but it doesn't add directly (the same applies in miscellaneous other systems - cf. notes on 3E, bughunters, below).

Some options include:
 
*Auto-Win!: a roll of maximum on the dice automatically passes: e.g. 20 on d20 automatically hits.
(special cases: T&T 7E and later uses this in a way in combat with 'spite damage' - 6s on d6 in the combat pool are automatic damage that go through armour, though much less than what a character actually rolling higher in combat is likely to do).

*Special bonus: Capes, Cowls and VillainsFoul  is a d12 take highest system (usually maxing out at about 3 dice), but sometimes extra Trait bonus. A natural '12' on d12 lets characters double the extra Trait Bonus (e.g. +3 to +6).
Another thing that's maybe similar to this is the "Repeating 20" in 1st Ed. AD&D's combat tables. There is a row of six 20s with a natural 20 counting as the highest 20, sort of (IIRC) treating a roll of natural 20 as getting five column shifts/being equivalent to a '25', rather than have it be an automatic success.

*Additional roll: a very good/maximum roll will succeed, providing the character passes a second, separate, die roll.
3E D&Ds critical hit confirms are a good example of this (with fairly sound math backing it up). One of the weirder instances of this would be the Bughunters! game (Amazing Engine) Donor Background Table. Rolls are d100+PC Position score (the social status attribute); rolls of 100+ make the character reroll vs. target number 100. 1 successful extra roll makes them a Corporate Executive (or equivalent), 2 makes them a Millionare or Government Leader and 3 successful extra rolls makes them a Billionaire - this system being intended to keep Billionaires rare in spite of the basic Position attribute being somewhat variable, such that it was not possible to build a d100 table reducing it to a set 2% or so. (starting Position is not just rolled randomly but with varying pool of dice depending on PC prioritization, and with new PCs even able to get experience bonuses to stats due to the "Player Core" rules rules, where multiple characters by the same player can share XP).
Similar to this is Aria's  Shifting entire 'result':

Quote from: woodelf;91104result shifts: some mechanics, rather than  simply adding more to the number the die generates on a particularly good result (or subtracting on a particularly poor result), instead shift the entire result. Aria, frex: if you roll a 10 or 1 (on a d10), you then roll again, and if the new roll is a failure or success (respectively), the result is one step worse or better than it would've been just by applying the 10 or the 1 to your skill. And it can repeat, if you continue to roll 10s or 1s. What's distinct about this is that (1) it does this even if that first roll isn't a failure/success, so you can turn a failure into a success, and vice versa, in this way; and (2) it shifts by steps of result, rather than simply adding more numbers to the [numerical] result.

*It's going to Cost You: Shadowrun 4E has a "Long Shot" rule letting a character perform a normally (slightly) impossible stunt by spending a point of Edge. This lets characters attempt very difficult tasks, but rarely and at cost.
(See also earlier post on 'safety valves').
 
*variable difficulty: Alternity expresses difficulty factors as dice (i.e. "impossible" -3d20 to character skill). Almost any roll can theoretically be made given a low roll for penalty.
 
*special result (if using a table of results). This relates more often to 'qualitative' results rather than raw numbers but characters can roll a result on a table that gives overwhelming success, or 'roll twice' etc.

The common solution to the problem however is to allow "rolling up" of some kind. Here certain rolls increase further, so that any target number can theoretically be made - it just becomes increasingly less likely the more ridiculous the number required is. Rolling up is sometimes seen for damage systems, even when not used for other mechanics - e.g. HackMaster damage or the 2nd ed. D&D arquebus (d10, 10s roll and add)(Combat & Tactics later made the rolling up a function of the Knockdown die, rather than the base damage die).
 
Examples include:
*Doubles roll up - (Tunnels and Trolls, DC Heroes). DC Heroes has the additional rule that double-1 automatically fails - even on successive rolls - so that PCs may wish to not re-roll in case they mess up. Note the probability curve of doubles-roll-up is odd looking (screwing up one of the main reasons to use multiple dice to begin with, although in T&Ts case its partly to limit the game to using six-sided-dice), but normally any number can be rolled (unlike the "maximums reroll" method). Chance of doubles on two dice is the same as rolling any given number on the dice i.e. 1-in-6 on 2d6.
Unlike where maximums roll up, doubles rolling up alters basic success chances for most characters, not just those attempting to make unlikely rolls.
Doubles rolling up makes extra dice as a bonus or penalty (i.e. take lowest or take highest ala BoL bonus dice/penalty dice, similar to 5E advantage/disadvantage) more awkward - not usually used. Potentially these can be colour-coded and not count toward a double; or bonus dice increasing odds of doubles could be a feature rather than a bug. and/or a 'penalty die' could also block rolling-up.
Freerpg Hi-Lo Heroes uses 2d6 (take higher or lower), but with the rule that doubles are added together instead. This way of counting doubles might barely be called 'rolling up' (it happens only once and there's no extra roll), but does periodically drive up the die roll considerably. 'Silent Death' damage rolls (cf. Damage) work similarly.

*a roll of 1 is rerolled, with new roll doubled (Ars Magica stress die).

*rolling up on some lolrandomly chosen numbers. In 2E Creative Campaigning by Jacquays, a flintlock does d12 damage will 'rolling up' on 8,10, or 12. Presumably the number of rolls triggering this is to keep roll up frequency higher than smaller weapons, like the flintlock pistol that deals d8 with roll up on 8. Having some lower numbers roll up partly reduces discontinuities (e.g. a 10 or 12 can still be rolled, with 8+2 or 8+4,10+2 respectively) although irregularly, much more rarely than other numbers in the range.
 
