Opposed Tests (in RPGs)

Most role-playing games use opposed tests. E.g., RuneQuest:

An opposed skill roll occurs when one skill is actively resisted by another. For example, a thief attempts to sneak past a wily palace guard who, being vigilant is on the look-out for potential crooks. (pg 34)

(This is a confused concept in RuneQuest because combat rolls aren't exactly considered opposed tests, which is a little discombobulating because surely combat tests are "actively resisted by another.")

Or Diaspora:

You want to beat someone else at something. The defender rolls defensively and you need to meet or beat that roll offensively. (pg 9)

Opposed tests don't change your odds of success. However, some tasks that you could never achieve with a single roll may be achievable with an opposed test as it opens out a larger range of results. The inverse is also true, you can fail when you normally wouldn't.

I don't know where the idea for opposed tests came from, but they're a wacky idea. One of the main issues is figuring out, philosophically, what is and is not an opposed test. In RuneQuest, sneaking past an alert guard is an opposed roll, but trying to cut her throat whilst she attempts the same to you, is not, technically. This isn't solely an issue with RuneQuest, most games seem to struggle with the concept.

Opposed tests are usually reserved for resolving a conflict of one sentient being against another. Why is that? If one wants to cross a dangerous suspension bridge, one isn't allowed to roll an opposed test against the designers/builders of the bridge. However, if one of those builders were shaking the bridge from the other end, you might be allowed an opposed test. That seems quite odd.

I think that the only logical use of an opposed tests is to use them when you want, for whatever you want and just because they are fun. Playing with opposed tests makes it feel like there is a real conflict going on. And you can stunningly succeed or fail, so that has to be fun, surely. Of course, if a game never used opposed tests, it wouldn't be any less of a game and it would definitely speed the game up a little too.

FUDGE dice

FUDGE dice? See picture. You roll 4dF, add the pluses and minuses and that becomes your result, ranging from -4 to 4 (e.g., -1 in the picture). They're great. Why? Well, not because of the reasons I've read around the place. e.g.,

"A bell curve distribution such as this is excellent for RPG gaming because though it does indeed introduce a degree of randomness into an event, the bell curve's statistical properties still favor character traits over absolute randomness." (FATE wiki)

That statement is 100% false. Using FUDGE dice, or any dice rolling method, is no more or less random than any other (except weighted dice, I guess). The table they provide on the website clearly states that.

4dF Modifier Result	Odds	Chance of rolling this result exactly	Chance of rolling this result or higher	Chance of rolling this result or lower
+4	1/81	1.2%	1.2%	100.0%
+3	4/81	4.9%	6.2%	98.8%
+2	10/81	12.3%	18.5%	93.8%
+1	16/81	19.8%	38.3%	81.5%
0	19/81	23.5%	61.7%	61.7%
-1	16/81	19.8%	81.5%	38.3%
-2	10/81	12.3%	93.8%	18.5%
-3	4/81	4.9%	98.8%	6.2%
-4	1/81	1.2%	100.0%	1.2%

A "bell curve" property does not favour character traits over "absolute" randomness. e.g., your character has an engineering skill of 2. Lets say that to succeed at a task, she needs a result of 4. Using FUDGE dice, her chance is 18.5% (i.e., the chance of rolling two or more pluses.) Or use percentile dice, where less than 19% is a success. The randomness is essentially equivalent (give or take .5%) even though percentile dice are a uniform distribution rather than the normal distribution of FUDGE dice. Use one die, four dice, percentile dice, or a million dice, the randomness is the same. The chance of success is whatever the game designer, game master or players decide it is.

What FUDGE dice do, however, is give you a non-uniform distribution that you can use when you want to define varying possibly outcomes, each having varying probability. So, you could, for instance, define a series of results, such as:

• 4: Your sword cuts deep into your opponents neck. They slump to the ground and die, quickly, as blood seeps from the mortal wound;
• 3: The blade gashes armour and flesh from your opponent's left arm. They drop their weapon.
• 1 or 2: Your blade strikes hard against your foe's armour. They're shaken, morale faltering, yet steady themselves and grimace.
• 0, -1 or -2: Shield meets shield, bronze meets bronze. There is noise and sharp flashes of pain, but little else.
• -3: You trip and fumble, slicing into your left thigh. Walking will be painful and slow, at least for two weeks.
• -4: Not only do you fail to land a blow, your enemy ripostes and strikes your right hand. The weapon falls to the ground - you won't be able to use a weapon for two months.

