A while back I wrote an article comparing different ways to roll some dice and get a result that produced the same average result but had different probability profiles. Today I wanted to talk about a way to make use of some of those features: Making the method of dice rolling tie into the theme of a game.
Consider Zombicide. If we grab ourselves a precision rifle and fire on a zombie we roll 1D6 and will kill it on a 3+. One the other hand if we go for the submachinegun we roll 3D6 and will kill it if any of them work out as a 5+. The rules never explicitly state "Accurate weapons roll fewer dice but need lower numbers to hit, inaccurate ones do the opposite" but the pattern is established through repetition on most of the games weapons.
This is a good feature for a game to have. Ideally a game should have a lot of little things that are needed for the game to progress and serve other gameplay purposes building on each other to establish links between the theme of the game and what the players are actually doing. Even if the probability is the same if you set off some kind of huge explosion throwing a large pile of dice is more satisfyingly "explosiony" than throwing a small pile.
However as well as the visceral feel we should also remember what different systems do to the probability curve. Thematically you might want an explosion to be and feel chaotic compared to - say - a sniper. Throwing a boatload of dice has that visceral feel, but in terms of what it actually does the "many dice" thing tends to be more reliable because when you roll several dice together you get a bell curve. That is to say that the average result occurs more often and the extreme result less often, compared to rolling one dice where rolling a middle number and rolling the highest or lowest number all have the same chance to happen.
So are we stuck in a situation where the visceral feel of a thing is directly opposed to its actual effect on the game? Of course not!
We can think about how we apply modifiers. If someone is rolling some D6s and needs X+ on each one to get a hit we've got three levers: We can change how many dice are rolled, we can change what result is needed for a hit and we can change how many hits are needed.
On a side note, it's generally desirable to modify as few things as possible so that when someone sees "-1" they know what it applies to because the game is consistent - but it's still worth considering which one to modify.
If a modifier applies to the number of dice it has a more profound effect on "1D6 3+" than "3D6 5+". Adding an extra dice increases the chance of success by 23% for the first pool, only by 9% for the second. Taking one away is even more profound since with zero dice the first pool can't succeed at all.
By contrast if it applies to the number that has to be rolled it will affect the "Big dice, high number needed" pool more dramatically since that target number applies to every dice and it has more dice to be affected.
So if we're looking to make it so that we can use a big pile of dice for explosions or shotguns or risky behaviour in general but also have the probability profile make those things riskier rather than more certain - where does this mean we put our modifiers?
The answer is "It depends". Specifically it depends on why you might be modifying a dice roll. If the most common sort of modifier is a positive modifier because the character doing it is really skilled it makes the most sense for it to be a dice modifier. That way a skilled character gets the most out of doing a precision activity - the game will "feel right" when a champion marksman adds more to a sniper rifle than a scattergun.
On the other hand if the most common modifiers are negative situational modifiers because the weapon's old or you moved or whatever then applying them to the target number may have the desired effect. The chaotic weapon will break down when the circumstances are against it but the reliable one will - well - be reliable.
Modifiers aren't our only option either. A lot of games use rerolls as a means to provide reliability. If you're happy that your game won't be slowed down too much by the extra decision and roll step involved in having one then providing them can be a way to distinguish risky but dynamic actions from reliable less dynamic ones. That way we can still give our grenade a huge dice pool but make our sniper rifle's smaller dice pool stick more closely to the bell curve - if the pool is smaller but less than half the size then providing one reroll makes it effectively larger in terms of reliability - so it can be small for the visceral action of picking dice up and doing things with them but large in the abstract mathematical sense of how it actually behaves.
Finally - the most important thing to consider is how a game breaks free of a fail/success binary. The examples above talked about "Roll one hit to succeed" but even in the Zombicide example, there's a reason to roll more than one hit. If the player scores several hits they kill several zombies - good times.
This feeds into the theme as well. It means that "3D6 5+" has an advantage over "1D6 3+" not only in having a better average and being able to more consistently score a success - but also in that it can potentially kill up to 3 zombies where the other version will only ever kill 1.
It didn't have to be this way - the rule could have been "Look at only the highest dice, if it's below the target number nothing happens, otherwise it kills a zombie plus an additional zombie for each point it exceeds the target by". Then a 3+ could kill up to 4 zombies and 5+ could only get 2 even if it had lots of dice.
The rule makes sense for that game - it's intuitive that a spray of automatic fire could kill several zombies were one very well placed shot usually wouldn't - but perhaps your game isn't about shooting zombies. Perhaps your player is rolling for their ad campaign to convince the nation that keeping the planet inhabitable to humans is more important than saving a few quid on groceries. If your critical success is "Convinced some persuasive celebrity" then maybe a "Brute force the campaign with lots of money" approach should roll lots of dice and be consistently effective, but you want the best chance of a critical effect to lie with a "Carefully targetted ads" approach.
There's not only one way to do these things - the point of this article is to remind us to be conscious of them. There are a hundred ways to resolve "I'd like the player to throw some randomisers to see if this works" into a rule. It's worth taking the time to pick the one that not only makes your game work best as an abstract mathematical model, but also the one that'll help players to be invested in the theme and for the things that happen to seem like they intuitively make sense from the actions the mechanics are describing.