*Maximum rolls again and adds (various). Usually this means that certain numbers become unrollable (if a d10 rerolls on a "10", you can't roll a 10 since that will become at least an 11), giving a "discontinuity" or "jump" in the progression (this is mostly an aesthetic thing though - it generally has little or no functional consequence). Some system may add a roll of [die-1] etc. The added reroll needn't necessarily be the same sort of die originally rolled. In most cases, rolling up maximums will have little effect on success chance but may cause blowouts in margin-of-success.
Elaborations of this include:
-Shadowrun 1E had a d6 dice pool system where individual dice rolled up, so difficulties could be over 6. This wasn't always satisfying since a high roll only let character reach ridiculous difficulties, not increase the 'effect' of their success. A character might roll a 20 on one of their normal dice (initial 6-reroll of 6-reroll of 6-reroll of 2) but this still only counted as one success ( which might not even be enough to pass the task anyway, if it needed 2+ successes).
-JoeNuttall in his blog (http://explorebeneathandbeyond.blogspot.co.uk/)suggests a method whereby a roll is 2d10 and a roll of 10 is replaced with another 2d10 roll (and so on) instead of adding directly.
-Savage Worlds rolls up maximums, but in Savage Worlds' step-die system chance of maximum being rolled ("acing") decreases as the die grows larger. This leads to a mathematically oddity that the chances of reaching TN 6 is slightly (about 2%) more likely using d4 than using d6 i.e. a lower skill is better in this one case. The same happens with d6/d8 vs. TN 8, and d10/d12 vs. TN 12. Unlike most other systems there are usually no gaps in numbers that can be rolled for Savage Worlds, since a character will roll two dice and take the best - as long as they are different sizes (i.e. d6+d4) any result is possible.
A Step die system can also potentially reroll using [die of next size] rather than adding i.e. 4 on d4 lets the character roll a d6, then take whichever roll is higher. This makes rolling up much less dramatic, however. Another fix for Savage Worlds probabilities is to reroll and add [dice-1].
EDIT: It is also interesting to compare the psychology of Savage Worlds' rolling up system with other games. In most cases "raises" have primarily a narrative effect and don't give dramatic increases in power (e.g. 27 to hit = +d6 to damage...), but adding the rolls directly to get a big number makes them feel huge. (Another game with say a dice pool and a rule where '10s give you an extra dice to roll' might have explodes be as important mechanically, but still feel less dramatic).
In Savage Worlds exploding/Acing is fairly necessary for getting the system to work - as otherwise e.g. large Parry ratings would be unhittable. Its interesting to compare vs. Cortex, which has no rolling up but which lets story points be spent to similarly narrow gaps in ability, controllably.
[Note that where step dice are used and maximum rolls up, you can increase the chance of rolling up by 'stepping down' the die and adding a compensatory bonus - for instance replacing d10 with [d6+4] increases chance of getting into the 11+ range from 10% to 16%. This would also need the original roll to be used when 'rolling up' however.]
-MasterBook uses a 2d10 roll where either die rolling a "10" adds and rerolls, conventionally enough. However, it also sometimes limits if roll-ups are possible: a character can be "stymied" meaning one of their roll-ups (whether from rolling 10s on the dice or by spending luck Points, called Life Points in MB) is cancelled. Shatterzone is very similar but on a double-10 only a single 10 rerolls unless the character has a 'specialty'. Untrained characters don't get to roll up in either system.  The rolling up in both is a somewhat curious design decision given that the bell curve effect of rolling 2d10 (deliberately chosen for that reason) is mostly invalidated by having a 19% chance of a roll up event [giving an average result in this case of 10+2d10 = 21 result, before considering any secondary explosions]. It also very slightly biases rolls in favour of the attacker on skill rolls, though only slightly since if one roll was a 10 they probably would've succeeded anyway).
-Bedrock Games in-development 'The Meddlers' RPG uses a d4-take-highest dice pool, with an optional rule that if a character rolls multiple 4s, the d4 rolls up. An interesting idea in that one die can't roll up, roll-ups are relatively rare despite using d4s; this also eliminates the discontinuity (making both 4 and 4+ rollable).
-D6 system (adding together a number of d6s) allows "rolling up" only on a single die, the Wild Die (normally a different colour to the other dice).This gives a fairly limited increase compared to potential dice pool size.
-Last Unicorn Games' 'ICON' system as in Star Trek (not to be confused with the 'Icons' supers RPG) uses a d6 take-highest dice pool -the highest roll adds to skill rating. One of the dice is designed as a 'Drama Die' - if a 6 is rolled, the second highest die is added to the total as well.
-Similar to this, Silhoutte uses multiple d6s, with the highest roll (+bonuses) taken, but any additional '6s' each add a further +1.
-Anima: Beyond Fantasy is a d100 additive system where high rolls explode (like Rolemaster) but with the wrinkle (reportedly) that the first roll explodes on 91+, the second 92+, the third needs 93+, etc. (A sort of interesting idea, but IMHO making a difference so rarely that its probably not worth the bother).
-original Cortex "Meta-talents" (super-skills) have a "Better, Faster, Stronger" stunt effect; if either dice rolls max. a Plot Point can be spent to reroll the dice and add. (Cortex doesn't otherwise open-end the way Savage Worlds does).
-one friends' step-die system (Savage Worlds descended) allows for a 'catastrophe token' to be spend on a roll, a form of safety valve, for a +2 if declared in advance or +1 after. Maximum rolls on the dice normally roll up, and if this takes the roll to the maximum (say a 6 on d8 is raised to , then the dice roll up. Note the point spending is less likely to generate 'rolling up' with larger dice.

A dice pool system might 'roll up' maximums by adding to the dice rolls, or by just getting bonus dice. Shadowrun 1E does the former (Target Numbers can exceed 6, so 6s roll up and add again so that some of the dice can technically be considered to be rolls of "8" or "10"). oWoD Storyteller did the other version with Specialties: any 10s rolled granted characters a bonus dice, to try to score extra successes. This limited target numbers to no more than 10, but meant characters' possible # successes were open-ended. (It would also be possible to have a system where the player could choose to either roll up, or treat the number as a bonus die - which might be either before or after rolling).
-Rolemaster uses additive d100, with rerolls at 96-100. This scale is fine enough that slight modifications can be made to the likelihood of reroll (i.e. something might up the reroll chance to a roll of 95-100, or 94-100).
-Earthdawn allows maximums to roll and add normally. In 2E ED, there's an 'Ice mace and chain' power which damages a character, and hinders them unless 'bonus damage' is rolled for the mace which makes it shatter. Since ED is a step-dice system a powerful wizard's mace may be slightly less likely to shatter usually, though the step die progression is erratic enough that the odds fluctuate weirdly.
-Infinite Power is a multidie-additive d8 system where any 8s rolled reroll and add; a normal stat of say 2 would mean 2d8, 8s add and roll over; roll ups therefore occur fairly frequently and slow down the roll (nearly a quarter of the time with just 2d8).

MetaScape possibly warrants special mention here - it has an odd scale system where you can both roll up and roll down - using a custom d16 labelled (C), t, 1,1,1,1,1,1, 2,2,2,2,2,4,4,8,16.
A standard roll in Metascape has a designation such as "6L" or "8H" or "10LV" which breaks down as follows:
*The first number is a normal die type (i.e. d6 for 6L, or d8 for 8H); Metascape only uses d6 thru d10.
*L, M or H indicate a "category" of either Light (x1), Medium (x2) or Heavy (x4).
*Finally the last letter in the code is a scale multiplier or "type"-this letter is omitted for "personal" scale (x1), but also includes B or bantam (x/10), V or Vehicle (x10), S for Ship (x100), W for World (x1000), C for Celestial (x10000), G for Galactic (x100,000) or U for Universal (x a million).
A roll in Metascape is multiplicative and uses the normal die (i.e. d6) x the doubling die result x the multiplier for Light/Medium/heavy. Note that a "16" rerolls and the result multiplies again.
 
For the special results, a "(c)" changes the category toward Light (i.e. a x4 would become a x2), while the "t" changes the category toward personal - dividing the multiplier by 10 unless it was Bantam, which instead goes up to x1. For either a (C) or t the d16 is rerolled unless the multiplier is already x1, in which case it counts as a 1.
Circumstantial adjustments can also be applied to the dice/category/type.
For example a roll of "8LV" would be a d8 x 1 (light) x 10 (vehicle), times the custom d16. If the d8 rolled a 3 and the d16 a 2, result would be [3x2x10] = 60. If the roll was a 3 and a 16, the die would be rolled again - if the reroll was a 2 the final would be [3x16x10x2] or 960.

Thought in closing:
 "Open-ended rolls sounded like a fun way to have exceptional results on occasion, but in practise in every system I've ever used them in (with the notable exception of TORG, which keeps them in check via its results table) the fact that the GM rolls far more dice per session than the PCs means that exploding dice inevitably turn in to exploding PCs." - Grymbok

Generally single-die systems where dice size is d12 or smaller have problems with either explode/autosuccess or fumbles being too common...possibly a reason for why single-d10 systems [Unisystem, Cyberpunk/Interlock] are rarer than single-d20 based systems (along from D&D founder effects)

Note: averages for rolling up on normal polyhedral dice are in post 192 by ggroy.

Rolling up in character generation
'Rolling up' may be seen in character generation (if it uses rolling) as well as active rolls during the game - although this is not so much about reaching impossible difficulties. For example, Tunnels and Trolls 7E and Deluxe roll stats with 3d6, triples add and roll over. Palladium allows a bonus +d6 if a 16-18 is rolled on 3d6 (or 12 if rolled on 2d6 in Palladium Fantasy).
Weirder elaborations here include Team Characters in TMNT (Palladium); all characters in the team must be the same animal type e.g. turtle, and if any of them roll a 16-18 and so roll up they all get the same +d6 to that stat.
Character generation is more complex than a single roll/result value, so may have 'feedback loops' involving multiple quantities (increase in X leads to increase in Y that leads back to increase in X) ala older HERO (buying down derived attributes to buy up the base score again) or World of Synnibarr (where a high stat gives bonus 'skill points' that can be spent to get skills or mutations that then increase the stat again). Another case may be the infamous (and disputed) Pun-Pun D&D 3.5 build. Character generation is also more likely to include qualitative 'rolling up' on tables and the like i.e. where a character rolls a random skill (mutation, psi power, whatever) and gets a "roll twice" result.

