Peggy steals an artifact

Simulating Fallen RPG skill checks

The Fallen RPG

Fallen is a “baroque and grim fantasy” tabletop role-playing game by Perplexing Ruins. The setting is a supernatural world analogous to the 17th & 18th centuries:

Stagecoaches pound over muddy lanes through the woods, the light of its two lanterns a gauzy haze in the descending mist. Donning a splattered and torn long coat and tricorne hat, your Rogue desperately hangs on to the rear of the bounding vehicle while taking aim at the shrieking creature that pursues your party. The mission? To get the last archivist with knowledge of damning evidence safely to the town. One silver bullet left!

Much like MÖRK BORG, Fallen has a generous third-party license that allows people to create content for the system.

In fact, I’ve made a Compleat Booke of Experiments (print too) for it!

Fallen Skill Checks

Fallen is mostly a six-sided die (d6) based system. Ability and skill checks are made and adjusted based on how difficult the task might be. Instead of adjusting a Difficulty Rating (DR) like MÖRK BORG, Fallen adjusts the number of dice rolled and advantage/disadvantage:

• Normal: Roll 2d6

• Difficult: Roll 3d6 and take the two lowest

• Easy: Roll 3d6 and take the two highest

In each case, you’d add the relevant Ability Score or Skill Level to the result.

The outcome is based on the final dice result:

• Success (10+): Everything goes as planned.

• Complication (7-9): Some success, but with difficulty or perhaps some loss.

• Miss (1-6): Nothing works, and additional challenges appear.

Our Hero

Fallen is becoming popular with solo RPG players partly, I think, because of the wealth of random tables included in the 44-page rulebook. Motivations, names, surnames, gear, and more. It’s easy to roll up a new character, so let’s do that!

Peggy Aldelbarth begins at The Raised House tavern, motivated by debt:

• Starting equipment and gear: 5 coins, torches, rations, a shoddy hooded cloak, some worn clothes, a hat with fancy plumage, small cart, horse, and some rags

• Weapon and protection: hunting knife, leather long coat, and a Twilight Honey elixir

• Skills: Healing (1), Investigation (2), Lore (1)

• Quirk: Obsessed with magic

She plans to steal an artifact from a noble in a small village out of desperation. Perhaps an item that she believes will allow her magic to get her out of debt?

The Challenge

Let’s say Peggy is trying to do some sleuthing to prep for her heist. She might be gathering historical information about the noble’s estate to find a secret way inside (i.e. Lore). Perhaps she is already inside and is searching rooms for the item (i.e. Investigation).

If it’s an Investigation check she would be at +2, and if it’s a Lore check she would be at +1. We’d also have to decide if this is difficult (i.e. Disadvantage) or easy (i.e. Advantage).

Here is our first question: What is Peggy’s chance of success?

Let’s write some Python and find out.

The Simulation

This one is easier than last week’s Therg Fights a Skeleton because we are just rolling some dice and adding them. So there aren’t as many assumptions, but there are a few:

• No modifiers are higher than +4. Ability and skill modifiers can be a maximum of +4 and no higher. That’s in the rulebook.

• Luck is ignored. Fallen allows you to “burn” your ability modifier dice to add additional dice to your skill check pool. After burning them, your modifier is +0 for the rest of the day.

• No special items are used. Fallen has magic in the form of elixirs and pamphlets, including an interesting system of incantations. They add considerable interest and excitement to the game, but they are ignored in this simulation.

For the Advantage/Disadvantage, an easy way to get the two lowest or two highest items from a list is to use the sorted() function:

# Sorted list of 3d6
pool = sorted(
   [randint(1,6), 
    randint(1,6), 
    randint(1,6)]) 

# Keep two lowest rolls
pool = [ pool[0], pool[1] ]

As always, we could do some basic probability math or use an online calculator to figure this out, but that’s not as much fun. Related to that, if you haven’t yet checked out Statistics for Hackers by Jake Vanderplas, you really should.

Here’s what a single scenario looks like when we do the roll 100,000 times:

Iterations: 100000
Roll type: NORMAL
Ability modifier: 1
Success: 28071 28.071%
Complication: 44229 44.229%
Miss: 27700 27.700%
Results: Min: 3, Max: 13, Avg: 8.01.

With a normal roll of 2d6+1 the average result is 8, which is less than the 10 required for a success. With just a 28% chance of success, it’s far more likely that Peggy will get a complication.

Modifiers vs. Advantage

This presents an interesting question: Is it better to have a flat ability bonus (e.g. 2d6+1) or to have advantage (e.g. 3d6, drop lowest)?

We can run the same simulation but with combinations of skill bonuses and Advantage/Disadvantage. Each one will run 100,000 times.

The box and whisker plot above isn’t a bad way to look at this. To keep it small enough, this just has Ability Scores +0, +2, and +4. For each of those it runs it as Normal (2d6), Advantage (3d6, take two highest), and Disadvantage (3d6, take two lowest).

There’s no surprise that +4 Advantage is the best (89% success) and +0 Disadvantage is the worst (5% success). What might be interesting is that +4 Disadvantage (48% success) is better than +0 Advantage (36% success). Having advantage or disadvantage feels like a huge benefit when playing, and can add some excitement to dice rolling, but sometimes it’s better to just have a boring flat modifier.

Here is another way of visualizing this data.

The options are sorted from highest success percent to lowest, with stacked bars for Success (dark green), Complication (light green) and Miss (gray). The success percent is almost a straight or linear progression (R^2=0.992), while the complication chance is higher in the middle options.

Even having Disadvantage at +3 (32% success) is still better than having +0 or +1 and a Normal roll (28% and 17% success).

Conclusion

When simulating a tiny part of a game, it is rarely representative of the actual play experience. This is true in the case of role-playing games where a GM would be ensuring that the flow of game is correct and everyone is having a good time.

KDE plot just because I love how it looks.

That said, I think there are some interesting game design things to think about:

• Simple Modifiers: They aren’t too exciting. The “+1 Magic Sword” has become almost a cliché. They still remain, however, the easiest way to give a significant boost to a given dice roll and success percent. Negative modifiers (e.g. curses) work just as well in the other direction.

• Advantage/Disadvantage: What makes advantage and disadvantage interesting is that it doesn’t just shift the probability curve left or right as the modifier does, it changes the shape of the distribution. You can see that in the box plot, as the main box (IQR) is shifted up or down, and the median line is no longer centered. It’s also visible in the KDE plot above. And, at least as far as I’m concerned, it’s quite a bit more fun when rolling the dice.

• Burning Dice: I didn’t simulate burning dice this time just to keep things simple, but it’s a really interesting mechanism. If it were a permanent loss (+0 forever), I’m not sure it would ever be worth it. As a temporary (i.e. one in-game day) loss, it provides interesting choice, a chance to push your luck, and increased player agency in the dice rolls. Adding things like this to games is definitely something to consider.

An additional question that comes from this: Should players know the success probability ahead of time?

Player board from John Company 2nd Edition, designed by Cole Wehrle

In almost all cases, my answer would be “no” when it comes to role-playing games and perhaps most board games.

John Company 2nd Edition, however, includes the “Chances of Success” right on the player boards (above), and I found that to be really helpful. It added to the choices in the game, and didn’t seem to detract from them. So I’m not sure there is a clear or right answer.

What do you think? Should chances of success be made openly available to players in role-playing and/or board games?

See you next week!

— E.P. 💀