Dice Mechanics are Inherently Broken

The real question is: how broken do you want to allow them to be in your game?

Let’s back up a bit, and frame this conversation properly. A few days ago, I found a blog by someone I’ve never met, known, or even heard of, ranting about how D&D and Pathfinder suck.


While I don’t disagree with his sentiments, I felt compelled to say something, since I’m presently running two D&D 5e groups. Admittedly, I had the ulterior motive to try to drive traffic toward my own blog. I find it interesting though, that his first reply to my comment was to refer me to a wiki site that explains the rules to his own homebrew system.

I went and perused through it. I’ve never heard of his system, and while it seemed straightforward enough, I was struck by the fact that his system uses an exploding dice mechanic. It’s not the only system I’ve seen or played that limits to only six-sided dice, nor is the only system that uses an exploding mechanic.

If you’re new to Role Playing Games, let me explain a couple things:

Table-top Role Playing Games (RPGs) are, at the core, codified versions of the game “House” you played when you were little. You be the mommy, I’ll be the daddy, and we’ll pretend to live like someone else. Here, players take on the roles of heroic adventurers, super-spies, private investigators, or a near-infinite list of other potential characters, that live in an imaginary world, seeking fame, fortune, or the just successful completion of their goals. There are thousands of rule systems, some are more commonly used and popular than others. Conceptually, these rules outline how characters are built and how, more importantly, how challenges to those characters are resolved.

(I make the distinction between table-top RPGs and online RPG games. While the latter is based on the former, the two are distinctly different in more ways than I want to get into. This conversation is specific to table-top RPGs.)

RPG systems run the gamut from a minimalistic approach where the rules are vague and the focus is on telling the story unfettered, to gritty rules where every potential situation is explained and the focus is on simulated realism. Some players like the former, some like the latter, and, in my experience, most prefer a reasonable balance between the two.

This is where we get to dice mechanics. Challenge and conflict resolution are at the heart of most RPG systems. When you played “House” as a child, and the Mommy and Daddy wanted to fight, usually, the real mom just stepped in and told the guest to go home for the day. In a game system, however, conflicts are usually resolved using a randomizing mechanic. I’ll roll a die and you roll a die, and whoever rolls higher wins. Pretty simple, right? Oh, wait. One character is stronger than the other, so that character should get a bonus. Conversely, the other character is quicker, so the bonus is negated. And so on.

Each character in the RPG system is represented by a list of descriptors. These go by many names, like stats, attributes, prime abilities, skills, and so on. These are commonly assigned numbers on a relative scale that lead to various bonuses and penalties when called upon to resolve various types of challenges. When dice are rolled, the simulation becomes a little more realistic. We not only have rules to resolve combat, but we have rules on how to deal with other challenges, like, “Will the guard believe my story and let me into the castle?”, or “Can I use my good looks to convince the beautiful Russian spy to give me the secret password?”, or “I want use my experience as a fighter pilot to guide the alien spaceship to a safe landing and save the crew.”

Now that I’ve gone around my toe to get to my knee, I can focus on the premise of this article. My thesis statement is that Dice Mechanics are Inherently Broken.

Here’s where we get into a bit of teeth gnashing, because so many people freak out when a blanket statement is made. First, they take things out of context. Second, they accuse me of being stupid. While the latter may be true, the first condition needs to be clear: Dice Mechanics in most RPG Simulation Systems are Inherently Broken. Why the hell didn’t I just say that from the outset? Because if I did, you probably would have ignored this post and gone on your merry way. Thank you for reading this far. I hope you keep going, and allow me to support my thesis.

And take note that in my 3.5 years of college, I never wrote a thesis statement, so excuse me if I don’t follow proper formatting, or whatever the heck you call it. Also, let me state that I’m not a quantum physicist, nor am I an actuarial statistician. I am a gamer first and foremost, and, professionally, I am responsible for testing and validating (non-clinical) pharmaceutical data. Basically, I know how to create test scenarios and write code (usually T-SQL) to support and execute those tests.