Quote from: Bloody Stupid Johnson;513155OK attempting this topic...
 
The most merciful thing in the world, I think, is the inability of the inferior roleplayer to correlate all MetaScapeII's contents. We live on a placid island of roleplaying ignorance in the midst of black seas of infinite levels, and it was not meant that we should voyage far. The booklets, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of roleplaying, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.
-from thread "Metascape: Pretentious Much?" on TBP
 
MetaScape possibly warrants special mention here - it has an odd scale system where you can both roll up and roll down - using a custom d16 labelled (C), t, 1,1,1,1,1,1, 2,2,2,2,2,4,4,8,16.
A standard roll in Metascape has a designation such as "6L" or "8H" or "10LV" which breaks down as follows:
*The first number is a normal die type (i.e. d6 for 6L, or d8 for 8H); Metascape only uses d6 thru d10.
*L, M or H indicate a "category" of either Light (x1), Medium (x2) or Heavy (x4).
*Finally the last letter in the code is a scale multiplier or "type"-this letter is omitted for "personal" scale (x1), but also includes B or bantam (x/10), V or Vehicle (x10), S for Ship (x100), W for World (x1000), C for Celestial (x10000), G for Galactic (x100,000) or U for Universal (x a million).
A roll in Metascape is multiplicative and uses the normal die (i.e. d6) x the doubling die result x the multiplier for Light/Medium/heavy. Note that a "16" rerolls and the result multiplies again.
 
For the special results, a "(c)" changes the category toward Light (i.e. a x4 would become a x2), while the "t" changes the category toward personal - dividing the multiplier by 10 unless it was Bantam, which instead goes up to x1. For either a (C) or t the d16 is rerolled unless the multiplier is already x1, in which case it counts as a 1.
Circumstantial adjustments can also be applied to the dice/category/type.
For example a roll of "8LV" would be a d8 x 1 (light) x 10 (vehicle), times the custom d16. If the d8 rolled a 3 and the d16 a 2, result would be [3x2x10] = 60. If the roll was a 3 and a 16, the die would be rolled again - if the reroll was a 2 the final would be [3x16x10x2] or 960.

Wow, I was not aware the awesomeness that is Metascape. That is some impressive open-ending there. I will have to attempt to assimilate it's superior intellect at some point, rather like the Necromonicon, it will make me starkly aware of my insignificance in the great cosmic awfulness that is the universe:) Oh now, There is now a Metascape 3rd edition (  http://youtu.be/zsf9D0IpOLU ) For those who would dare their sanity and test their intellect  http://metascapegame.blogspot.com/

Oh, and this bit in the announcement, you too can someday be raised to a second class citizen by toiling for you ominscient masters

QuoteCongratulations to Trevor Nielsen. For his years of dedicated playtesting and design help. I've moved him up in the credits to Master Playtester!

Thought I'd add one of the quirkier 'open ending/up rolling' systems I've encountered, from Cthulhutech. Rolls are made by rolling a number of D10 equal to your skill expertise (1 to 4) plus optional specialty dice, and take the highest roll. You add your Base = to your attribute score. However, there are two 'up-rolling' options. you can take the highest set of multiples and add them together, or if you have 3 or more dice, you can count the highest 'straight' as in poker. So if you rolled a 9,4,5,6 you could add the 4-5-6 'straight' to get 15 for your roll.

Quote from: RobMuadib;513196Wow, I was not aware the awesomeness that is Metascape. That is some impressive open-ending there. I will have to attempt to assimilate it's superior intellect at some point, rather like the Necromonicon, it will make me starkly aware of my insignificance in the great cosmic awfulness that is the universe:) Oh now, There is now a Metascape 3rd edition (  http://youtu.be/zsf9D0IpOLU ) For those who would dare their sanity and test their intellect  http://metascapegame.blogspot.com/

Oh, and this bit in the announcement, you too can someday be raised to a second class citizen by toiling for you ominscient masters

eep we're up to 3 now...? Okaay...
After playing MetaScape you will see how great it is to be able to roll 50,000 damage with your light blaster and accidentally destroy the Death Star! Normal RPGs will no longer be sufficient!
(There's a note in the rulebook about how the highest roll they ever saw during playtesting was 130,000+. Makes my rolling a 34 once playing Tunnels and Trolls look pretty lame in comparison...)

I've always wondered what would happen if we got this guy, and Synnibarr's Raven McCracken together (maybe with SenZar's Todd King too). I don't know what the final RPG would look like, but it'd need some big dice.

Oh and thanks for the notes on CthulhuTech.. I probably wouldn't have thought of Ars Magica if you hadn't mentioned it initially, either.

Above: Cthulhu vs. Godzilla
　

This post deals with actions which are resisted by another character/characters.

A general concern in many approaches is 'asymmetry' where it is relatively more difficult to mount an equivalent defense vs. an attack or vice versa. This can be deliberate however, if it models a realistic concern for example, or if an attack has a heavy resource cost for the attacker (as in spell slots or in-game money).

Asymmetry tends to occur less directly in straight 'opposed rolls' - although there can be problems of scaling e.g. a Trip attempt in 3.5 D&D normally uses just an opposed Strength or Dexterity roll. A mounted target can also be unhorsed with a trip, but instead resists with a Ride skill check; this is likely to be an extra +4 at 1st level minimum, grows steadily with level, and gives a character access to possible other boosts (feats, synergy, etc.).

Systems using point-buy chargen can also have scaling problems with unreasonable bonuses when attacks/defenses have the same cost and scale, as attackers tend to put most of their eggs in one basket while defense needs to be spread across most conceivable attack forms. Games may use either escalating costs or lower costs for defenses for this reason, or may have defenses that default to character attributes rather than separately-purchased defensive powers (e.g. a psionic attack that is normally resisted by Willpower is less effective than one that's only stopped by a rare 'Psychic Defense' power).
Asymmetry can also be sometimes counter-balanced (e.g. an AD&D character's gains in chance to hit vs. AC and extra attacks, balanced by gains in HPs)


Deciding who wins in a contest can involve various methods e.g.

Non-dice-based:
*highest score automatically wins [Amber diceless, mostly]
*non-numerical tactical comparisons.
*bidding of points

Dice-based:
*roll with no adjustment (defender abilities aren't considered at all)(Apocalypse World).
*'attacker' rolls, with difficulty adjusted for the defender.
*directly opposed rolls.
*separate rolls, comparing margin of success [similar to directly opposed rolls]
*separate rolls, trying to roll against the highest difficulty.
*Multiple rolls - systems may also require multiple successful rolls to determine the outcome of a conflict.
*a more complex opposed roll, by which I mean a hybrid of 'opposed roll' and 'difficulty adjustment' where a defender roll modifies the attackers' difficulty but not at 1:1 - see e.g. Marvel Super Heroes below. This method gives asymmetry.
*an opposed comparison of 'effect' following a roll.
*Other systems

Non-Dice Based

Highest score wins is usually fairly straightforward (although circumstance modifiers might apply to scores before final comparisons, that may also involve tactical factors).
 
Bidding of points: (e.g. sometimes seen with initiative systems e.g. Secret of Zi'ran, IIRC). Related to this but also including rolling, Dying Earth uses an opposed roll system where skill just gives a number of rolls/re-rolls for a skill each session; characters roll d6 (unmodified) on a simple table, with high rolls forcing an opponent to spend more points to re-roll. Gumshoe (by the same author) gives a base d6 roll for free, plus allows point spending from a skill pool to increase the roll (+1 per point).

