About Game Design: Of Dice and Games

About Game Design: Of Dice and Games

By John H. Reiher

This article is first of series of articles on game mechanics, specifically on how to use dice in your game rules.

As role players, we love our dice. Just about every dedicated gamer has a bag or two full of all colors and kinds of dice, in all shapes and sizes. Some of us, me included, have dice old enough to drink. When it comes to generating random numbers, you just can’t beat dice.

However, there is the dark side to dice: obsessive behavior over a bit of plastic and paint.  More specifically, we see GMs who abrogate their authority to the dice, players who obsess over their lucky dice and players who try to roll all the “one’s” out of their dice.

This bugaboo includes game designers. We use dice to generate random encounters, determine the success or failure of a task, resolve combat situations, and create characters, ad nauseum. Sometimes we use the same dice rolling mechanism for all these uses. Sometimes we use a different die for each. It’s all up to the designer’s tastes and what they want to simulate in their game.

Some designers even go as far as create a unique set of dice for their game, such as F.U.D.G.E. and Hollow Earth Expedition. Albeit, you don’t need these special dice, it’s just a lot easier to make the die rolls if you do buy a set.

In the end, though, it all boils down to how do you resolve conflict and tasks in your game.  GM fiat or something beyond? (Not that GM fiat is all that bad, especially in the hands of a good GM.)

One solution is going diceless, though some diceless games use a 52-sided random modifier, i.e. cards, to determine the outcome of a task or conflict. I don’t have a problem with these diceless systems — except when they evangelize about the evils of randomization while indulging in what is merely a different flavor of the same.

Randomization in and of itself is not evil. In fact, in the right hands or situation, it can lead to interesting events and situations that neither the GM nor her players would have thought of. The main drawback of randomization is that it can lead to frustration when a player hits a long streak of bad luck with their dice rolling.

A good game design can help deal with both of those situations.

K.I.S.S And The Art Of Game Design

“But how do I do that in my rules?” you ask.  You do it by remembering that it’s the GM that runs the game.  Not you, not your rules, and especially not the dice. If your rules require a lot of number crunching, especially before you roll the dice, for something as simple as determining whether or not you hit the floor with your hat, no one is going to use them!


Take Cover!

Take Cover!

I hate to say this, but leave realism for video games. Anything that involves more than simple addition and subtraction during gameplay should be avoided as best you can. Combat is notorious for all sorts of modifiers, especially ranged combat. Does your game need six types of combat modifiers, and do you need to subdivide those types into a half dozen subtypes? Do you really need five variants of cover or to worry about the size of your opponent other than when they are exceptionally tiny or huge? 


To summarize:  are you really looking forward to having players buy your games for your wonderful settings, then look you in the face and tell you “Love your game, but I don’t use your rules. I use [insert favorite system here] instead.”

The old adage of KISS: Keep It Simple [Insert invective], really applies to gameplay. If a takes half an hour to resolve a combat round that takes place in 6 seconds of game time, you’ve gone far overboard. And falling in love with your dice mechanics can aggravate this syndrome.

The Average Person


Average People

Average People

Now before I go into the different systems, you, as a game designer, need to define what an “Average Person” is in your game and then use that person and not a “Player Character” to see if your rules make sense. (Of course, character creation is another topic) 


The Average Person defines what the average Joe or Jane can do within the game rules. They are your baseline for all forms of task resolution.

So, how do you define what Average difficulty is?  An Average difficulty is one that the Average Person can succeed in completing on average. This means that typically the Average Person has sufficient skill + attribute modifiers to succeed at the task, even if you don’t roll the dice.

Keeping this Av3 rule of thumb in mind is important, as it will keep you from having babies capable of throwing a football 70 yards or characters hampered by a miserly 50/50 chance of picking up a glass from a table.

Dice Systems

So let’s talk about dice systems in games.

Most systems breakdown to just a couple of types:

·       Target Number: Rolling dice to beat or roll under a target number.

·       Success Rolls: You must roll a specific value to count as a success or failure.

There are others, but these are the primary types of dice mechanics.