You can assign fairly extreme results to 4 and -4 because they don't occur very often (1.2% chance). Zero, being the most common result can mean the status quo is maintained. Positive results can favour the roller and negative can punish them. They're good for making up a whole range of results, common and run of the mill to unlikely and extreme.

You can do all this on percentile dice, of course, but FUDGE dice are much faster to assign. You can also apply modifiers with ease using FUDGE dice, which is quite impractical using percentile dice.

Every roleplayer needs a set of FUDGE dice. Don't leave home without them.

The FATE RPG makes great use of FUDGE dice.

RuneQuest II: Modifying the maths

Okay, you've realised that the maths in RuneQuest II (and virtually all RPGs) isn't great, what do you do? You could ditch the game system and play free-form. That's a good idea. However, unlike most RPGs, fixing the maths in RuneQuest might not be too difficult. Here's what you could do:

Free Skill Points

1. Adventurers initially receive 500 free skill points to distribute.
   
2. Starting adventurers may assign no more than 30 points (i.e., 30%) to Common Skills and Combat Styles.
3. Advanced skills learnt as part of the Cultural Background or Profession process can by improved by 30 points.
4. Advanced skills, chosen by the player, cost 10 skill points to achieve the base level. These may be improved by no more than 20 points.
5. Adventurers never receive additional skill points (see below for Improvement Points).

Common Magic

1. Adventurers receive a total of 12 points to use in buying Common Magic spells.
2. Initially, the maximum magnitude of a Common Magic spell is 2.
3. Adventurers never receive any more points to buy more Common Magic, though they can swap spells out for others using Improvement Points (see below).

Improvement Points

Improvement Points are distributed by the GM, at the appropriate time, as usual. These points can be used, to not increase Characteristics, Skills, and magic, but to shuffle them around.

For Skills:

• Select the skill to be increased and roll 1D100. Add the Adventurer’s INT characteristic to the result of the 1D100 roll.
• If this 1D100 result is greater than the skill’s current score, the skill increases by 1D4+1 points.
• If this 1D100 result is equal to or less than the skill’s current score, the skill only increases by one point.
• Select another skill. Reduce this skill by the same amount that you increased the first skill.
• A common skill can never be reduced below its base - i.e., Characteristic + background and profession modifiers.
• Skill percentages may only be increased up to 90%.

Learning new advanced skills functions in the same way as described in the core rulebook. Any improvement beyond the basic characteristic-derived score, however, follows the same rules as above.

For teaching, mentors and learning new advanced skills, they work in the same sort of way as described in the RuneQuest II core rulebook. Keep in mind that you may not have a net increase in skills - you must decrease a skill in order to learn another.

For Characteristics:

• Select the Characteristic that you want to increase.
• Select the Characteristic that you want to decrease.
  
• The difference between the two Characteristics is the number of Improvement Points that you that need to spend in order increase/decrease the Characteristics by one point.

For Common Magic:

Common Magic spells can be improved, learnt or discarded by using Improvement Points. This improvement works along the same lines as Skills and Characteristics. To increase the magnitude of a Common Magic spell, one needs to decrease or discard a current spell. Use the Learning Common Magic Spells table (page 107) from the core rulebook to see the costs of improving Common Magic. e.g., Arlyn knows Bladesharp 2 and Warmth 2. She uses 2 Improvement Points to increase Warmth to magnitude of 3. At the same time Bladesharp decreases to magnitude 1. Note: To learn/change Common Magic spells, the adventurer is still required to locate a teacher willing to reveal its secrets.

Skill mechanics

Critical success, fumble and opposed rolls work exactly the same way as described in the core rulebook. Adventurers' skills can never rise above 90%, so generally you can ignore rules for skills over 100%. Occasionally, however, you'll want a powerful opponent with percentage over 100% (a dragon, perhaps?)

Profession and Cultural Background

During a period of downtime, a new profession may be taken-up by an adventurer. In doing so, they gain all of the benefits of the new profession. However, they also lose all the benefits of the old profession.

Over a period of years, the cultural background of an adventurer may be changed (if they spend a considerable amount of time within the new culture). All the benefits of the old background are lost. All the benefits of the new background are gained.