Non-Numerical Tactical Comparisons
Contests in the wider sense of the word, i.e. going beyond just 'opposed rolls' can include detailed attack-and-counter comparison. Consider paper-scissors-stone as an example of this, maybe. Game systems can set up more complex versions of this for specific instances, though they are not usually generalizeable to universal resolution mechanics. For example, the Immortals book for Basic D&D had a series of 'power combat' options that was essentially this.
Sometimes such a system is combined with a highest-wins approach - there is a number comparison but with particular attack vs. defense combinations getting a bonus or penalty. An example of this for instance would be the mental-attack-vs.-mental-defense charts for psionics in AD&D.
Another example of this would be perhaps 3E D&D spells, which have a number of checks-and-balances possible through various counter-spells; a GM may be able to 'balance' encounters by essentially pulling out various counter-measures, until players start using sourcebooks that are unknown to them. (Interesting link here).


Dice Based

No adjustment:  the simplest case, but still weird e.g. Apocalypse World, which uses only rolling for players. It has no contested actions as such - NPCs aren't modelled as characters so much as they are an environmental effect. An NPC can force a PC to check but there is no difficulty adjustment for NPC ability (NPCs have health, damage and armour but no stats) and don't roll themselves.
　
This situation can occur in other games though it might be seen as poor design. Very simple systems where a single-characteristic is used for checks may struggle with any sort of 'opposed' roll, meaning that a check will default to either a characteristic check for side A, or a characteristic check for side B (An example being the combat example from 5E T&T, where there is some confusion as to whether boulders hitting the PCs should require Luck rolls from the PCs or Dexterity rolls by the ogres attacking them - entirely different rolls with different chances of success). Spawn of Fashan likewise has some dodging involve a Luck roll for either one side or the other - wholly GM discretion. (the easiest fix for this would be just a Runequest-type roll where a successful attack by one side is blocked by a dodge roll by the other - which changes the likelihood of success but would at least be non-arbitrary).

Attacker rolls, with difficulty adjusted for defender.
The simplest case here is similar to an 'opposed roll' but where difficulty = average roll + bonuses.

Using average rolls as defenses can be complicated by re-rolls/extra dice: e.g. in Savage Worlds' in particular, a PC attacker has a chance to hit better than 50/50 (despite Parry roll being equal to 2 + half Fighting) due to their extra d6 "Wild Die" (see next post)

Other variations here: Cadillacs & Dinosaurs is roll under, and suggests using a roll under [attacker score - defender score] on an opposed check. Consequently, a roll between evenly matched opponents (for instance, someone with Str 5 trying to push open a door held shut by someone likewise of Str 5) automatically fails! Similar (but working) versions of this are seen in SPI's old Dallas TV show 'rpg', and in Dragon Warriors - for both of these separate separate 'attack' and 'resistance' scores are defined. Dallas has e.g. a separate attack/resistance score listed for each character (e.g. J.R. Ewing 'Coercion 24/20') with a difference of about 4 common, and the difference 'spread' being rolled under on 2d6 (The low chance of success also probably assumes use of 'power tokens' to increase the attack value). Dragon Warriors has e.g. separate derived scores for 'Attack' (avg. 15 or so) and Defense (avg. 3-5 or so) with a roll to hit made on d20 under [attack-defense].
 
Another asymmetric case of this would be Werewolf, which used a streamlined version of Vampire's Storyteller system where most rolls were attacker [Attribute + Skill] against a target number of [defender attribute + skill]. This gave very different results for a stat-1-vs-stat-1 contest (1 automatic success unless attacker botches), a stat 6 vs. stat 6 (minimal chance of failure, average outcome of about 3 successes) and a stat-10-vs.-stat 10 (50% likely to fail due to 1s cancelling any 10s rolled in oWoD botching rules.).

A third case of 'asymmetry' that's basically just poor design would be some uses of 'skill levels' in Mercenaries, Spies and Private Eyes, e.g. Tactics.
In most cases a skill level gives +1 to an attribute check, whereas in other cases it sets the 'difficulty level' of a saving roll (SR); since an SR has a difficulty of 15 +5 per level, that increases difficulty 5x as fast. It also has the same problem as Cadillacs & Dinosaurs on occasion, with an opposed check often using the opponent's score as the to-hit number despite the defender getting a bonus +2d6 for rolling the dice.

A sort of weird case that's sort of semi-asymmetric would be 2nd Edition AD&D 'fast talking'; this was a proficiency check (Charisma check of d20 under Charisma) modified by Int modifier and Wis modifier separately off a table; 9-12 is no modifier, 13-15 -1, 16-17 -2 Int or -3 Wis, 18 -3 Int or -5 Wis; a Cha 10 vs. Int 10/Wis 10 is balanced at 50%, whereas an 18 Cha is balanced against 18 Wis/18 Int i.e. penalty of 8 (rarer since two stats).

Directly Opposed Rolls: These are most straightforward in additive systems, where everyone rolls a die and adds their bonus. Ties are sometimes broken by highest modifier, rolling again, or even a roll against another attribute; the defender may also win ties automatically or it may trigger a special 'deadlock' result.
Mutant Chronicles 3 (reportedly) breaks ties in favour of PCs.

Dice pool systems are similarly straightforward, although these give a smaller spread of results that most other dice rolling mechanisms, meaning ties are more likely. As well as being quick both additive systems and dice pools generally give symmetrical results; two characters with the same bonuses have an equal chance of winning, regardless of whether those bonuses are +0 or +1000. (although for a dice pool, I think the actual distribution does change as the pool grows larger).

As noted above by Rob, an opposed roll has a different distribution to a single die roll (so having both sides roll is different to using an "average" roll as a defense). Particularly noticeable in original FUDGE; presumably also there to a point in in some of the more recent FATE variants, though most of these use [d6-d6].
Elaborations: Risus includes rules for 'promotion'. Where an opposed roll occurs and one participant would have no dice due to their abilities being wholly inappropriate, everyone gets a +2 dice bonus (both the character with no dice and the characters with dice). An interesting alternative to the usual "OK, here have a default rating of 1 die/+0/whatever".
An opposed roll can also use comparisons of a 'result level' instead of the exact roll to make ties more likely i.e. if an 11-15 is a 'partial success', rolls of 12 and 14 both might be 'partial successes' and hence a tie. This setup might also be mandated as a result of other mechanics that make it possible to meddle with 'result level' without the raw number being modified ('Blue Mages always score at least a Purple Success on spellcasting rolls" or something.)
 
Separate rolls, comparing margin of success:
A roll-under system that counts margin of success gives very similar results to an additive system, except that a very poor roll on the part of the attacker may result in a 'miss' which means the defender needn't bother to roll at all, giving the defender an advantage in cripple fights. The same effect could be implemented in an additive system, if you wanted, with a rule stating that an attack of [less than X] is automatically unsuccessful.
Elaborations here: SenZar, as noted in the core mechanics section, die this with d20 (roll over target number) but sometimes changing from d20 to d100 (with a monstrous blowout to the margin of success generated).
Complete Gladiator for AD&D 2E had a weird way of calculating opposed (d20 roll under) Strength checks, although the final result is basically no different:

QuoteExample: A half-giant with 24 Strength vies for control of an impaler against a mul with 19 Strength. The halfgiant rolls a 19, while the mul rolls a 15. Since the difference between 19 and 24 is greater than the difference between 15 and 13, the half-giant wins the contest of strength and, therefore, control of the impaler.

Note that the exact numbers here - they are first comparing the scores, then comparing the dice rolls, instead of comparing each score to a dice roll and then comparing the differences, although the result is the same.

