Dice Systems

[zabbarot]

I'm working on a game and I'm undecided on what kind of dice system to use. The basic systems I can think of are roll over, roll under, and success counting. Roll over includes d20 games. Roll under would be games like Dark Heresy or GURPS. Success (or dice pool, I guess) would be games like WoD.

Basically I'm trying to figure out what the pros and cons of each system would be.

[atomicpenguin]

Imma throw some concepts your way and see if they help. Feel free to ignore anything you already understand.

First of all, you should think about why we use dice. In RPGs, we are given stats, the abilities and skills, which are represented by numbers on a predefined scale in order to abstractly represent our capabilities in a given area. You could actually run a game without dice at all, simply stating how high a character's abilities need to be in a specific area to do a specific task and checking their stats to see if they are above or below the given benchmark. However, most games like to inject an element of chance into the system, since in life you can have everything going for you and still fall on your face sometimes. So instead we do the above process, but set the benchmark high enough that a high ability score alone will rarely reach the mark, then modify the score with a roll of the dice. Really, any random number generator will do for this. While dice is a favorite, other systems have used playing cards, tarot decks, and all sorts of crazy stuff. Take this into account and choose a random number generator that serves the theme of your game and has a curve that makes success as common as you want it to be (all talk about this as I go).

Secondly, you need to decide what dice you'll be using. There are three different approaches to this that I can think of. Firstly, single roll. Simply pick a die type. d20 is popular but you could just as easily use a d6 or a d10 like in Unisystem. You could also do a collection of dice, like using three d6's in GURPS, but for a single die every number has an equal chance of coming up, while rolling three d6's means that on average the results will be more moderate, coming up with more average rolls than really good or really bad. But the point of single roll systems is that you roll the same thing for every single roll. These systems are simple and easy to learn and every roll has more or less the same chance of success. The next type is variable roll, where the dice you roll can change. A good example of this is Savage Worlds, where skills and abilities receive die types instead of numbers and for a test you roll the appropriate die type for the skill/ability. What this means is that being better in an area literally increases the odds of success. Lastly, there are dice pool systems, where you roll a handful of dice, which are the same type and where the number of dice is determined by your stats, and whichever dice roll above a certain number are considered "successes". Typically, at least one success is required, but more can be required for more difficult tasks. Bigger pools are better not because they increase the odds of success per se, but because they offer the payer more opportunities to get a success.

Lastly, I'll talk about the different ways of applying stats to dice rolls. First of all, there's your basic application system. Like in d20, simply roll the dice, add whatever modifier from whatever stat is applicable, and see if that number is equal to or higher than the number required for success. Then there's low roll systems, where you roll the dice and get a number lower than your score in the appropriate stat. This sounds confusing, but you still advance and increase your stats just like any other game. The only difference is that instead of making your numbers more likely to be higher than a benchmark, the numbers stay the same and you make the benchmark easier to beat. Lastly, there's static application systems, which are similar to basic application systems except that the benchmark always stays the same and instead you impose penalties or bonuses on the roll of the player.

As far as choosing a dice roll system, first I recommend you read up on a lot of games. They already did the math for you so the easiest route is to draw inspiration from what has already been done. Play the games if you can or at least draw up a character and roll for a few made up challenges to really get a feel for how often success and failure happen. Second, really think about how often you want success to occur, especially critical success. Mutants and Masterminds, for example, uses a variant of d20 that allows for more successful rolls than dungeons and dragons because it doesn't make sense for super heroes to "fail" to use their super powers.

[NichG]

I've been thinking about this a bit of late. Some elements to consider:

- Granularity. Even if your system is success/failure based, the granularity of your randomness controls how big a bonus is. This controls a lot of the feel of the character building or advantage-hoarding parts of the system (e.g. accumulating buffs, environmental benefits, assistance from others, etc). The smallest bonus on a d20 roll (vs flat DC) is a 5% change in success rate. The smallest bonus on a d100 roll is a 1% change. The smallest bonus on a d4 roll is a 25% change. With something like 3d6, there are 18 distinct values, but they're separated by different amounts so a bonus changes value depending on the difference between your modifier and the success number.

- Variability versus the mean. At low levels in D&D, things are very random since the majority of the result of a check is coming from the d20 part, not the static modifier. At high levels this flips around (especially for skill checks) and the system becomes less and less random at a linear rate. For something like success counting this is slower, as the system converges to its mean like sqrt(N). You could even have a system like FUDGE where the amount of variability might be somewhat under the control of the players (since you can add FUDGE dice without changing the mean, you can within reason let the players decide how many to add).

- Boundedness of results. Some players feel very different about a system where certain rolls are literally impossible, versus one in which those rolls are just extremely unlikely. Something like D&D's crit success mechanism means that even if you are outside the range of variability, no outcome is ever less likely than 5%. Exploding dice mean that the result of the roll is unbounded above, even if it tapers off very fast.

[AttilaTheGeek]

This graph (http://anydice.com/program/209a) should give you the idea of what some different distributions look like. "1dX" looks like a flat line (just as likely to roll 1 as to roll X), "XdY" gives a bell curve that's more likely to give mediocre results, and "XdY, highest Z" gives a bell curve that's tilted toward the upper end.

[Razanir]

You could also do a collection of dice, like using three d6's in GURPS, but for a single die every number has an equal chance of coming up, while rolling three d6's means that on average the results will be more moderate, coming up with more average rolls than really good or really bad.

Just a nit-picky thing. On average, you'll get the same types of rolls with 1d20 and 3d6. E[1d20] = E[3d6] = 10.5. What you're referring to is the variance. Var(1d20) = 33.25, Var(3d6) = .324. As you can see, 3d6 is much less variable

E[AdX] = A * (X+1) / 2
Var[AdX] = (X² - 1) / (12A²)

[qwertyu63]

Rather then comment on existing systems, here are a couple unique ones you could use.

Match Pool: The difficulty of tasks is measured on a scale of 1-7. Roll that many 6-sided dice, and if any match, you fail. Advantages lower the number, while disadvantages raise it.

Simple Dice Toggle: Each character has dice sizes assigned to various pairs of skills, but the skills in each pair are always opposed (Strength/Intelligence, Speed/Defence, Magic/Weapons, Charm/Intimidate, etc.) When rolling for the first skill in a pair you want to roll high, but when using the second skill in a pair you want to roll low. Therefore, picking a larger die for a pair makes you better at the first skill, while a smaller dice makes you better at the second.

(Disclaimer: I just made these up on the spot. I make no claim as to if they are any good. Just some unique ideas.)

[Siosilvar]

Roll-under and roll-over are exactly equivalent. The only useful distinction between the two is qualitative: do you want people to be rolling low numbers on dice to succeed, or high ones? [If high ones, please use roll-and-add instead of roll-over; making numbers lower to get better at things is unintuitive.]


Some other dice mechanics for consideration:

Roll two dice, subtract the lower from the higher. Unlike 1dX-1dX, this isn't equivalent to 2dX with all target numbers shifted down.

Matching; rolling more of the same number means you do whatever you're doing faster, while rolling higher numbers means you do it better.

Roll and Keep: Roll [stat] dice, keep [skill] of them.

Exploding dice, which can be combined with any or all of the other mechanics. Rolling the highest result lets you reroll and count the die as that much higher.