My gaming group has begun a short Vampire:The Masquerade mini campaign, which I haven’t yet joined, but I happen to think that the World of Darkness system is quite terrible. At the same time we’ve all been yearning for some classic fantasy, and the manifold shortcomings of Traveler’s system have become obvious, even though I think it could be quite good with some tweaks and have suggested it as an alternative structure for Warhammer 2. This has led to some debate about which dice systems and basic mechanics are best – not which systems, because systems load a whole bunch of other non-dicey stuff on top of what they do, but just which basic mechanics. Most of my group are very fond of the World of Darkness (WoD) basic mechanic, but in my opinion it is terribly flawed to start with, and handled very badly by the designers. During this debate some alternatives such as the Warhammer 2 system or d20 system were discussed and generally dismissed as terrible. At the same time I downloaded a cute Steampunk game called Mechanika which uses FUDGE dice, the core mechanic of the Fate system. Some of my group have previously shown an interest in the Fate system, and one of them recommended Mindjammer as a basis for the Spiral Confederacy campaign, so I thought they might be interested in that system as an alternative for use in a classic fantasy setting. However, when I googled FUDGE dice I was taken to the Wikipedia page, which includes the probability distribution for the dice. This distribution has its most likely value at 0 and ranges from -4 to 4, which means that if you add 6 to all the numbers, the FUDGE dice are almost exactly the same probability distribution as 2d5 (check yourself if you don’t believe me!)

This debate made me realize that there are essentially only three key canonical dice structures that almost all RPGs follow, and aside from some extra weird systems, they basically only follow these three possible structures. I will describe each of these here and outline why I think most systems can be reduced to them.

**Uniform distributions**

These are the classics of d20/Pathfinder, Cyberpunk and Rolemaster. The primary difference between the mechanics of individual systems is how they assign difficulty – by a simple flat mechanic like d20, with a variety of arbitrary subsystems like Cyberpunk, or with some godawful sprawling complex of tables like Rolemaster. With these systems the main determinant of how much fun they are is the relative magnitude of the range of random values to the modifiers, and all the other things attached to the system. So for example d20 has a very wide random range that allows for a lot of nuance of ability differences between characters, and lots of nuance in defensive and attacking differences too; while Cyberpunk has only half as much random range, and the modifiers are generally much larger, so that success or failure become baked into your character design rather than having much to do with the dice. These systems are old classics and for good reason: they’re easy to understand and very simple to use.

Some of these systems, like Talislanta and Cyberpunk, allow the defender of a skill check to set the difficulty randomly. For example in Cyberpunk melee combat the difficulty to hit someone is d10 plus their escape/dodge. This means that the difficulty target can be random in some cases, but on average it still means that the difficulty will be 5+escape/dodge (in this case) on average. If you did this in d20, for example, the difficulty of hitting someone on average would be 10+AC, even if they rolled a d20 +AC every time. This process of rolling for difficulty like this is not a waste of time, however – it actually causes the random distribution of the sample to become *approximately* equivalent to rolling the sum of the two dice being used. To see this, consider the example of a Pathfinder attack in its most basic form, where we allow the defender to roll d20 to set the difficulty of the attack. Then denote the attacker’s dice roll result by A, and the defenders by D. We have A+attack bonus vs. D+AC, where the attacker wins if A+attack>=D+AC. This is equivalent to A-D+attack-AC>=0. But the distribution of the difference of two uniform distributions is a triangular distribution across their range, centred at the middle of all the possible values of the difference (see this pdf for the case of a uniform distribution on the interval [0,1]). In the case of A-D described here, the peak would be at 0 with values from -19 to 19, and it would look very much like a normal distribution. So in fact, if you allow both attacker and defender to roll their attack and the target difficulty, your system will converge in those cases to the second kind of canonical dice system, the additive dice pool.

**Additive dice pools**

The classic additive dice pool system is Traveler, which uses 2d6 +skill+attribute vs. a target difficulty of 8. The alternative Cyberpunk system uses 3d6, so is effectively the same. I think there are a few other systems like Numenera that also use summed dice, and I ran a whole campaign using 2d10 instead of 1d20 for dice mechanics on a d20 system base, so that campaign would have been in this class too. As discussed above, the FUDGE dice effectively produce the same distribution as 2d5. These distributions all have the property of being approximately symmetric, with the peak probability in the middle of the distribution (typically at the median) and very low probabilities in the tales. From the Central Limit Theorem, the more dice in the pool the more normally distributed it looks, but even with 2d6 or 3d6 you are looking very close to normal. This makes it very easy for the GM to understand probabilities, though not as easy as the uniform distribution because specific values vary, and you know that half the probability lies to the right of a fixed number, and half to the left. In the case of 2d6 there are only 11 unique values so it is easy to memorize a few key numbers: 8+ has a 42% probability, 12 and 2 have 3%, and so on, so working with these dice is easy. This was the basis of my recommendation of 2d6 for Warhammer 2. The only thing that makes these pools less useful than uniform distributions is that you need to add up the dice, which takes a moment longer.

Additive dice pools are also internally consistent if you choose to use opposed dice tests where your opponent rolls the dice pool plus skill/attribute to set difficulty. By the same logic as for uniform distributions, this is equivalent to generating a difference of the two dice pools. If we approximate the dice pools as normally distributed, then we can say that the resulting distribution is the difference of two normal distributions (approximately) – and this is also normally distributed. So in this case the result of the roll becomes effectively another additive dice pool, centred at 0 but wider and more normally distributed than the original.