Magic & Spells

Nothing may increase a skill beyond 90%. e.g., If you have the Sword and Shield Combat Style of 80% and cast Bladesharp 3 (normally +15% to combat style) on yourself, your chance of success is 90%, not 95%. It's no fun unless you always have a decent chance of failure. (You still get a +3 bonus to damage.)

A note on rewards

The gamemaster should not reward magic items that permanently increase either skills or damage. This will ruin the maths and start the illusory arms race all over again. Get creative! Don't just reward players with numbers.

People already understand this idea. Carl Walmsley, in Compendium I, wrote alternate rewards for players/adventurers to help avoid the maths getting out of hand. For example:

Potion of Fortune
Drinking this potion makes the character unfeasibly lucky. It is as though the universe smiles down on him and everything seems to go his way. The character receives a +10% bonus on all Skill tests, and adventurers who attempt any actions which are to the detriment of the character receive a -10% penalty. In addition, the character gains either an additional Hero Point or an additional Combat Action (determine this benefit randomly), usable within the potion’s duration. At the end of the potion’s duration the Hero Point or Combat Action is lost as the luck ebbs away. A Potion of Fortune’s effects last for 12 hours.

This magic item is a fantastic example of what you can do to reward plays without breaking the maths. If one contrasts this with a reward from Summons of the Wyter (an otherwise excellent adventure), one can see the difference in effect.

The Needle – a broadsword with a strangely carved hilt, handle and pommel (it is made of a human arm). The broadsword has the normal characteristics of a broadsword but is also capable of the Sunder Combat Manoeuvre and is treated as a weapon cast with a permanent Bladesharp 3 spell (so, +15% to the Combat Style and +3 damage).

They're similar items in many ways (grant a bonus to skills). The Potion of Fortune is, in many ways, more powerful, but the power won't last long. The Needle, on the other hand, is a permanent Bladesharp 3 spell. A item like this will start the Maths Wars all over again.

A note on cults

Cults are a great way for adventurers to advance. Gamemasters should grant the usual bonuses (new spells, social standing, etc.). However, don't forget that with this advancement comes new responsibilities.

A note on published material

Published material, by Mongoose Publishing or whomever, will operate along the lines of the Rules as Written. This is may appear, at first, to be a big issue. However, as every gamemaster already knows, one often needs to mold the adventure to fit with the current abilities of the party. In fact, the only reason adventures need to be manipulated like this is because the maths in RPGs is all screwy. If RuneQuest II used rules similar to the ones above, any adventure, if it fit with the story and development of the adventurers, would be suitable to play without any fudging of rules whatsoever.

Mongoose Publishing, thus far, have created material that is generally usable. The creatures in the core rulebook and Monster Coliseum have not been power-mathed. Hopefully, the forthcoming Monster Island will follow a similar vein.

Conclusion

These rule changes fix the bulk of the maths issues found in RuneQuest II. One may need to revise a few more things, here and there, but generally the resulting adventurers will be balanced and fun to play for the entirety of the campaign. In many ways they'll begin quite powerful (with double the Skill points and Common Magic than normal starting characters) though this will be spread across many skills and spells. Players can still take pleasure in the advancement of their adventurer, in a real sense, as they move from generalists to specialists, over a number of game sessions. Admittedly, they could never compete with "Hero" level adventurers, but these changes are about creating interesting and challenging situations and stories for everyone involved (players and gamemasters), rather than trying to out maths each other. Using these rules and the accompanying notes should allow the gamemaster to focus on the story rather than worrying too much about numbers.

Advancement rules in roleplaying games

Numerical advancement in roleplaying games, where there is a net increase in values (skills, stats, attributes, etc.), is like treading water in a river flowing downstream. You may feel like you're swimming, but it's the current that's taking you along for the ride.

Lets take Dungeons and Dragons in the simplest form. You start with a +2 bonus. Roll a twenty-sided die and add the bonus. Against a goblin, 15 or above is a success. A little later you "advance". You now get a +4 bonus. Against the same goblin, your chance of success has improved. If that's all there was to it, it would be a real improvement. Of course, that isn't all there is to it. If you advance a few more times, your chance of success gets so high that there is barely any point in rolling. So what does the game master do to spice things up? Simple. A goblin with a helmet (need 18 or above). Or two goblins. Or an Orc (24 or above). That is, the game master has to change the odds to stop the game from becoming boring. It becomes an illusory arms race. Once you do the arithmetic, however, you're back to where you started.