Multiple rolls : e.g. a character might need to win the most rolls out of three, or accumulate successes. May also involve a resource cost/roll. One interesting elaboration I have seen here was an ability that, after a character failed a normal simple opposed roll, converted it into a best-of-three contest instead of just failing.
More abstractly, 'combat' could be viewed as a sort of multiple roll resolution, with damage accruing from each hit roll. See also e.g. dice pools used as a resource (e.g. Dogs In The Vineyard).

Separate rolls, trying to roll against at the highest difficulty.
Rarely seen. For instance, if I roll against my skill at -2, the opponent might have to make a roll at -3 in order to win (regardless of what I actually rolled - as long as I succeeded). Turn order can make a difference here i.e. whether both have to declare simultaneously or whether defender reacts.
Maybe tangentially related to this is Rolemaster initiative (IIRC), where a character can choose to roll at a bonus but then takes a penalty to an attacks on their turn.

More complex opposed rolls:
*Marvel Super Heroes had a defender roll on the action table using its normal rules - giving a Green, Yellow or Red success. Green imposed a -2 rank shift, Yellow a -4 and Red a -6 (equating to a -10%, -20% or -30% penalty). Green results are always 30% likely, while Yellow had a chance of about 5% per rank (including rank 0) and Red a very low chance (base 1% and increasing irregularly). Active defense did not count as a full action, but inflicted -2 CS (-10%) to the character's own attack roll.

*the gladiator manuevers of the 2 August 2013 D&D 'Next' playtest. Here an attack is followed by a d6 roll which is compared to the stat modifier of the target; i.e. if their DEX modifier is +3, a roll of 4+ might be needed to hamstring them. This 'expertise' mechanic is very different to a normal (opposed d20) contest in the system. This idea may be derived from the fighter 'deed die' in DCC.

*Alternity (which used a d20 roll under, with a bonus/penalty step die) rolls under stat for checks, but with a 'resistance' step adjustment applied to an attacker (for instance, if a penalty to shoot an opponent was normally -d0 it would remain that for an opponent with Dex 10, or be increased one step to -d4 if the opponent had Dex 11-12). This averaged about -1 per step but could be more or less at some steps e.g. from -0 to +d4, or from -2d20 to -3d20 at the far end of the scale.

*roll under systems with successful roll to 'attack'  blocked by a successful roll under 'defense' skill.
In this as skills increase toward 100% on both sides, a stand-off becomes increasingly likely - which might be a deliberate design decision. BRP I believe does this; GURPS optionally switches between that and counting margins of success (the 'quick combat system' in 3E).

Another variant for BRP in Ringworld was that a successful % roll less than defender skill, gave a penalty to the attacker equal to the defender's skill. HarnMaster uses simple attack vs. defense, except that "critical successes" are also possible (1/5th of skill) for either attack or defense - a table cross-referencing these determines base weapon damage (see top of chart here: A*1, A*2, or A*3 are impact damage dice; DTA (Defender Tactical Advantage) is basically a free "attack of opportunity")
http://www.columbiagames.com/resources/4001/harnmaster-combattables.pdf )
World of Synnibarr has something similar with shot rolls (attacks) vs. dodge, where a character rolls a d100+bonuses to hit, then the opponent rolls under their Dodge to be missed, unless the shot roll was (IIRC) 100+ in which case no Dodge is allowed.

An opposed comparison of 'effect' following a roll
For instance, two characters might have a contest of Strength by rolling Willpower and then adding the margin of success to their Strength scores. See effect post for ideas here. This covers more or less anything else, and indeed some of the other examples could be placed in this category (including opposed rolls where 'result levels' are compared rather than raw rolls, and separate rolls where the highest penalty wins).
Effect can also be converted back into a target number or difficulty adjustment (e.g. in Savage Worlds  a 'raise' result on spellcasting with some spells such as Burst (i.e. a +4 or more over the target number of the spellcasting skill roll) only gives a -2 to the defender's save.


Other, Weirder Systems for opposed checks
*Aberrant had a system for "Mega-attribute" checks with various comparisons used depending on the combatants. If two characters didn't have Mega-attributes, they rolled a fairly normal Storyteller opposed roll (i.e. roll dice equal to stat; Str 5 = 5d10). If opponents had Mega-attributes however, the higher score would win automatically, unless the weaker character spent a Willpower in which case both rolled just their Mega-attribute dice (humans with a base five in their stat could do this as well, and would get 1 die; humans rated at 4 or less automatically failed). If both had the same mega-stat however, they would instead roll off using their normal attribute score dice.
None of this applied to normal skill or power rolls, where Mega-attributes just added bonus dice (although each success counted as 2 successes, or 3 on a roll of "10").
 
Whitehack has a peculiar 'auction' system based on rolling a d6 and bluffing about the result, more or less described here: http://www.therpgsite.com/showthread.php?p=838488#post838488

*Proportionality: a couple of weirder dice rolling systems have been set up specifically to give %s on opposed rolls that are proportional to the ratio between scores. (See posts #25 in the thread; notes on "Conflicts in Sorcery & Super Science" and multiplicative systems). A % system can also reduce two scores to a ratio and use that to roll a chance of success (i.e. in the 'You Stupid Bitch' game for control checks; apparently combat rolls in "Supergame" (1980).
Synnibarr modifies Hand-to-hand grappling base % by subtracting the % stronger an opponent is - based off 'liftable weight' rather than score i.e. if your opponent is 150% stronger than you, the penalty is -150%. Note that this sort of "proportionality" calculation has two possible outcomes depending on which is divided by which (e.g. in a contest between Strength 10 and Str 25, either the 25 is 150% higher or the 10 is 60% lower - Synnibarr chose the more drastic way of assessing the penalty).
Proportional systems such as this allow an open-ended scale for the stats being compared. A proportionality system is consistent with a linear rather than logarithmic scale for attributes.

Other Elaborations
*City of Terrors 'Netmaster' combat for Tunnels and Trolls gives an unusual use of multipliers on an opposed attack roll. In the net combat, a character with low DEX doubles the opponent's attack, while a character with moderate DEX halves their attack (high DEX means no modifiers). This gives no change in relative chance of success for low vs. moderate DEX, but because damage equals the difference in rolls, a character with low DEX takes twice as much damage if their attack does fail.

*AD&D "Dispel Magic" spell is deliberately asymmetric - the base chance of a successful dispel is 50%, this increases by 5% for each level the caster is higher, or decreases by only 2% for each level the caster is lower - a 5th level caster trying to dispel a 15th level effect still has a 30% chance, instead of 0%. The rationale for that may be that the dispel has a significant resource cost (3rd level spell slot), or because there's a definite tendency for the GM to assign really high levels to NPCs anyway. This sort of adjustment is difficult to build with e.g. 3E's d20+mods system.

Some errata to the above with regard to Savage Worlds; there I've noted that the Wild Die skews the attacker result upward. What I didn't notice before, is that the way Fighting is calculated itself gives a weird asymmetry thats normally skewed towards the defender - at least if the attacker isn't a wild card. If they're extras, two guys with d10 fighting are more likely to hit each other than two guys with d4.
Parry below is calculated (2 + half dice max. for Fighting).
 
Mirror Match (same Fighting score) to-hit odds:
 
Fight    Parry     % to hit (non wild card)     % to hit (wild card)
d4-2        2        25%                           87.5%
d4         4        25%                             62.5%
d6         5        33.3%                          55.5%
d8         6        37.5%                          47.9%
d10       7        40%                             50%
d12       8        41.57%                        49.69%        
d12+1   8        50%                             58.33%
d12+2   9        50%                             56.95%
d12+3   9        58.3%                          65.25%
d12+4  10       58.3%                          65.25%            
The second set of %s factors in factors in the Wild die, which is always d6 (6s roll up) plus or minus any fixed modifiers i.e. untrained character has a wild die of d6-2, while the d12+3 character has a d6+3 wild die. The increase in the chance to hit from the wild die starts high and decreases, mitigating the shifts in the normal die results.