Target Number:

This is the most popular method of determining the success or failure of a task or conflict. D&D uses this, as does GURPS, Savage Worlds, the Omni RPG system, and most others.  They all use one of the two variants of the Target Number method, which boils down to either Probability Spread or Simple Die Resolution.


Image by <a href=

Image by Free-StockPhotos.com

Most Target Number systems are “High is good” systems, in which higher is better better. Any modifiers in these systems affect the dice totals, increasing or decreasing the values rolled.


Some, like Tri Tac Games’ original Bureau 13, or Heroic Journey Publishing’s i20 Bounty Head Bebop, use a “Low is good” system, where you try to roll equal to or under the target number, with the target number based on the character’s skill levels and/or attribute levels. Modifiers adjust the target number, not the roll.

So which is better? “High is good” systems are better at replicating pulp, cinematic types of adventures, while “Low is good” systems tend to be viewed as being more realistic. Note that exceptions to both of these views exist, so take this comparison with a grain of salt.

Probability Spread


d20 bell curve

d20 bell curve

With probability spread, you’re rolling multiple dice, adding their values together, and then comparing this total against a target number of some sort.  You are attempting to better either a fixed difficulty or an opposed value rolled by an opponent.  GURPS uses this method and finessing the probability is part and parcel of the game. You have to take into account what the average value is for the number and type of dice the players roll, what the possible modifiers are for this roll in terms of skill values and situational modifiers, and then adjust the target number for the different levels of difficulty appropriately.


Simple Die Resolution

D&D, Savage Worlds, and other game rules use a simple die roll against a fixed or variable target number, similar to the probability subtype. Skills, situational modifiers, and other bonuses and minuses also modify this roll. This resolution system is easy to rank as to difficulty, as you are dealing with a random distribution of values and not a probabilistic bell curve. This makes it easier to gauge how your Average person will fare with an Average task.

Savage Worlds complicates this by using a feature referred to colloquially as “exploding dice” better known elsewhere as “open ended rolls”.


When dice explode

When dice explode

“Exploding dice” means that when you roll the maximum possible value on a die, you get to roll that die again, adding the new value to the previous value. Some RPGs let you roll again if you roll the reroll number a second time and keep on rerolling until you roll a value other than the reroll number. So far, I know of no probability spread subtypes that use exploding dice. Perhaps they would explode if you rolled dead average. This is just something for game designers to think about out there.


Another variant on the simple die resolution is the dice pool, as used by Dogs in the Vineyard. A dice pool is where your skill levels or attributes represent a set number of dice that you can roll for task resolution. In Dogs in the Vineyard you make an opposed roll using your dice pool against the GM or another player. Then you select two or three dice from the pool as a your “bet” and your opponent selects enough dice to beat that bet. Then you select more dice from your pool and ante up again. The winner is the person who uses the better “hand” of dice and artfully matches and counter matches the other player. Still, in essence, it’s a variable target number mechanic.

Success Rolls:

The success roll type typically counts the number of successes rolled on the dice, where a success is counted when you roll a specific value on the die, either the highest value or lowest value. Hollow Earth Expedition uses a variation of this, counting the number of even value dice vs. odd value dice. You get to choose if even or odd represents a success.

F.U.D.G.E. counts 1 & 2 as a negative value, 3 & 4 as neutral, and 5 & 6 is a positive value, and your goal is to get an overall positive result from a task roll.

Urchin uses a dice pool of d6s and counts a “6” as a success and a “1” as “rot”. Rot does bad things to your characters. Your goal is to roll more successes than the GM or the other players in an opposed roll to succeed and not take various kinds of damage. Urchin chews up characters and spits them out like well-masticated gum. What else can you say about a game that encourages you to use paper pulled from a garbage can for a character sheet?

Success rolls either use a minimum number of successes to complete a task, or they use opposed rolls for everything. You’re still playing with probability here, as you have to calculate what the chance is to roll a particular number of successes. In this case, you need to know what your Average Person has for an average dice pool, and then work out the chances of them rolling an average success.