If you're someone what doesn't understand maths, there isn't an issue. It's fun to think your character is getting better and better (rather than more and more uselessly complex). But what do you do if you want to play RPGs and you understand maths? You could pretend the issue doesn't exist, find a game without these silly advancement rules or modify an existing game so there is no superficial advancement.

In our next game session, I'm going to modify RuneQuest so it's not tied to any form of net numerical advancement. The only logical way to do this is to completely excise the game system. Drastic, but the entire system is tied to advancement, so it all has to go. What's left? Lots of stuff:

• An evocative explanation of how ancient forms of combat worked
• Great descriptions of ancient weapons and equipment
• Good lists of professions
• Great ideas for magic and spell descriptions

In fact, hardly anything is really lost. And there is still Glorantha. Glorious Glorantha.

Are there any RPGs that don't try this rather trite gimmick? Everything (D&D/Pathfinder, RuneQuest/HeroQuest, Traveller, Rolemaster/MERP, Burning Wheel, FUDGE/FATE, HarnMaster, T&T, Savage Worlds, Warhammer Fantasy Roleplay, etc.) but two games; Fiasco and Diaspora. (There may be more.)

I am left wondering how any of this came to be. I've got a few ideas.

• The market. You can sell a lot more books if you convince people that they'll need tougher monsters and better magic items. You need more and more and more.
• People don't understand maths. They really don't. (Myself included, a lot of the time.) It can be very confusing. So many dice, so many game systems, so much options and layers. It's difficult to figure it all out.
• Legacy. Some guys thought it up in the 70s, so it must be right, huh?
• Bourgeois ideology. The need to reproduce notions of progress is so deeply embedded in all thought and practice in the modern world that any progress, even non-existent progress, is clutched at.
• People love inventing systems. Even if the system is nonsense, people just love to invent them. I don't know why.
  

Burning Wheel forum is an interesting read

Whoa, I'm getting some rather harsh (somewhat unfair?) criticism from The Burning Wheel forum. I must truly be a moron because the captcha keeps blocking my registration. Therefore...

"He thinks the DoW is too complicated and doesn't understand it at all, nor can he see how anyone else might understand it."

I believe I understand duel of wits and say nothing about other peoples' understanding. The reason I like Fight! compared with DoW is probably due to history. I expect combat in RPGs to be complicated. I like how old style games don't prescribe rule systems for non-combat. It leaves the players to determine all that. I enjoy the dichotomy of freedom and roleplay for social stuff, complex and strict for combat.

I think, if I were to design an RPG, I would do the exact opposite of The Burning Wheel. Instead of bringing systems into non-combat, I'd take the system out of combat. In fact, I'd probably design something that is almost no system at all. The players/GM would be responsible for providing all the continuity and determining the results of events. Dice, probably just a d10, would be used when you want chance to assist in determining outcomes. Anyways...

"Well, I like d100 in theory... but it's boils down to the tens die. Once you roll that, it doesn't matter about the other die in 9/10s of the cases."

Quite correct, except if you use critical success and fumble. Then it's 7/10. Or opposed test, 6/10. Still annoying, however. If only physical d100s weren't so crap...

"The dice pool thing is some personal problem he has..."

"I'm amused that he gets the complex ideas (BITs and Let It Ride) but doesn't get dice pools."

Personal problem? Well, yes, you can call it that, if you want. It sort of belittles things like alcoholism and depression, but whatever. Another way of putting it is "I don't like dice pools for reasons x, y, and z." I do understand them, however. Why do people often conclude that just because you don't like something you don't understand it?

"he wants straight ExP awards in place of Arthas. So he hasn't gone through the rewards cycle, advancing skills/stats, shade shifting to get a feel for it."

Not true. I want something simple. If ExP (I assume you mean D&D XP) is simple, I want it. I like RuneQuest's reward system. It's immediate and you can apply it to things like improving skills/stats, learning new skills and learning new magic. It blows away stupid stuff like going up levels in D&D, for example.

---

None of these generally absurd comments improve my disposition towards The Burning Wheel. It doesn't turn me off in any way either. One day I'd like to discover a forum that wasn't 75% tools, but it'll probably never happen.

The Burning Wheel review

I've heard some good things about The Burning Wheel role-playing game. It attempts to fully integrate character actions into the story. This is a very good idea and what should drive RPGs.