This is going to be a weird post - dealing with the idea of limitations built into systems and how they are dealt with.
Some systems are just more flexible than others - some core mechanics for example seriously limit possible operations, or at least significantly overcomplicate some things to the point where you're better off not doing them. Here I'll discuss a few particularly limited systems and interesting workarounds.
 
One Roll Engine: the core mechanic here (roll X d10s, count the matches) generates a "height" and a "Width" to the roll. This has a limited range because # dice going over 10 guarantees a success - consequently modifiers have to be uncommon. (I suppose a workaround might be to require more multiple-successes for some tasks). It also doesn't have 'critical failures' or 'critical successes', and the large jumps in probability of success as dice pools increase mean that all rolls are [one stat + one skill], putting constrains on its skill list to be inclusive. Reading ORE (Godlike) I was struck by how few options were available; my impression was that the rules had been written the only way they could have been written, given the core mechanic.
 
(Edit: I'm now rethinking this a bit in that there are some options for combining an ORE type engine onto another system - for instance using its hit locations on damage rolls rather than to-hit rolls. Cf. the 'Hybridization' post. These still lack the benefit of true one roll resolution, however.)

Savage Worlds (sorry I keep going on about this game!! ): the main constraint in this system is granularity; there are a limited range of possible skill ranks (d4,d6,d8,d10,d12) with very noticeable jumps between them. (You could potentially increase the number of steps using Zocchi dice like d7s and whatnot, but few people own a set). Keeping characters down to rolling a single die on attacks, limits options even more than with other step-die games like Earthdawn or Cortex.
The limited range of values largely prohibits a level-based advancement system where all of a characters' stats (attack, AC, defenses, skill numbers) go up every level - "vertical advancement". What is interesting is that the system has extensive "horizontal" advancement to replace this: characters look like they do advance in a rapid enough fashion to be fun; while they do so by gaining points across various skills (e.g. in combat there are 3 different skills to advance (Fighting, Shooting, Throwing), the main way to improve is to gain various Edges; abilities somewhat analogous to the Feats of 3.x D&D - Quick Draw (draw weapon without an action), No Mercy (reroll damage rolls), Danger Sense, etc. The overall rules framework may look surprisingly complex for such a simple step-die system until you realize that detailed combat and tactical subsystems are needed to make Edges worthwhile, and so make the advancement system work.
(the Dark Heresy games (i.e. also Deathwatch, Rogue Trader) are another system that relies on 'horizontal advancement' with lots of talents - in its case driven by a need to make rolls stat-based rather than have separate skill values).  

Jeff Moore's freerpg Hi/Lo Heroes (thanks to danbuter for bringing this up on the main forum): again a granular system you roll 2 dice, with your stat (Hi or Lo) determining if you take the best or worst of the two rolls. Additional modifiers are possible as a flat "+" to the dice. As a supers game, this limited the degree of versimilitude possible; attribute effects in game world terms are very fuzzy. However the system looks very well balanced because of the low range.
The system is sort of like a seriously constrained 'take-highest' dice pool mechanic - some of these have an extension allowing dice pools below 1 die by having a negative dice pool 'take lowest' instead of 'take highest' (free Thunder RPG 'Under the Broken Moon), except that here the intermediary step (rolling a single die) is omitted. Limiting the roll to 2 dice in all cases opened up the potential to use "doubles" as the basis for some mechanics e.g. earning xp and special results. The system struggles a bit adding extra modifiers - for instance, "career skills" use an attribute check (which therefore will be either Take Highest or Take Lowest; in order to add a modifier for trained/untrained use, it makes the GM roll an opposed roll, which is either High or Low depending on whether the skill is trained.

Tunnels & Trolls is another possible case - which is currently up to 7 editions with limited change. It has a combat system where a character rolls combat dice (based off weapon) plus combat adds (STR, DEX, and CON add a point for each point above 12) and compares to the enemy total, with difference (less armour) being damage. The core system has a number of issues e.g.:
-no difference between hit/damage bonuses
-combat/noncombat use different resolution systems
-large differences in combat results between characters/ weight of stat (adds) too high
-lots of mathing required to compare attack totals
-no transparency in probabilities
On the plus side T&T is also very simple, fast, and allows for monsters with only a single stat - Monster Rating - needed to give their 'HP' and combat dice+adds, and allows for use of attributes as damage sinks directly, with scores having large values and despite that no breakpoints. It is very difficult to fix any issues with the core system here without replacing it entirely and losing these advantages as well.

(you can compare this to the idea of a 'local maxima' in evolutionary biology - an organism can reach a plateau of fitness from which it can't be improved without a number of changes that individually would decrease the fitness of the system, and so are unlikely to co-occur - a 'brain size gain' gene is very useful if you also have a 'head size gain' gene, but one of these on its own results in either just your head exploding or an increased maternal death rate, and so are selected against. Systems are designed rather than 'evolving' through natural selection, but you get the idea - the move to a different setup that's genuinely better can require a major conceptual leap. In any case, a rebuild to fix a problem can require a revolutionary change and be essentially a wholly new system.)

Inherent in most systems are attempts to control the total probability of actions/events, such that rolls only rarely and when appropriate reach a 100% chance of success and become dull, or so that opposed rolls do not become too one-sided.
A control can be put on how individual bonuses are calculated, and/or on how many modifiers can be applied.
Systems can sometimes be too constrained in how bonuses are calculated, in which case tasks can be unreasonably difficult or dangerous even for expert/experienced characters. This might flow through into other game balance issues (e.g. if magic is reliable but skills aren't, and skill-user/magic-user are different character classes, skill users may struggle).  Or Margaret Weis in the introduction to Marvel Heroic relates a story about her playing Captain America and being beaten into unconsciousness by random thugs during playtesting,
In some respects this post is the complement of the post on 'cutting down excess rolling' inasmuch as if bonuses are too high - systems to cut down bonuses are needed as described here: if bonuses are too low, artificial ways are needed to skip over rolls that fail too often.  (as seen in 3.x "take 10", or Apocalypse World/Dungeon World's general advice to not roll to "hack n' slash" if someone is surprised and just automatically deal damage, or MSH 'Automatic FEATs' and Intensity rules [see earlier post on Implementation - Effect].).

Calculating Base Chance
The 'base chance' of success (the expected main determinant of success) could itself be viewed as a 'modifier' - adding to what would otherwise be an 0% success chance.
The "base chance" is usually a permanent character statistic, so growth in this can be slowed down via e.g. a set maximum value by class/race/level, or nonlinear-cost advancement rules (math that most would consider painful for a one-off, on-the-fly modifier calculation , but less of a hassle as part of chargen - this hasn't always stopped people though e.g. see page 18 for mention of the 'Diminishing Returns Function'). Maximum value here might well be set by the designer with some consideration of what extra modifiers might likely be applied, to make getting over 100% even with those tricky.
The core mechanic itself can include some sort of 'diminishing returns' e.g. MSH again builds "diminishing returns" into the system through its 'universal table'. Shifting up from a base stat of 10 (Good) to a base stat of 50 (Amazing) moves a character up four ranks -through Excellent (20), Remarkable (30), and Incredible (40) - to give only +20% to their base chance of minimal (Green) success, the equivalent of +4 on a d20, and with even less increase to the chance of Yellow or Red success levels.  
Bell curve rolls can also keep rolls at less than 100%, as extra bonuses provide less and less increase in success chance each time. Count-success dice pools also follow a 'bell curve' and gradually slow as they approach 100% (though ORE-type pools don't). 'Rolling up' can give opposed rolls some chance of always failing (i.e. if the opponent's roll blows out).