For example: Hollow Earth Expeditions defines an Average person as having a 2 in every attribute, a 4 in every secondary attribute, and a 4 or 5 in every skill. Average difficulty is defined at rolling 2 successes. So an Average person has 50:50 chance at succeeding at a task. Well, no. Hollow Earth Expeditions makes use of a feature called “Taking the Average”.  In essence, this feature lets you succeed if the average roll of your dice pool would be equal to or greater than minimum number of successes.  More on this later.

Taking the Average:

In the early years of RPG game design, dice rolls, no matter what, decided all tasks. The unintended consequence of this was an unacceptably high failure rate for mundane tasks. Taken to the extreme, this implied that airliners fell out of the sky like rain in Seattle, cars crashed together like eggs in a paint can on a paint can shaker, and you’d have a 1 in 20 chance of dying just walking to the store. Many of these were highlighted in the ever-insightful “Murphy’s Rules”.

Game designers took heed of this criticism and created the concept of “taking the average.” Some games state outright that you only roll for success in situations that are out of the ordinary. Others say you don’t need to roll for mundane tasks. Basically, both are saying that the target number is 1 for mundane tasks and you get to take the average on them, which is better than 1.

D20 Modern called this “Take 10”, other games call it “Take the Average”, but no matter what, it’s a way let experienced characters perform tasks that are ordinary to them but hard for others.

Operationally, taking the average is nothing more than taking the average value of the dice that you’re rolling, adding them to any applicable modifiers, skills, and attributes, and then comparing this value to the target number. Depending on whether or not the dice are “High is good” or “Low is good”, you see if you succeed.



A critical success at stealth.

A critical success at stealth.

Some games make use of the concept of the “Critical success” and/or “Critical failure”. A critical occurs when you roll one of the extreme end values, high or low, for the type of die being used. Dungeon & Dragons has long determined that rolling a “natural” 20 on a d20 is a critical success. Bounty Head Bebop (Which is a “Low is good” system) has value ranges that are “semi-critical”, such as rolling a value as close to the target number as possible. In Tri Tac Games’ original rule set, rolling under half the target number value bestows some semi-critical benefits, such as double damage.


Critical effects are typically well defined for combat situations, but almost always woefully undefined for all other task resolutions. In some situations this is understandable: “OK, I’m making a rug using my Craft (textile) skills. I roll a 20! A critical Success! What does that do?”

Indeed, what does it mean to roll a critical success on making a rug, or cooking dinner? These tasks are far more complex than just hacking at someone with a sword. The effects of a critical success are harder to nail down than whether or not you do double damage.

And here we see the fatal flaw of using a single die for task resolution. Most games use a d20, which means that you always have a 1 in 20 chance of critical success or failure. So one in twenty planes falls from the sky.

So we need to decide where criticals are applicable, and within those boundaries define their effects well.


“Which one of the many dice systems is best for me?” you ask? To be honest, in my opinion it’s the one you like the best. Beyond that, it’s just a matter of flavor. I’ve played pulp games using all of the systems outlined in this article and they all worked fine. This should tell you something. While dice are important, dice do not a game make. What’s more important is how your rules interpret those dice rolls. Which is a topic for the future.

Just keep in mind that there are always some shortcomings to every dice system, and you need to know what they are and how they can affect your game. Playtest, playtest, playtest.  Then, once you’ve playtested your rules, be prepared to throw the system out if it doesn’t work the way you wanted it to.


4 Responses

  1. Garry Stahl and I had a discussion about this article on the Bureau 13 Yahoo! Group. With his permission, here is the conversation:

    GS: Interesting read. I’ve had much the same discussion on the Pen and Paper forum. Dice, ratios and bell curves. Yea, I have a few dice old enough to drink. I think all we old farts do.

    But the kind of thing you were discussing is where one of my rules of GMing comes from. “A die roll is not required even if a die roll is required.”
    JR: Thanks Garry. I think the hardest part of writing this article was making sure I could find games that represented the two types of dice rolling resolution. I was going to talk about “matching values” but the only rule set that did that was One Roll: Wushu and Godlike use One Roll as their base systems, and even then, I realized that it was a Success roll more than anything else, so I dropped that type from the article.
    GS: Method also matters. I’ve tried to identify all the dice resolution methods I could think up.