Game System

I dislike the basic game system. It uses dice pools. You roll a number of six-sided dice and count results of 4 or more. If the count fulfils the number required, you succeed in your action. If not, you fail. The reason why I dislike this system is that you always have to grab different numbers of dice, spend a couple of seconds figuring out if you succeeded (not really knowing what your chances were) and pick up, from the floor, a lost die because you had to roll 5 of them. It just screams of a design by someone who doesn't understand probability or how to get take the tedium out of RPGs.

What you are looking for when rolling a die is a way to take a decision out of the hands of the players and game master, and into the hands of chance. Generally, the result is binary (success/fail), occasionally more interesting (critical success, success, fail, fumble), but it's never anything that requires such an involved method as what Burning Wheel uses. Obviously, flipping a coin won't work. However, does that mean you want varying numbers of dice, a variable "success" requirement (4 or above, 3 or above, 2 or more) or varying counts required to succeed? E.g., in The Burning Wheel, you could need 5 "successes" with 7 dice, each "success" being a roll of 3 or more. Not only that, occasionally when you roll a six you get to roll another die! Argh! What is the point of all this complexity?

What is better: Take all those variables into account and figure out your percentage chance of success and roll a d100. What is best: Ditch the system entirely and use something sensible.

RPG advice

It's not all bad news. The book is really very good in describing what roleplaying games are all about. It's about characters and story and their interaction. Dice, the book explains, are used whenever you can't just say "yes" to a request by a player. That is, if the character wants something that someone doesn't want it to have, you roll. Keeping this in mind when playing RPGs is invaluable.

There is also the "Let it Ride" rule. This is such a simple and seemingly obvious rule that I'm surprised I've never used it. It can apply to any RPG. It is, essentially: Just roll once to perform a task, no matter the subtlety or the game time involved. Rolling multiple times can often mean you didn't get the result you really wanted. Learn to deal with the result rather than re-rolling.

Characters

Another extremely good idea are the beliefs, instincts and traits of a character. (In reality, only beliefs and instincts are innovative. Traits already exist in many games, like Savage Worlds' edges and hindrances and RuneQuest's gifts and compulsions.) A player is instructed to write down three beliefs that their character has (e.g., "the poor are little more than pebbles to be trodden on"). If the player plays their character inline with their beliefs, they are rewarded. Attributing beliefs, instincts and traits to characters distinguishes them from other characters much better than stats ("my character is strong") or roles ("my character is the thief") do.

However, having described these new ways of characterisation, The Burning Wheel then imposes a rather complex reward mechanism that the author calls "artha". It's all too much complexity and I can't see how it does anything other than detract from the storytelling, which seems at odds with the overall idea of the RPG. I'd much rather have my players write down their beliefs, instincts and traits and simply award a RuneQuest improvement point (or D&D XP) whenever they play their characters correctly. A storytelling RPG should be all about simplifying and adding ways to improve the storytelling process, not hindering it by adding complexity.

Duel of Wits

The duel of wits sub-game is an clever attempt to undertake social conflict as part of a game. It's an expanded rock-paper-scissors. Players write down a series of argumental/rhetorical volleys, each as a type of action. In a duel of wits, the player may:

• Avoid the topic
• Dismiss your interlocutor
• Feint
• Incite
• Obfuscate
• Make a point
• Rebut
  

Each action interacts with the other actions differently. Each speaker writes down a series of three actions at a time and they are played off against each other. The actions resolve simultaneously. This all needs to be role-played at the same time too. You can't just say "I make an eloquent point."

It's a clever system, but it seems too complicated. I don't see why one needs to formulate social interaction. In fact, once you have the idea of a debate in your head, you couldn't you allow the discussion to evolve more organically, rather than systematising it?

Combat System

The combat system is similar to the duel of wits. Players write down their actions in a series of volleys and all combat occurs simultaneously (like in Diplomacy). Actions are:

• Avoid
• Beat and bind (attempt to knock away a weapon)
• Block
• Charge/Tackle
• Counterstrike
• Disarm
• Feint
• Great Strike
• Lock (i.e., grapple)
  
• Push
• Strike
• Throw Opponent

I like it. It's simpler than most combat systems and yet there are a whole heap of cinematic options that could result in some fairly interestingly unpredictable battles. Still, I do kind of like the control you get in turn-based games like RuneQuest (which has all those combat manoeuvres and more).