Extrinsic vs. Intrinsic Modifiers
Modifiers can apply within the 'base chance' rather than being a purely 'additional' modifier - I term these "Intrinsic" vs "Extrinsic" Modifiers.
For instance, Marvel Super Heroes usually adds a bonus as a 'column shift' which effectively adds to attribute before the table lookup (the exception being spending Karma, which instead adds to the die roll)[Intrinsic]. On the other hand, Savage Worlds never modifies the raw die roll for a stat, but adds huge circumstance modifiers (which could well be -4 to +4, and note the modifier can add to either the stat die or the 'wild die')[Extrinsic]. 3E D&D does both: a character might get a bonus to Strength from a magic item which indirectly raises their Jump check, and a straight-up magic bonus to Jump. Intrinsic bonuses are generally under tighter controls, as they may inherit rules as to maximums etc. that normally apply to the attribute (or whatever) e.g. in MSH a score can't be pushed below 'Shift-0' or above 'Shift-Z'.
(This is similar or parallel to how advancement costs of a skill might be based on a single attribute/skill total bonus e.g. WEG Star Wars D6, vs. increases for stat and skill handled separately e.g. d20 - compare advancement)

Additional Modifiers / Limiting # of Modifiers
Depending on how fine-grained modifiers are a +1 might be a small amount and so be very common (Runequest), or a huge shift and so be given out fairly rarely (Feng Shui).  Some games rarely apply modifiers despite bonuses not being signicant - AD&D ability checks or saving throws rarely get a modifier (AD&D deliberately making a save a low chance to begin with...cf. EGG's DMG advice on allowing a save even when chained up vs. dragon breath ), while Apocalypse World/Dungeon World uses virtually no difficulty adjustments (DW has a particular problem that the GM may only 'move' when a roll is failed, limiting GM involvement if rolls got too high).
Modifiers can be limited by type (for instance 3.x defines bonus types like 'enhancement', 'inherent', 'sacred', 'profane', etc. and only the largest bonus of each type applies. (This is complicated slightly in that, actually, bonus can be applied first intrinsically then extrinsically - e.g. a character could have both an 'enhancement bonus' to Strength - though geared down at 2:1 via the use of the ability modifiers table - and a direct 'enhancement bonus' to Jump checks). 3E also had probably too many bonus types, with some types being questionable (e.g. 'sacred' and 'profane' separate rather than a single 'alignment' bonus) and with sourcebooks inventing more, e.g. 'alchemical' and 'deformity' bonuses in Book of Vile Darkness. Another similar approach to limiting 'stacking' is to hand out the same bonus through various means - 5E D&D gives elves free 'Perception' skill and half-orcs free 'Intimidate', meaning the bonuses for race and class (if their class also has this as a class skill) overlap and so can't be doubled up.

Other Approaches:
*scaling down modifiers in general i.e. attributes bonus tables let modifiers scale at a different rate to the attributes themselves
*biggest bonus only (e.g. circumstance-type modifiers in Weapons of the Gods) - only the largest bonus and penalty applies to a check.
*Relatedly, bonus substitution: A 'bonus' might simultaneously take away other potential bonuses: i.e. "apply DEX modifier in place of STR modifier" (Weapon Finesse).
*adding a resource cost to applying a modifier. Factors that help can then also be represented as a larger resource pool to give occasional bonuses, instead of adding to every roll. E.g. FATE uses 'Fate Points' to restrict use of Aspects, or Over the Edge has its "experience pool" where experience gives a characters' number of bonus dice/session, instead of characters getting +level to every roll.
*using fixed numbers instead of a modifier (converting a variable to a parameter): some sorts of modifiers break some dice-rolling mechanics, and become balanceable best if they are eliminated and replaced with a system-defined number. For example, Shadowrun-1 had variable 'staging' by weapon (# to-hit successes to push up damage), while in SR-2 the staging number was set at 2. Similar damage divisors exist in other systems (e.g. the /2 in Ork! or /4 in Savage Worlds - see list of damage calculations by system) which could potentially be replaced with a variable but at risk of breaking the system. As a half-way compromise, a fixed number might be adjusted by a (rare) Advantage, instead of being innately variable due to being attribute-, skill- or weapon-based.
*"remap to binomial" (named this after a data-mining process term): rather than use an exact number, a number can be mapped to a yes/no category with a fixed bonus. This prevents excessive bonuses from applying directly.
This last can include:
-value at X or higher get a +1 e.g. 'if you have 5 or more ranks in Tumble, you get a +2 to Jump'; 'You can assist a Strength check for +2  if your Strength is at least 50% of the main player's"
-rolling to get a bonus. That is, a character might have to make a second check, and if successful their main roll gains a +1. This sort of thing allows bonuses that are less than '+1' in the core system (handy where resolution is fairly coarse i.e. rolls are of d6, or small dice pools).  Bonuses can pile up on the second roll without breaking the main roll.
-relative modifiers [thanks to Talysman]; on an opposed roll two characters may compare numbers, with the higher getting a limited bonus. For example take a rule stating "on an opposed skill check, the character with the most years of experience gets +2 to the roll". This allows the experience number to scale infinitely while never giving more than a +2.
*for actions, blocking synergies between these by specifying circumstances such that both can't usually be initiated at once. The only caveat with using this is that it should again be able to produce 'logical' results, rather than requiring system mastery to determine what can be done in combat.
* Modifiers to rolls can be limited by stating very specifically how/when these apply. e.g. Harnmaster rolls the total of all wound levels taken for shock rolls, but 'kill' rolls fairly arbitrarily use the wound level of that specific killing wound only. (This allows normal damage to mount up and have a chance to KO a character while keeping the likelihood of kill rolls fixed).
*not applying a modifier on the justification its 'already accounted for': 4E D&D would sometimes give an [unmodified d20] 'saving throw' to avoid extra effects on a hit, unmodified because defensive bonuses were already applied as part of Defense calculation. So the tarrasque's roll to resist being pushed back is unmodified because you need to hit [Fortitude defense 49] to hit the thing in the first place.
*Tunnels & Trolls 5E is interesting also in applying some modifiers stepwise. A saving roll target number is calculated by using [target number - stat], with minimum 5. This is mostly equivalent to additive except that for some rolls noted in the Elaborations section - Luck saving rolls to absorb Gunne damage, and penalties to marksmanship for being wounded or over-tired apply to the target number at the final step. Therefore attribute bonuses break the dice range, are discarded, then the penalties are applied. Even a very minor wound generates considerable increases in difficulty e.g. 3 damage will push the base roll needed on 2d6 from 5 to 8, much harsher than actual stat reduction would be.


Alternatives to giving out bonuses:  Other options can include:
-difficulty reductions: abilities like skill specializations reduce a penalty instead of a roll getting a + (hence, easy tasks don't get easier).
-bonus to damage/effect instead of bonus to-hit/success chance: for example in 3E D&D a charge ability may give a to-hit bonus but in 5E D&D this more often gives a damage bonus (e.g. the Charger feat - +5 damage). Or 5E paladin 'Smiting' is another ability that gets a damage bonus instead of to-hit.
-A reroll often provides a big increase in chance of success, but may be preferable where otherwise a bonus might take success chance to beyond 100%.(D&D 5E's advantage/disadvantage might be considered an example of this).
-rather than a full reroll, a character might roll a separate 'failsafe' percentage. For instance, instead of Dwarves getting +2 to save vs. poison they might have a separate Poison Resistance of 10% (or whatever).

*[as noted in post #31, non-integrated systems] D&D also sometimes handles a situational change by shunting a roll to an entirely different subsystem, rather than applying a modifier e.g. rolling the 'bend bars/lift gates' %, instead of a d20 roll under strength to make a check more difficult, or perhaps going from a Con roll on d20 to a poison save to resist dwarven ale instead of regular ale. [/FONT] (cf. SineNomine's post here). Other games have done this deliberately e.g. Savage Worlds card-based initiative, or  T&T occasionally cops out of using an attribute 'saving throw' check that would seem to apply to instead assign a 1-in-6 chance or other unusual roll. An increase/decrease in a value can even directly trigger a change to a different system [e.g. SenZar, Soothsayer - see step dice, post #15]. A change in subsystems can also be used as a way to give a bonus to success chance - e.g. 3E D&D characters who are dying normally have a flat 10% chance of stabilizing, but psionic characters can instead make an Autohypnosis check, letting them add skill/stat bonuses.

