System Hack: All About Dice

So far, System Hack has highlighted Seamus working through the process of writing a hack for an existing role-playing game, specifically a mecha hack for Genesys. In my first System Hack outing, I’m going broad, super broad! We’re not talking about a specific hack, or even a specific game. Instead, I’m going to talk about a design choice that is so prevalent, so widely assumed, so transparent, that it’s not a given that everyone will give it much thought. What’s that, you may ask? Well, it’s dice. Good old dice.

Dice are at the core of most role-playing games, though there are a few that use other randomizers and a few that don’t use randomizers at all. Still, most games are going to have at least one type of dice used in play, and will have at least one die roll used to determine the outcome of uncertain events. Now, outside of literally making your own die faces (like Fantasy Flight Games has done), there isn’t much invention left in dice mechanics. That’s all right, though, because due to the magic of math, it’s not hard at all to figure out how your dice mechanics will impact your game, and what dice mechanics contribute to how your game feels. Though there’s a lot of options out there, we can start very simply: rolling dice to see what number you get.

Target Number Rolling: Saved by the Bell Curve

Target number rolling is what most of us think of when we think “rolling dice”: You roll a die or a few dice, and you compare the result to either a static target or an opposed roll. Depending on the system, either the highest number or the lowest number wins. There’s one mechanical change that alters how this system works, and that’s the number of dice you roll. Every die roll has a range (the possible results), a mean (the average result), and a standard deviation (the range of results within a constrained probability). Without getting too far into the statistics, rolling more dice means that, for a similar range, you have a smaller standard deviation. Take D&D and GURPS as examples. In D&D, you roll a d20 to determine most outcomes. When you roll that die, a 1 and a 20 have an equal chance of coming up, meaning you don’t really know what you’re going to get when you throw the die. In GURPS, you roll 3d6. The range is a bit smaller, from 3 to 18 instead of 1 to 20, but the real difference is the results. Among three dice, there is one way to roll a three, one way to roll an eighteen, and a whopping 27 different ways to roll a 10. This means that results closer to the mean (which is 10.5 for both 3d6 and 1d20) are significantly more probable. In other words, you’re going to get an average roll more of the time, whereas with a d20 the result is equally likely to swing in either direction. While using a single die is easier to design for, using multiple dice and producing a bell curve can give results that feel more ‘right’ to players. Games with one die will often use larger static modifiers to compensate for the larger degree of variability. This does mean that as characters get more powerful, the variability of the die roll matters less. GURPS uses dynamic target numbers instead, which keeps the variance of any given roll consistent.

Incrementing Dice: You’re Just Not My Type

So what else can you do to denote advancement, other than add modifiers or give more favorable target numbers? Another mechanic, made popular by Savage Worlds, is to increase the size of the die the player gets to roll as they increase in ability. This does produce a higher average result, though the steps between dice are relatively small. What makes incrementing dice feel odd, though, is that the standard deviation keeps increasing as the dice get larger, so the benefit of going to larger dice gets smaller and smaller. If you’re rolling for a target number of 4, you’re going from a 25% chance on a d4 to a 50% chance on a d6, but then to a 62.5% chance on a d8 and a 70% chance on a d10. This diminishing return of ability gains can feel realistic, if it is properly designed for. Savage Worlds has character advances at consistent intervals, but higher advances have smaller effects, which encourages creating broad rather than deep characters. This only really works with static target numbers, though, as the range has to be reachable by every die type (or at least most of them).

Roll and Keep: She’s a Keeper

Another variant on rolling for a target number is to, instead of changing the target or adding modifiers, give the player more dice to roll. The problem here is that the range can get very large…a system where a player can roll between one to five dice has a minimum result of 1 and a maximum result of 30, 50, or 100 depending on the type of dice you’re using. The game effect of this is either that many tasks are impossible for more humble characters or far too easy for powerful characters. A useful mitigating mechanic for this issue is roll and keep. The player may get to roll 5, 6, or 7 dice, but only keep one or two of them. Games like Legend of the Five Rings use this mechanic for their core rolls, while Dungeons and Dragons includes it in the form of the Advantage/Disadvantage mechanic. Intuitively, getting to pick the highest result among a number of dice will result in a higher result on average than if you merely had one die to roll. So while more dice will still improve your roll, you have the constrained range of only rolling two dice, making target numbers and wide power curves easier to manage.

Dice Pools: Jumping in the Deep End

Dice Pools are the ultimate way to get your players to roll tons of dice if they want to. What makes dice pools different is that there’s no longer a value being targeted overall, instead each die has a target number, and hitting that number or higher will make the die into a success. This means that instead of calculating the probability of reaching a value, we’re calculating the probability of a series of binary events. Let’s use Burning Wheel dice as an example. In Burning Wheel, a black shade die (the mundane shade which most abilities use) is a success on a 4,5, or 6, which is half of the time. So if you’re aiming for one success with one die, the odds are 50%. If you’re aiming for one success with two dice, you have the 50% chance you roll the success on the first die, and then the 50% chance you roll the success on the second die provided the first one is not a success (50% times 50%). This adds up to 75%. Add a third die, and you add the 50% chance of success on the third die provided the other two aren’t successful, which adds up to 87.5%. The probabilities get more complicated to calculate once you’re looking for more successes, but the basic idea is that like incrementing dice, each additional die increases the likelihood of success by a diminishing amount. In a simple dice pool system, the mechanisms you have to modify the odds of success are either moving the target number, adding or taking away dice, or changing the number of difficulties needed to succeed. In Burning Wheel, the target number is only changed in the case of literally extraordinary abilities, which makes sense given the large difference the target number makes on a six-sided die. Otherwise, all basic actions have a number of successes needed, which is modified if there is additional challenge, and a number of dice to roll, which is modified if there is available help. With these three avenues of modification (compared to one for a straight target number roll, and two for both incrementing dice and roll and keep), there are a lot of ways to write interesting dice pool mechanics. The One-Roll Engine (ORE) and Fantasy Flight’s Narrative Dice have pushed the dice pool furthest; ORE counts both value and quantity of dice when determining results, while Narrative Dice (as seen in Genesys and FFG Star Wars) has both rewritten the dice with custom symbols as well as made every roll a comparison between two separately built pools, one for ability and one for opposition.

When you write or modify a game, dice are going to affect how that game works. As an example, one common and (relatively) small hack for D&D is to replace the d20 with 3d6 in order to produce a bell curve of die results. With the same average result and only a slight change in range, this generally works, though it makes a couple significant changes. First, of course, the critical hit rules no longer work. This isn’t too difficult to work around, though since there is now a different probability distribution it does require some thought. More significant, though, is how the change works against monster design. Fights against monsters of average or easy challenge ratings are now much easier, since the PCs will hit more often. Fights against hard monsters, though, become very difficult. First, monsters with high ACs may go from getting hit 25% of the time to less than 10% of the time. Second, the monsters are going to hit way more often, knocking PCs out faster. Now, these complications don’t imply that one die roll is better than the other, rather that most games are designed with a dice mechanic in mind. Even if a bell curve seems more “realistic”, it doesn’t mean it will jive perfectly with a pre-existing design.

Dice provide a lot to how a game feels. D&D feels right with a d20, and Shadowrun will always mean rolling buckets of d6s to many people. The key to mucking around with dice mechanics, either as part of a new game or a modification of an existing game, is to balance how dice feel with the statistical results that they produce. There’s no way around it, there’s math. But through researching what’s been done before and using available tools, it can be easy to hack dice to do what you want them to.

Want to muck around with dice and dice stats? AnyDice is the best free tool for dice statistics and statistical visualizations.

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