I want to geek out about random numbers
Apr. 14th, 2024 10:52 pmI've been sitting on a dice mechanic for over a decade, without anything obvious to do with it. With the possibility that I might actually make a detective game on my mind, I want to talk about it with someone.
So, on one hand, the classic 1d20 roll is so completely random that it tends to outshine the effect of bonuses and penalties unless they get so big as to "break the RNG", as in D&D 3.x. This tends to make characters feel inconsistent in what are supposed to be their areas of expertise.
On the other, triangular and bell curves are strongly weighted towards the middle — especially bell curves. As such, they make results too predictable for my taste, and have made, for example, GURPS players wonder how they can make combat a bit less deterministic.
At least one game system, the Sine Nomine house system, tries to square the circle by just using 1d20 for combat and 3d6 for everything else. But I'm not so sure combat should be quite that random, or skills quite that deterministic.
Aside from the linear curve of a single die roll or the bell curve of totaling three dice, the triangular curve of totaling two dice is out there... especially in Powered by the Apocalypse game and their relatives. That still weights things relatively strongly towards the middle, though. On top of that, PbtA does one other thing that's not to my taste that I've seen in many other games too: weighting the results towards "yes, but". If 1d20 makes an expert feel inconsistent, 2d6 where the 7 — or even the 6 — is made to most commonly land in the "yes, but" range makes them feel outright incompetent.
Of course, there are also dice pool systems, but those have the downside that it's hard to intuitively grasp the probabilities involved, which makes it hard to know what your character would confidently try, what they'd hedge their bets on, and what they would avoid as too risky.
Fortunately, linear, triangular, and bell curves are not the only possible non-dice-pool options. A close friend of mine was the first to suggest to me rolling three large dice and keeping the middle result. I'm ashamed to admit that I laughed at first, but when I looked more carefully, I could see the brilliance of it. Compared to 1d20, middle-1-of-3d20 has ten outcomes that are notably more likely, eight that are less likely (four high, four low), and two that are very similar. Unlike a bell curve, the chances of the less-likely outcomes aren't vanishingly low. Unlike both bell and triangular curves, the results aren't nearly as strongly clustered towards the middle, and the most probable results are only about half again as likely as any given number on 1d20, rather than about twice as likely. This strikes me as nicely balancing plausibility and chaos.
Furthermore, I could see a way to get even more information out of that roll of the dice. Inevitably, if you roll three dice, sometimes two of them will show the same number, and on rare occasions all three will. It occurred to me that this could be a way to generate "yes, but" at a more reasonable rate — along with "yes, and", "no, but", and "no, and". The idea is simple: if you roll doubles, the number you roll twice determines whether you succeed or fail (only one of it; don't add both copies together), but the outlier is also checked to see whether it would succeed or fail if it were the outcome. If the result is the same for both the double and the outlier, it's an "and". If the outcomes are different, it's a "but". Collectively, these would be called Twists.
This, I believe, should generate "and" and "but" results infrequently enough that they come as a surprise, and don't exhaust people's creative juices in figuring out what "and" or "but" could mean. Furthermore, unlike many systems with but/and results, "yes, but" would not be the most common result, so you don't feel like you're bumbling through the adventure. Given that characters tend to feel more competent if the odds are skewed in their favor, "yes, and" would end up being the most common Twist, but still an uncommon result compared to simple success or simple failure.
Of course, there's also the question of what happens when you roll triples. This coincides with my feeling that on one hand some (but not all) DMs in D&D are too quick to exaggerate the results of "nat 1s" and "nat 20s", but on the other the "memetic nat 1" and "memetic nat 20" can be incredibly fun moments in moderation. Thus, my thought is that rolling triples on 3d20 results in an Absurdity. That's a 1 in 400 chance. Whether the Absurdity is absurdly good or absurdly bad depends on whether the number rolled (only one of it, not the total) would have succeeded or failed.