    Straight target number, be that high or low, no matter the die type, single die. “Window” fixed target number low is good, die type varies. Die test: Fixed dice, high is good, target number slides. Reverse die test, Fixed target, low is good, number of dice varies. Dice pool. Fixed target roll for number of successes.

    I know I’m missing some of the ones I’ve seen.

    Also the changing of the dice can have a huge affect on the game. For example instead of a d20 someone suggested using 2d10. You can do it, bu the value of a single +1 goes way up as a result. It skews the result table and virtually creates a new game in the process.
    JR: That’s why I covered the types in general. I figured that dice were the low hanging fruit of game design. Next up will be task resolution and doing things, that’s a whole ‘nuther kind of fruit.

    I once contemplated using 4d6-4 for the 0-20 range. That gives you a 1:1,296 chance of rolling either a 20 or a 0. That would be a definition of a critical success or failure. Of course that’s still higher than reality, but a heck of a lot better than 1:20 chance.
    GS: That is why I use confirms and roll through. I’m an old time D&D player and yes, a automatic critical success or failure at 5% each is way too high.

    So, if you need a 20 to hit, you cannot get a critical unless you roll through for a second 20. If you can’t miss on a one you have to roll through on a one to see if you miss.

    If the character cannot hit on a 20 and rolls a 20 they roll through to see if they can hit.

    It evens out the rather crude scale of the d20 system. It still does little for the scaling problem.
    JR: Well, you may have noted that in 4th Ed. of D&D, they dropped the confirm roll for criticals. It was the most hated feature of the 3.0 and 3.5 editions.

    If you go with a 4d6-4 range, you have to redefine your target numbers on probability scale. Which means you need to draw the bell curve for the range and define your target numbers based on that curve. So average difficulty rolls would have a target number of 10, but nearly impossible difficulty rolls would be 20+. Above average target numbers would be 12 or 13.

    It would look like:

    Average: 10
    Above average: 12
    Hard: 14
    Difficult: 16
    Very difficult: 17-18
    Impossible: 20
    GS: Ayup. Changes the whole character of the game. You pretty much have to redesign from the ground up if you change the dice.
    JR: Well, maybe, and maybe not. It depends on how your rules interpret the results of the die rolls.

  2. Some comments from Anthony Jackson on the sfconsim-l Yahoo! group.

    Hm. Some reactions:

    The way you’ve divided dice systems into ‘target number’ and ‘success rolls’ is very odd. For example, I would call FUDGE a target number system, because you’re adding them up, it’s just that dice are labeled -1, 0, +1. In general, there seem to be a couple of variants:

    1) Roll one die against a target number, which might be high or low. Skill typically gives a flat bonus, difficulty typically adjusts target number, though either one can also be implemented by adjusting the die type. Example: D&D. Often well suited to rolling multiple tasks at once, such as wargames where you roll all your units attacking at once.

    2) Roll two or more dice, add them together, and compare to a target number, as (1). Skill and difficulty can work the same as 1d, or they can modify the number of dice rolled. Examples: GURPS (skill and difficulty are flat modifiers), Star Wars (skill adds dice, difficulty is a flat modifier)

    3) Roll two or more dice and apply each die against a target number, as per (1); count how many of your dice succeed. Skill might modify target number, or might add dice; difficulty might modify target number, or might require extra successes. Examples: Shadowrun, Vampire.

    4) Roll two or more dice and select one, such as the worst, the best, or the middle value, then apply as per (1). Skill and difficulty, again, can either modify target number or dice. Examples: Heavy Gear, Deadlands.

    5) Roll two or more dice and look for patterns, such as doubles. Examples: Exalted.

    6) Any of the above, plus a more complex die rolling pattern, such as rerolls on certain types of dice.

    *High is Good vs Low is Good*
    Your distinction here is bogus; mechanically, roll high and roll low are identical, it’s just that one requires you to perform subtraction, the other requires you to perform addition. As most humans are better at addition than subtraction, roll high usually has a mild advantage.

