Hot Take: Mathematical “elegance” is overrated (RPG Design)

rpg design

I realize I am tossing a hot iron in the room here (because some folks love the very thing I’m about to dog on), but:

Thesis: Mathematical “elegance” and transparent percentage probabilities are fun intellectual exercises but bad RPG design.


  • People are terrible at percentage probabilities and statistics, on par.

  • Even for people who are good at them, it is not immediately intuitive.

    • Which do you more immediately and intuitively grasp: 14.3% or a 1 in 7 chance?

  • Perceptions of fairness are often directly at odds with formal odds.

    • The classic example is 50/50 odds will feel unfair to players. This is well explored design space from tabletop to video games. It takes around 3/5 to 2/3 odds to get people feeling it is fair and balanced, even though it actually favors them about 2:1.

  • As paradoxical as it seems, less transparent odds often reduce complaints about balance and fairness. And not just through obscurity. You can also rephrase the odds to make them more user friendly.

    • A good example is marketing polling shows people feel even infamously broken dice pools are more fair and intuitive than basic d20 systems. Though the probabilities are difficult to calculate, they typically make it easy for players to have a broad but certain sense of how good their character is at a thing. They couldn’t tell you their probabilities in most cases, but players can usually very quickly score it on an easy to hard scale.

    • A lot of it has to do with phrasing and presentation as well, echoing the second main point. In a d100 system a 17% rating is (infamously) discouraging and will rarely be attempted. In a simple d6 system, where they need to a 6 to succeed (equivalent odds), players will more often take the chance viewing a 1 in 6 chance of rolling that 6 as a gamble. Mathematically equivalent, but entirely different table responses. The less transparent/exact math is more appealing.

  • A lot of “elegant” designs also lean heavily into complexity. While they obey the above point in a strict sense, they rely on a similar error as it is meant to correct. They assume the elegance and “obviousness” of the math will be useful to players. Mind you, in some small niches of math loving folks, this will be true. (In a limited sense, see the second main point.) But in most cases, it obscures things in a bad way and puts the focus on the math over the game.

  • Even advocates of % systems openly admit the problems with low skills, people not grasping a practical sense of the chances, and so on.


  • Design games based on end user feel and responses, not mathematical models.

  • Understand that “fair” math and even math are two very different animals.

  • “Hiding” or “obscuring” the real probabilities is not a real concern. Focus on whether it is intuitive and understandable for the players.

  • The beauty of the math cannot overcome functional issues or comprehension barriers.

  • Players are never wrong, only designs are. If there is a hangup or misperception, the design needs to be improved.

  • Listen when even fans of systems and approaches openly confess their flaws.

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