The whole point of rolling dice in almost any game, especially RPGs, is to randomly determine the outcome of some sort of event. The pre-supposes three things: 1: There are more than one possible outcomes, 2: The outcome can be randomly determined, and 3: The odds of each potential outcome can be assigned a probability. Before we get into the fallacy of these concepts, let’s talk a moment about why this is done in the first place.

Games are played because they are fun. Some games are based on skill: Can you hit a ball with a metal stick and make it fall into a hole a quarter mile away? Some games are based on teamwork: Can you and your team pass the black disk back and forth, keeping it away from the players on the other team, and shoot it past a guy wearing oversized pads? Some rely on luck: Can I roll a 7 on two dice, and if I don’t, can I roll the same number I rolled earlier, without rolling a 7? Most games depend upon a combination of these factors, and probably many others I’ve not listed. Nor do I care to. RPGs are no different. As a player, I’m trying to overcome some sort of challenge that has been presented to me – be it defeating the fire-breathing dragon or uploading a retro-virus into an alien computer system using a laptop equipped with blue-tooth. At some point, someone, usually a game master, under the guidance of a ruleset, comes up with a list of potential outcomes then determines the likelihood of each of them. You roll your dice and the outcome is revealed. Regardless the determined outcome, the story goes on. The essence of randomness, coupled with good story telling, gaming skill, and the opportunity to spend time with your friends, makes the gaming experience what it is.

Ultimately, the players can decide to forgo dice and adjudicate the outcome through some other means. There are some game systems that allow for this.

But I still haven’t made my case. I want to get back to one of the points made in the blog that started this conversation: “Using a 20-sided dice with smaller adjustments makes the spread too wide.”

I believe what he’s basically saying that 5% increments provide too much granularity because the change of success or failure isn’t reasonably balanced based upon the task. His example is when faced with a challenge, the player rolls a 2 one time and fails the task, but rolls a 17 another time and succeeds, and he believes this is unrealistic.

However, to make the claim stick, a lot of factors are missing. What is the “difficulty level” of the challenge? Is it easy, hard, or near-impossible?  In D&D, for example, a difficulty level of 10 is considered somewhat easy. You can still screw it up occasionally but most of the time, you’ll have no problem with it. Conversely, a difficulty level of 20 is considered hard. Here, most of the time you’ll screw it up, but occasionally you’ll get it right. The more you do something, the theory goes, the better at it you’ll get. As you gain in experience, your skill level increases, which progressively improves your chance of success. If my combination of stats says I get “+7” to my die roll, the target number is 10, representing an easy task, and the rules say I must “match or exceed the target number to succeed,” then, per his example, rolling a 2 is a failure. Running the numbers, simply enough, means that there is a 10% chance of failure and a 90% chance of success. To me, it doesn’t matter what type of dice I use if this probability is accommodated.

If I compare it to real life, I would say that throwing a tennis ball and hitting a two-foot target should be easy. I don’t have the time nor inclination to test this, but I’ll bet I can do it successfully nine out of ten times. By extension, saying that I have a +7 on my chance, the challenge level is 10 (easy), and I roll a 20-sided die ten times, likely, I’ll miss that target once. Maybe I’ll miss it two or three times, or maybe I won’t miss at all. It’s remotely possible for me to miss all ten throws, too. I could be having a bad day, or I could be distracted by something. Who knows? The point is, however, is that the best the game mechanic can do is to simulate the potential outcomes. In this example, the only outcomes are success and failure. We’re not talking about other potential outcomes, like my ball hits the target in such a way that it knocks it off the nail holding on the wall, rendering all future attempts impossible. Or maybe a passing bird catches my ball and flies away with it.

Let’s take my example to an extreme, and prove why the system doesn’t work, when I just finished proving that it did. D&D has this concept of automatic success and automatic failure. While this has changed as the game has evolved, the general concept is that if I roll a natural 20, I always succeed, and if I roll a natural 1, I always fail. Other rules exist to mitigate the extremes, but for the sake of argument, let’s break it down.

