Character competency, game feel and dice randomness

In the recent years I've explored a number of systems with my group. We've played some games with Godbound, Chronicles of Darkness, Powered by the Apocalypse and Star Trek Adventures systems. I'm a very system-focused player, so I enjoy exploring how the different systems play and what's their "game feel" like. Most importantly, I was really keen on exploring the most core mechanic of almost every role playing game - the dice mechanics.

Character competency

Whenever I would start playing a new system, I would inevitably ask myself - "does this roll as well as World of Darkness"? Vampire the Masquerade has been the first system I've played extensively and say what you will about how clunky it might be at times, the dice rolls in that game felt great. You always rolled a nice handful of dice (but not a crazy amount like Exalted or Shadowrun!), and you felt like your character was competent - it wasn't hard to roll a success, and you could rely on your character performing their specialities more often than not.

To contrast that, we've played about a year worth of Godbound between our Exalted game, Ancalia game, and doing one-shots. The system used a single d20 roll extensively, keeping with its OSR roots. Despite the system being geared towards feeling epic and grand, whenever a roll was required the characters didn't feel nearly as competent. It wasn't that uncommon to get a streak of low-value results and fail entirely, despite playing demigods.

I've been trying to figure out why those systems felt so different, and I think I figured something interesting out...

Binomial vs linear distribution

Two basic, simplified math concepts. Binomial distribution is a randomness distribution that looks like a bell-curve. It's similar to a normal distribution, but there are only a finite amount of values it can take. You can get extreme results from either end, but you're a lot more likely to land somewhere in the middle. 2D6 roll has a binomial distribution - you're most likely to end up with a 7, but 2 or 12 also happen on occasion. Linear distribution means you're as likely to get any one result as another one. 1D6 has a linear distribution - you're as likely to roll a 1, a 6 or a 3.

A useful spreadsheet to reference.

My guess is the difference in game feel between Chronicles of Darkness (the modern, updated version of World of Darkness, here is our game) and Godbound lies in the way dice rolling is handled. In CoD, the more skilled you are, the more dice you roll. Each dice landing on a 8, 9 or 10 is a success, 5 or more successes is an exceptional success. You often roll 5 or more dice. In Godbound, you always roll a single D20, add some modifiers and you have to roll above some threshold - 20 for example.

CoD feels good because you can rely on your dice rolls thanks to the binomial distribution - you know you're very likely to roll at least one success - having just two dice (a very paltry amount) you're already more likely to succeed than fail, 4 dice gives you 75%, 6 is over 88%, and 9 gives you 95%. Godbound feels worse due to the linear nature of its rolls - rolling a 1 is as likely as rolling a 10 or 20. You have to get +10 to reach 50% success rate, +15 gives you 75%, +18 gives you 90%, and you only get 95% at +19.

Why are those percentages important? Because that's basically halving the chance of failure - a half (0.5), a half again (0.25), and again (0.125) and again (0.0625).

Progression between 2, 4, 6 and 9 is a fairly linear one in CoD (the previous editions were a bit harder), while in Godbound you start somewhere in the middle of the progression and polishing up to the final few points is a challenge.

So subjectively at least, it seems having a binomial distribution in your game is the key to having a good game feel. Now, the question is, how many dice do you really need to pull this off?

Many dice, or just two?

I've played with two systems that tackle the binomial distribution in fundamentally different ways. First one is the already mentioned Chronicles of Darkness line of games. The other is Stars Without Number (it has a free edition, do check it out!, and here is our game), a game by the same author as Godbound.

In SWN, a skill roll is just a simple 2D6 roll, modified by your skill rating. So it's the simplest binomial distribution you can really get. The skills just shift the result. You usually have to get 7 or better to succeed at a basic task, 10 at something more complicated, or 12 at something very complicated.

How does this simple roll compare to rolling something like 10D10s in CoD? Well, looking at our handy spreadsheet, pretty favourably all things considered! Rolling 2D6 gives you a simple binomial distribution, and while rolling more D10s not only shifts the curve but also changes its shape a bit, it might not be enough to affect the game honestly (a binomial distribution that is thinner means results are very likely to end up near the centre, while a wider one as we see rolling a lot of D10s means there is a spread in the ranges - you're less likely to end up on the dead centre).

Both systems behave similarly - the higher your skill in SWN or the more dice you roll in CoD, your probability shifts upwards, meaning you're more likely to reliably land a success.

Honestly, as someone that was very much in love with CoD dice mechanics, it's surprising to see that rolling 2D6 is a fairly good substitute for having a handful of D10s.

Conclusions

It appears a binomial distribution from rolling two or more dice instead of one makes games feel a lot more satisfying and gives characters a degree of competency - the players can rely on their characters succeeding at a given task they're specialising in. It seems that you don't really need a lot of dice to achieve this either - rolling 2D6 and shifting the result accordingly might be enough to achieve this game feel. Rolling a single dice is generally the worst due to the linear nature of the probability distribution.

Other resources:

• Dice System Ease, Speed, and Probability Distribution in RPGs