Conclusion

The simultaneous conflict in Burning Wheel is a cool idea. I could see how that would be very fun to play. It might even speed up the often very slow combat sequences in RPGs. The way characters are created and played is also really cool. Nevertheless, I can't see why I'd ever play the Burning Wheel. The basic game mechanic (dice pools) is dire and infects every element of the game. It's too complicated and too tedious. Furthermore, there are too many rules! It's a 300 page book, almost entirely made up of rules. I'd need to completely re-work the whole thing to make far less mechanistic and complicated.

However, it's not all bad news. A lot of the ideas from the Burning Wheel went into making Diaspora. The end result for that RPG is very different. But that's for another day.

Probability in RPGs

Dice rolling is one of the core features of basically every role-playing game (except Amber Diceless). However, when probability is involved, people often get sucked into weird beliefs and numerological thinking.

There are a couple of good documents on probability in RPGs. See here and here. I have a few extra comments, especially regarding RuneQuest.

The percentile rolls in RPGs use two ten-sided dice. (I don't think anyone actually uses d100s.) One die represents the tens, the other, units. This means that one of the dice is an order of magnitude more important that the other. Only one in ten rolls of the second die is worth rolling (i.e., you need 64%; only a 6 on the tens die makes the second die relevant). RuneQuest, however, offers a couple of subtleties - critical successes and fumbles - that brings the usefulness up to 3 in 10 rolls. I've also noticed, with opposed rolls, that that number goes up to 4 in 10. Therefore, RuneQuest is mostly a d10 system, rather than percentile. However, the second die is used about a third of the time and gives some rare probabilities that makes it quite intruiging.

Comparing the percentile system of RuneQuest (Call of Cthulu, Basic Role-Playing and others) with D20 (D&D, Star Wars, etc.), I find the d100 system more satisfying. This is because

1. It's very easy to judge your chances of success when using percentiles. With D20, it's not immediately obvious what your chances are when you need 24+ and you roll 1d20+10. Sure, you can quickly figure it out, but it would be better if you didn't have to.
   
2. Little touches in RuneQuest, like fumbles that occur when rolling 99 or 100 and varying chances for critical success (depending on your skill level), break up the standard roll of 1 for automatic failure and 20/18-20 for critical success of D&D/D20.
3. Critical hits in D20 require re-rolls. This wastes more time.
4. In D20, the player, when rolling, does not know the chance of success unless they ask the game master. With percentile systems, the player knows the chance of success, unless the game master modifies it. The latter is better as it gives more determinacy of the result to the player.
   

The above concerns transparency and clarity, there isn't a real difference in probabilities between a percentile or D20 system. It's a single roll and the probability of each result is linear (can just as easily roll 33% or 99% in RuneQuest or 2 or 20 in D20). On the other hand, there are a few other game systems that provide either real differences to the probability or more superficial complexity. They are:

• Normal distribution systems, like the approach of Traveller, GURPS and Fudge. E.g., roll two dice and add them together. The non-linear distribution is cool in the sense that more often than not you'll roll near the average. However, the downside is the probability of success is tricky to figure out, especially when you don't want to have to put much effort into thinking about it. It also requires arithmetic, slowing down the evaluation of the result.
• The dice pools (e.g, grab a number of d10s relational to your ability) of World of Darkness, Warhammer Fantasy, d6 Star Wars and The Burning Wheel games also sounds pretty cool, but again, it's not overly obvious what your chances are to achieve a task. Also, more dice means more time to evaluate. Not good.
  
• The step dice of Savage Worlds, EarthDawn and Serenity seems very promising. You use 1d4 when unskilled, 1d6 if you're a bit more competent and 1d10 if you know what you're doing. The probability is easy to figure out and it's fast to evaluate. Having said that, Savage Worlds, at least, has complexities. Wild Cards (PCs and important NPCs) have two dice to roll (one normal die and one Wild Die) and re-roll if you ace (get a 6 on 1d6, for instance). This takes time and obscures the evaluation of probability. Nevertheless, I'd really like to play one of these games.

My preferences then, based on transparency and speed of evaluation are:

1. Percentiles (RuneQuest)
2. Step dice (Savage Worlds)
3. Roll and add modifiers (D20/D&D)
4. Normal distribution (Traveller)
5. Dice pools (World of Darkness)