I can't claim to be the only person to have thought of something this simple, though. Peter Kisner apparently also independently thought of something very similar to this.
So, on one hand, the classic 1d20 roll is so completely random that it tends to outshine the effect of bonuses and penalties unless they get so big as to "break the RNG", as in D&D 3.x. This tends to make characters feel inconsistent in what are supposed to be their areas of expertise.
On the other, triangular and bell curves are strongly weighted towards the middle — especially bell curves. As such, they make results too predictable for my taste, and have made, for example, GURPS players wonder how they can make combat a bit less deterministic.
At least one game system, the Sine Nomine house system, tries to square the circle by just using 1d20 for combat and 3d6 for everything else. But I'm not so sure combat should be quite that random, or skills quite that deterministic.
Aside from the linear curve of a single die roll or the bell curve of totaling three dice, the triangular curve of totaling two dice is out there... especially in Powered by the Apocalypse game and their relatives. That still weights things relatively strongly towards the middle, though. On top of that, PbtA does one other thing that's not to my taste that I've seen in many other games too: weighting the results towards "yes, but". If 1d20 makes an expert feel inconsistent, 2d6 where the 7 — or even the 6 — is made to most commonly land in the "yes, but" range makes them feel outright incompetent.
Of course, there are also dice pool systems, but those have the downside that it's hard to intuitively grasp the probabilities involved, which makes it hard to know what your character would confidently try, what they'd hedge their bets on, and what they would avoid as too risky.
Fortunately, linear, triangular, and bell curves are not the only possible non-dice-pool options. A close friend of mine was the first to suggest to me rolling three large dice and keeping the middle result. I'm ashamed to admit that I laughed at first, but when I looked more carefully, I could see the brilliance of it. Compared to 1d20, middle-1-of-3d20 has ten outcomes that are notably more likely, eight that are less likely (four high, four low), and two that are very similar. Unlike a bell curve, the chances of the less-likely outcomes aren't vanishingly low. Unlike both bell and triangular curves, the results aren't nearly as strongly clustered towards the middle, and the most probable results are only about half again as likely as any given number on 1d20, rather than about twice as likely. This strikes me as nicely balancing plausibility and chaos.
Furthermore, I could see a way to get even more information out of that roll of the dice. Inevitably, if you roll three dice, sometimes two of them will show the same number, and on rare occasions all three will. It occurred to me that this could be a way to generate "yes, but" at a more reasonable rate — along with "yes, and", "no, but", and "no, and". The idea is simple: if you roll doubles, the number you roll twice determines whether you succeed or fail (only one of it; don't add both copies together), but the outlier is also checked to see whether it would succeed or fail if it were the outcome. If the result is the same for both the double and the outlier, it's an "and". If the outcomes are different, it's a "but". Collectively, these would be called Twists.
This, I believe, should generate "and" and "but" results infrequently enough that they come as a surprise, and don't exhaust people's creative juices in figuring out what "and" or "but" could mean. Furthermore, unlike many systems with but/and results, "yes, but" would not be the most common result, so you don't feel like you're bumbling through the adventure. Given that characters tend to feel more competent if the odds are skewed in their favor, "yes, and" would end up being the most common Twist, but still an uncommon result compared to simple success or simple failure.
Of course, there's also the question of what happens when you roll triples. This coincides with my feeling that on one hand some (but not all) DMs in D&D are too quick to exaggerate the results of "nat 1s" and "nat 20s", but on the other the "memetic nat 1" and "memetic nat 20" can be incredibly fun moments in moderation. Thus, my thought is that rolling triples on 3d20 results in an Absurdity. That's a 1 in 400 chance. Whether the Absurdity is absurdly good or absurdly bad depends on whether the number rolled (only one of it, not the total) would have succeeded or failed.
I can't claim to be the only person to have thought of something this simple, though. Peter Kisner apparently also independently thought of something very similar to this.