    *Taking the Average*
    This is mostly a D&Dism. Common solutions include making the task so easy that the worst possible roll still succeeds, and simply declaring that you don’t roll for trivial tasks. Some dice pool systems also have ‘declaring successes’, but that usually doesn’t give you an average result, it gives you a substantially below average result.

    *Most games use the d20*
    While the biggest game uses the d20, most game systems do not; the d6 is the most commonly used die type.

    You mention that dice systems have shortcomings, which is true, but completely fail to identify what many of the shortcomings are.

  3. Some more commentary from Wyvern on the Space: 1889 Yahoo! Groups list:

    A couple of years ago I came up with a “taxonomy of dice systems” which I posted on the RPGNet forums (forum.rpg.net/showthread.php?t=295085). I’ve since revised it to include some additional variants and to correct some of the examples which I’d misclassified. Here’s the updated version — if you can help to fill in the gaps in my examples, I’d be grateful.

    1) Fixed Roll: Players roll either a single die (e.g. d20) or a fixed set of dice (e.g. 3d6), which are the same for all rolls. Difficulty modifiers may be added to the roll or to the target number.

    1a) Vs. attribute: Target number is determined by a character’s trait or traits. Always roll-under? Examples: GURPS, BRP, Alternity, Fading Suns.

    1b) Vs. difficulty: Traits are added to or subtracted from the roll and compared to a target number. May be roll-over (Examples: d20, Fudge, Unisystem) or roll-under (Example: Tri-Stat).

    2) Variable Roll: Players roll a die or some combination of dice which varies according to the trait being used.

    2a) Additive: Dice are added together (if more than one is rolled) and the total is compared to a target. May be roll-over (Example: Earthdawn) or roll-under (Example: ??).

    2b) Independent: Each die is individually compared to the target number. May be roll-over (Examples: Ironclaw, Savage Worlds) or roll-under (Example: The Window).

    2c) Inverse: Type or number of dice is determined by difficulty and target is determined by trait. May be roll-under (Example: Pokethulhu, Violence) or roll-over (Example: ??).

    3) Dice Pool: Players roll several dice of the same type, the number depending on the trait being used.

    3a) Additive: Dice are added together and the total is compared to a target. Always roll-over? Examples: Classic d6

    3b) Independent: Each die is individually compared to the target number, and “successes” are tallied. May be roll-over (Examples: Storyteller, Shadowrun, d6 Legend) or roll-under (Example: ??). Difficulty may be adjusted by changing the target number (Example: Original ST), the number of successes required (Example: ST Revised) and/or the number of dice rolled (Example: nWoD).

    3c) Select Best: The best die or dice rolled determines degree of success. May be roll-over (Examples: 7th Sea, ICON, Cartoon Action Hour) or roll-under (Example: ??), additive or independent.

    4) Orthogonal Dice Pool: Attributes and skills have different effects on dice rolls.

    4a) Skill vs. Attribute: Dice pool is determined by skill and target number is determined by attribute (modified by difficulty), or vice versa (Example: Iron Gauntlets). Always roll-under?

    4b) Skill x Attribute: Size of dice is determined by attribute and number of dice is determined by skill (or vice versa); target number is determined by difficulty. Always roll-over? (Example: Deadlands?)

    Note that I didn’t bother to include mechanics which are unique to a single game or game system, such as the One-Roll Engine.

    I had a few thoughts in response to Mr. Jackson’s comments which you quoted — I would’ve posted these to your original thread, but I didn’t feel like signing up for a WordPress account just for that.

    – He’s correct in pointing out that the distinction between “roll high” and “roll low” is cosmetic, but “roll low” systems don’t usually require subtraction, IME; they just require you to roll under a target number instead of over it.

    – I don’t know what he means by saying that “taking the average” is a “D&Dism”, especially since you explicitly associated it with the HEX engine.

    – I agree that it’s inaccurate to say that most game use the d20, although I’d add that between the various percentile-based games (BRP, WFRP, etc.) and the many permutations of the Storyteller system, I suspect that d10s are used almost as much as d6s.


  4. […] under: Uncategorized Here is an interesting and lengthy article about using dice in board games on Emerald City Gamefest. This may be a good blog to watch. The commentary is interesting as well. While the article mostly […]

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