There is another type of challenged skill check which both uniform and additive dice pools can use. In this case both people roll, and the attack only works if it succeeds against some target number and the defender fails against some target number. I think this sometimes happens in Traveler (though I don’t remember specific cases). If you use this mechanism, you no longer produce an additive dice pool mechanism. Instead, you have produced a special case of the third class of dice structure: counting dice pools.

**Counting dice pools**

Astute readers will have noticed that I haven’t included Warhammer 2 in the Uniform distribution category of systems, even though it uses percentile dice against a target threshold, and percentile dice are uniform. This is because rolling a percentile dice against a threshold probability is effectively equivalent to rolling a d10 and trying to get a number smaller than the threshold divided by 10 and rounded up. In that case, Warhammer 2 is effectively a game where everyone has a dice pool of one, and their die has a hundred sides, and the difficulty changes according to the attribute used. i.e., it’s effectively a variant of WoD with a single die in the pool. This is also the case if you use the success-conditional challenged skill check for either uniform or additive dice distributions – you’re really just constructing a really complex opposed dice pool. The Warhammer 2 system does this – you need to succeed against your attribute, and then your opponent has to fail their defensive check, in order for your action to work. In this case this is basically equivalent to a 1D vs. 1D WoD dice pool. This is particularly true at first level where most people’s attributes are between 25 and 35, so effectively what you’re doing is, to close approximation, rolling a d10 and trying to get over an 8. It’s WoD! Where everyone has one point in every attribute and no skills for most of the campaign, but once they’ve leveled up a few times maybe they can reduce the target to 7. WoD allows modification of difficulty targets for dice, so basically in essence Warhammer 2 is a game of WoD where every PC is completely useless at everything.

Who wants to play that?

Other dice pool systems are mostly variants on WoD, which is maybe not the original (I think Shadowrun might have been a bit before WoD but can’t be bothered googling). They all effectively use a variant of either dice pool vs. a fixed required number of successes, or dice pool vs. dice pool. I have shown here before that dice pool vs. dice pool opposed checks massively penalize the person who initiates the action vs. the person who defends against it, and I have also described how it is extremely difficult to design a consistent rule for defining target numbers and constructing dice pools based on attributes and skills. The only way appears to be to use (attribute + skill) to set dice pools and then divide (attribute + skill) by some number to set targets, but I have shown that this produces horrendous results in practice. I think the only solution that doesn’t produce these horrendous results is to have a table that relates the attribute+skill to a specific difficulty, and to have very large dice pools. But… very large dice pools effectively converge to a normal distribution (based on the normal approximation for the binomial distribution), so in effect if you use very large dice pools you’re producing an asymmetric version of an additive dice pool. So Exalted, for example, with its very large dice pools, really is just producing an asymmetric and needlessly complex version of an additive dice pool.

Dice pools will retain their flavour primarily if they are at around 3-12 dice, which is perhaps normal for Shadowrun but probably mostly below the numbers you might expect in WoD. Dice pools of this size are fun to fool around with – they feel hefty but aren’t insanely hard to calculate, and they produce some successes most times. The big disadvantage of dice pools though is that their probability distribution is fiddly and changes with every dice pool, and as a result judging and setting difficulties is extremely hard. WoD provides many examples of this. For example, I recently read a Vampiric mesmerize type power that uses a dice pool equal to some attribute plus some skill, which one might expect to be around 9 in a good campaign for a relatively tough vampire with attribute of 5 and skill of 4. Its difficulty is the target’s willpower, and the magnitude of the effect is determined by the number of successes. So against a person with willpower 3 you will need 4 successes to achieve anything – but getting 4 successes from a dice pool of 9 is difficult. So someone with quite an epic attribute and skill combination will fail to produce an effect against someone with just a slightly above average willpower on most occasions, and will almost never achieve a strong outcome. This means that the dice pool and the difficulty have been poorly fixed. But how would you fix the difficulty in this case? It’s not clear that there is a functioning method for doing so.

**Conclusion**

I have missed talking about a few systems, such as Warhammer 3 with its insane mixture of dice, Seventh Sea with its complex rules for balancing breadth and width of dice pools (I don’t remember details now) or Double Cross with its insane maximum value and exploding dice system. These don’t fit the standard categories, which makes them fun but also impossible to get used to for most gamers. But for most non-insane systems, they will either be directly or mathematically equivalent to one of the three canonical structures described above. For play I really like to construct and roll large dice pools, but I think I have made it clear by now in this and other posts that dice pool mechanisms are fundamentally broken. I think the only viable, operative and relatively easy system to use is an additive dice pool with two fairly simple dice – so 2d6, 2d8 or 2d10. They’re boring, but they consistently work. The challenge then is to produce a game that properly adjudicates difficulties, has interesting character creation and makes all the other aspects of the game work well. Traveler almost gets the dice mechanic working (almost!) but as my players have repeatedly told me, the rest of the system is boring due to lack of abilities and special crunch. Perhaps the only game that does all these things right, then, is Iron Kingdoms.

And the three games that do everything wrong are Shadowrun, WoD, and Warhammer 2. The classics, my friends, are irreparably broken!

August 21, 2016 at 4:32 pm

Shadowrun was first. The system for Shadowrun was designed by Tom Dowd, and he was hired as a consultant by the original WoD team to design the mechanics for the WoD game.

This is why it is the exact same system with a different sized die.

August 24, 2016 at 11:31 pm

Thanks for the clarification! I think they’re not exactly the same (shadow run is slightly better but more fiddly) but I only have version 4…