Justifications for Limiting Modifiers
Generally, the more nebulous a factor is, the more potential modifiers may apply, so if something is more narrowly defined it becomes more controllable. Hence what something is actually named can be important - an 'Intelligence' attribute modifies more checks than a 'Technical Aptitude' attribute does.
Similarly, something like "Armour Class" in D&D can receive various modifiers since the defensive value also considers dodging (Dex), deflection, etc. as well as armour; other systems might split out Dodging as a separate roll with essentially half the possible modifiers, then an armour bypass roll or Damage vs. Toughness save with the other half of the modifiers. Total number of modifiers involved isn’t reduced exactly, just split across multiple rolls...meaning all the rolls involved are less likely to reach 100%.
(There is an interesting exception or reversal of this here in e.g. 'Marvel Heroic'. Its actions are instead heavily abstracted, sometimes to a scene level - a pile of modifiers are applied as dice, then 'best two dice' taken out of the pile for the result, artificially limiting the bonus. Hence the effect of a high Str can be washed out by a high value on teamwork dice, bonus dice for a power, etc. Another effect of this on 'the fiction' is that its difficult to track which modifier actually made a roll success or failure - leaving it more open to narration, perhaps).

Offsetting Modifiers
Potentially a +1 can be countered just with a -1..especially easy in an additive system. For instance, 4E D&D has a level progression in DCs, where expected difficulty offsets gains from stats, magic items ('implements') and a +1/2 level progression - generating a sort of treadmill where character accuracy is relatively unchanged by level as long as characters fight 'level appropriate' monsters.
This shows a sort of general principle that in games with a high  level of escalation, bonuses can be countered by the GM as long as they're willing to exert the metagame pressure to do so (this being largely coded into the system in 4E). Game mechanics that automatically slow down bonus escalation, however, makes GM metagaming to match CR (or skill check DC) to the PCs less necessary.
Certain game mechanics are more directly suited to offsetting modifiers, notably if its common for a hard task to be [x1/2 bonuses] instead of a fixed penalty, this automatically gives some equalization. In other cases, EABA/Timelords had a table where difficulty acting as a % reduction to a characters' skill bonus. So, a difficult task had more effect on a character with a higher skill rating - keeping difficult tasks more difficult for characters regardless of skill.
'Rules lite' games can provide less details on expected difficulty of tasks to the GM, which then make it easier for the GM to surreptitiously allocate a difficulty that is easy or challenging. (With the more byzantine old-school systems, the actual sort of check can even be in question - a Dex check to avoid the falling block  or a 'breath weapon' save which might be much more difficult? - so the GM also has free rein in applying the "subsystem" approach above, or not). This approach is generally disliked by players who want the game to be strongly adversarial and/or a test of player skill at a mechanical level (e.g. character-building / tactics based strictly on game rules).
Situations which rely on player skill to an extent also bypass modifiers. For example, a 2E AD&D "Etiquette" NWP roll only determines that a character is performing any social protocols correctly - use of the right honorific etc. - not the total success of an attempt to 'Diplomacize' someone, which instead largely falls back on a player's ability to portray their character while making a convincing argument.

Automatic Success/Failure Chances
Capping bonuses at a maximum of "X%" (95% or 98%) is common, as are certain rolls automatically failing e.g. 1 on d20 (or 1 on d10 - Cyberpunk).

QuoteGuaranteed results (the "never fail" and "never succeed" stuff) tend to only work if the skill system is very, very well balanced, so that the guaranteed fails and successes only happen exactly when they "should". If the skill system's math is at all wonky or has corner cases where it breaks down, it makes the impossible-to-succeed and impossible-to-fail more likely to happen under the wrong circumstances. That's why skill systems that always have a chance of success and a chance of failure are so common: they insulate against design flaws in the system. It's not fun to be confronted with an impossible situation by surprise. - eggdropsoap

A tremendous bonus can also be mitigated by an automatic failure due to another independent roll for a situational factor, or vice versa with automatic successes. (e.g. the "sorry but your critical Seduction attempt fails -  I rolled and it happens they're gay").

What causes bonuses to get out of control?
Most often this occurs when a 1:1 transfer rate is used for simplicity (e.g. as recommended in Whitson Kirk's 'design patterns' book...), without considering if the numbers are going to overload the system. T&T again (in TrollZine #8) has a 'saving throw' alternate system for combat that showcases this: it converts combat to a saving roll, but lets characters spend personal adds 1:1 to boost this, up to 50% of the normal score despite adds being derived from three attributes, or four in 7E.
Another instance of bonus trouble due to over-simplification is the 3.x HP issue, where HP and damage bonuses use the same modifier on d6 (or other step die) as is normally applied to d20.

Systems Where Bonuses Are Out of Control
If you want to look at an example of system where bonuses are wholly out of control, Tunnels and Trolls is as good an example as any – despite success chance being based off a single attribute. Here open-ended difficulties can be applied to counteract character bonuses that are also out of control.
A T&T saving roll is 2d6 (doubles roll up) + stat; stats are initially rolled on 3d6 but may be increased potentially into the hundreds by magic, racial multipliers (i.e. Dwarf; x2 Str/Con) and level raises.
Saving rolls target numbers likewise start at about 20 and increase by 5 per difficulty level (i.e. a "20th level SR" - shooting a coin off someone's head at 150 yards away or resist certain spells cast at level-20, is target 115).
T&T does however consider a roll less than 5 that doesn't double (i.e. 1+2, or 1+3) an automatic fail - a kludge giving characters a 1-in-9 chance of automatic failure irrespective of godlike scores.
The game can work largely through the GM looking at the players' stats and deliberately creating challenges at about the right difficulty. Still, there's a very real chance of a character having to make a check, rolling up doubles three times at 200:1 odds, and still failing.
The T&T electronic (phone) game from Meta Arcade is interesting in that it rebuilt the original solo series as electronic adventures; it took out magical attribute raises (if it happens, its only a temporary raise for that adventure) but made it easier to gain levels and raise stats that way.

Another more common system with 'out of control' bonuses would be 3.5 D&D with open sourcebook abuse, especially for skill checks (which could sometimes have up to +30 or so racial, spell and/or magic item bonuses. Skills were less constrained as being less important that saves or attack rolls, but some special abilities could substitute skill rolls for saves or other checks, breaking expected values (also a problem with SAGA 'use the force' checks, IIRC). In 3E particularly, more and more content being written could result in more feats etc. supporting particular niches (charging really well, two weapon fighting, etc) which as characters still mostly had the same number of feats etc. available, leading to characters being unfortunately more specialized and overall useless even as they broke particular domains of the game). This sort of thing could lead to houserules on books allowed and, more interestingly, players might sometimes be allowed to (say) elect to use a particular sourcebook - meaning 'sourcebook allowed' becomes a sort of informal character option.

Edition change and modifiers
Fairly often an edition change includes some changes to rein in out-of-control modifiers (e.g. 3E D&D to 4E). Prior to that, 3E featured expanding numbers of modifiers as a result of attempting to systematize mechanics (such as monsters getting ability scores, single attribute bonus table, rolling various mechanics into the skill system, etc.) as well as remove arbitrary limitations of one kind or another. DC Heroes 1E to 2E dropped character attribute numbers dramatically.
Occasionally a random-roll may be replaced with a fixed number (e.g. set to the average).
WHFR-4E was interesting in replacing a d10 damage roll for combat with an 'opposed SL' (both sides in combat roll and the difference is compared) which significantly reduces variation; though Strength Bonus then adds as before and now looks relatively too large).