How To Make Good Games By Ruthlessly Cheating At Statistics

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The most impressive thing to me here is that this guy wrote all of this backwards.

So, I’ve discussed the sweeping idea of what a good central dice mechanic is, now I’m gonna do a more in-depth analysis on my other tabletop game project, Blackmarked, to see exactly how I go about reviewing these mechanics.

So, quick refresher: Blackmarked is a tabletop roleplaying game about cutthroats and killers trying to survive in a low-fantasy world of war, religious turmoil, plague, and the occasional undead sorcerer. This game is supposed to be vicious: characters die fast, combats are quick and dirty, and the best way to survive is usually to not fight. Nobody’s a hero, everything sucks, and possibly the only divine force in the world is a god of chaos who just wants to burn everything to the ground.

Cool, what’s the dice mechanic? Unfortunately, to my own admissions, what I have right now is pretty boring. Check it out:

  1. For a player attempting a check, they take 3d6, add a number of d6s equal to their relevant Skill, then add/subtract dice equal to the modifier, and roll ’em.
  2. Every die that comes up a 4, 5, or 6 is a success.
  3. Get a number of successes equal to the Difficulty Number + 1 to pass the check.

I don’t like this system for a number of reasons. First of all, it’s not terribly evocative of the game’s mood or, in fact, much of anything. On top of that, it’s full of details that seem initially arbitrary. Why do you get an initial dice pool of 3? Why the plus one to the difficulty number?

Despite all of this, I thought in my mind that these rules should create a sort of probability curve like I wanted: one where victories were not uncommon, but still had to be fought for. After all, the dice should come up a 4, 5 or 6 about half the time, so for a Difficulty Number of 2, you should succeed about half the time with no additional skills.

Here’s the trick of game design, though: don’t just trust your gut. Some people might be pained to hear this, but sometimes you’re better off applying some good ol’ fashioned math to your game to see exactly how things tick in the systems you’ve made. And with this wisdom in mind, I set off to determine the probabilistic equations I would need to determine the approximate likelihood of success in this system given Skill, modifiers, and Difficulty Number.

But, like, on the other hand, statistics is hard. There’s a bunch of numbers and stuff you have to work with, and generating an equation which outputs the number I want can get unwieldy when your dice mechanics get more complex, and you have to recalculate for every variable….

But wait! There’s a solution! There are two kinds of probability in statistics: theoretical probability, which is generated through math, and experimental probability, which is generated by just doing the thing a bunch of times and recording how many times the event you’re measuring for happens. I don’t have to crunch the numbers, I can just roll these dice a bunch of times and keep track of how many times I succeed.

And by “I”, I mean a computer can. I’m a programmer after all.

The Hacker
Hell yeah, cyberspace!

With that in mind, I modified this dice roller program in Python I had lying around to suit my needs. Basically, it just rolls according to my skill check rules above for every likely combination of Skill rating, modifier, and Difficulty Number, and tells me how many times that roll succeeded. So I whipped this up, told it to test every combination of variables a million times, and went to dinner, and let it chug.

When I came back, I found some interesting experimental results. Check out the output file.

The first thing I looked at was what I would consider baseline rolls. That is, a character of Skill level X attempting a challenge of Difficulty Number X with no modifiers. Let’s see how those numbers came out:

  • Skill 0, DN 0: 84.49% successful
  • Skill 1, DN 1: 68.82% successful
  • Skill 2, DN 2: 50.03% successful
  • Skill 3, DN 3: 34.35% successful
  • Skill 4, DN 4: 22.63% successful
  • Skill 5, DN 5: 14.51% successful

Whoa! No! These experimental probabilities seem to imply that really hard tasks are basically impossible, even if you have the very high skills , which doesn’t feel right to me. I’m all for punishing rolls, but I think a high-skill character should succeed at a hard thing more than fifteen percent of the time.

Furthermore, this curve feels weird from a narrative sense. An idiot can do an idiot task almost all of the time, while a genius can only do a genius thing a sliver of the time? So you’re incentivized to play an unskilled character and do unskilled things? Eew.

Let’s take another measurement. Let’s see how probable every Skill level is to succeed at a task of DN 2 (which I considered average), with no modifier:

  • Skill 0: 12.47% successful
  • Skill 1: 31.33% successful
  • Skill 2: 50.03% successful
  • Skill 3: 65.57% successful
  • Skill 4: 77.32% successful
  • Skill 5: 85.55% successful

Ok, so here’s the thing about these rolls. To even stand a 50/50 chance of succeeding at this average task, you have to have at least a Skill of 2, or else there’s little statistical probability you’ll succeed. Considering this is a system where failure usually leads to painful death, I don’t know that an RPG meant for long-term campaigns will be viable with these probabilities.

Moreover, think of how limited the GM’s design space for obstacles becomes. If he throws anything at their players of a DN greater than 2, unless that’s the thing which the player has specifically built their character to deal with (skill points are kinda sparse), they’re probably going to fail, meaning there are 3 viable Difficulty Numbers that will keep your party from immediately failing at everything they do, and a very small space in which to present foes. All of these quirks combined, plus how much I didn’t like the system to begin with, means I need to toss the whole damn thing out and start over.

Also of note is the fact that this doesn’t mean this system is inherently “wrong” or bad, it’s just not what I’m looking for. I don’t want a system this prone to failures, if I’m going to have failure in combat almost always lead to player maiming. I’m going to need something a bit more player-friendly. If you were designing a game in which the consequences for failure were lesser (maybe even a comedy game centered on failure), or just a game where the players are supposed to frequently get killed, this could be totally viable. It’s just not expressive for what I want. I’ll figure out a system that does that in the finale of this three-part blog.

 

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