The chance of rolling any specific number on a 20-sided die is 5%. I’m not going to get into arguments about plastic density, the accuracy of the mold when the die was made, or even metaphysical factors. Let’s just say that our d20 is perfectly random and the chance for any possible outcome is exactly 5%. Okay. I’m throwing a tennis ball at a 2-foot target mounted on a wall. Standing twenty feet away, we’ve established the challenge of hitting it is considered “easy” and, based upon my relative skill level, I’m probably going to hit it 9 times out of 10 tries. If I back away from the target 20 feet, making the range 40 feet, the difficulty level increases. Let’s say that it increases 5 for every 10 feet. This means, at 40 feet, the challenge level is now rated as “difficult,” and I need to match or exceed 20. Because my bonus is +7, I need to roll a 13 or better, meaning my chance to succeed is 35% and my chance to fail is 65%. With me so far?

Now let’s back up another 20 feet. By the calculation, the challenge level is in the “impossible” category at 30. Assuming I have the strength to throw a tennis ball 60 feet, is it truly impossible for me to hit the target? As we’ve explained so far, the answer is no. Let’s introduce auto-miss and auto-hit. If I roll a natural 20, I hit, regardless the difficulty level. 5% chance. Sounds fair. Let’s back up another 40 feet. Now I’m 100 feet away, and I need to achieve a threshold of 50 to hit the target. Not possible unless I roll a natural 20. Oh, wait! I have the same 5% chance of hitting the target at 60 feet as I do at 100 feet. That doesn’t seem right. At some point, my ability to throw that distance diminishes, and the GM (in this case, physics) will simply rule that it doesn’t matter what I roll, I will always miss. But until that happens, we can easily see how the d20 system is broken.

The same is true going the other way. If I’m standing next to the target, I don’t even have to throw the ball to hit the target, yet, by the extension of the rule, I will always have a 5% chance of missing.

This is where Geir’s argument has merit. His RPG system uses an exploding die. In general terms, this type of system adds a different rule: If you roll the maximum value of the die, rather than just assuming you succeed, you pick up the die, roll it again, and add the result. Depending on the rules, it may work that if you roll the maximum value again, you repeat (add and roll-again) until you no longer roll the max value. On the outset, this sounds cool, because the example of throwing the ball a long distance becomes possible, but the chance diminishes appropriately. Did we just fix the problem of the flat 5% auto-success? Perhaps.

Here’s where it breaks, and it breaks the same way D&D breaks. Your GM is stupid and allows players to play by the letter of the rules rather than the spirit. I want to throw the ball an incredible distance and still hit the target. Geir’s RPG system uses six-sided dice instead of twenty-sided dice. All that does is change the probabilities to 16.67% increments. The math is a little harder, but the point is the same. Using a different die type means scaling the difficulty benchmarks as well, but the real issue is that I could theoretically roll a 6 many times. Rolling 3 sixes in a row is a 1 in 216 chance (a little less than 0.5%) However, each time I pick up the die, the next roll is always a 16.67% chance of rolling a 6. In theory, I could roll six 1000 times in a row. The odds are astronomical but conceivable. This means I could potentially hit the target by bouncing the tennis ball off the moon. “Nothing but net.”

Okay, I get it. That’s just plain stupid. But I think I make my point. Any way you look at it, dice mechanics are inherently broken. You can take efforts to mitigate and adjust circumstances so that the odds of success or failure, or (something we only briefly touched on) the degree of success and failure or other possible outcomes, are accounted for, but you’re still simulating.

And that leads me to my final point. It ultimately doesn’t matter what system you’re using if you and your friends are having fun. You may believe that a given system sucks, but if that’s the system you and your friends have agreed do use, deal with it. Complain about it online, to the publishers, to other players all you want. If you are that dead-set against using a specific system, nobody is forcing you. Of course, you may show up at your favorite local game store looking for players, and if no one is interested in the system you want to play, you’re stuck playing it by yourself or not at all. It’s up to you.

Last thing. I promise. I look forward to reading your comments. However, if it’s obvious you haven’t read my entire post, or if all you want to do is tell me how stupid I am, your post will be deleted. I already know how stupid I am, and if you’re not willing to read what I have to say, why should I read what you have to say?

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