Dice… the core of many TTRPGs. They come in many different shapes and sizes – from itty-bitty d4s that could easily double as caltrops if you were ever to step on one, to massive d20s that are bigger than your head. In some cases, the die size is decided based on practicality, like with the standard size that is roughly an inch (~2.5cm) tall. This size is small enough to hold multiple in your hand for those big hits, but big enough that you aren’t squinting to read the numbers, or losing one every time you roll. However, some dice are chosen for a more niche purpose. With small dice, they could be for: decorations, having multiples of only one die, or just because you feel like it. On the contrary, large dice are likely a staple show piece or for that one outdoor session you had with your friends over the summer.
Now why is chance so fundamental? Well if you have ever played a grindy video game or done a menial task until you’ve become an expert at it, you’ve seen the inevitable outcome of reaching the end of the road for the game or activity you are partaking in. Now that doesn’t mean it can’t still be enjoyable, it’s just not the same after a while. With dice, every roll from the first to the last is all up to chance. Your first critical hit in a DND campaign as a level one fighter can be just as exciting as that natural 20 charisma roll for convincing the guard to let your friend, who you have been fighting alongside for the last 3 years of an ongoing campaign, go free. Each task you undertake always has a chance for success and a chance for utter failure.
Now, I’m guessing one of your next questions is: What are my odds of success, then? Well, that all depends on what you are trying to do. In many cases, your goal is to roll at least a certain number on a specific dice. In the case of the d6, the “standard” dice, you are typically rolling for a chance at an event or to see how much damage you do. In the case of damage, you are likely trying to roll as high as possible.
With a straight roll, one that is not modified in any way, you have a one in six chance of rolling any one of the numbers on the dice, one chance for each of the faces. However, the average roll for a d6 rounds to 4. So you are most likely going to roll something between 3 and 5.
Why is the average not in the middle, you might ask? Well, that comes down to the fact that the average of the numbers on the dice, the sum of all faces divided by the total number of faces, is typically not a round number. Numbers that are not followed by decimals, fractions, or other extra symbols and are always whole numbers are called integers. Technically, integers can also be negative, but for this example, we will only work with positive integers. In the case of the d6, the average of the dice is 6+5+4+3+2+1 which equals 21, then that number is divided by six, the total number of faces, to get 3.5. Since typical dice can only roll integers, the value of 3.5 is rounded to the nearest integer. Since 0.5 and higher, 0.5 through 0.99, rounds to 1, 3.5 similarly rounds to 4.
The same pattern for averages in die can be seen as the number of faces increase. A d8 will average to 4.5, rounded up to 5. A d10 will average to 5.5 (6), and a d12 will average to 6.5 (7). A d20, one of the most critical dice in DND, averages to a 10.5 (11). So what does this mean for your roll and how successful you will be? Well, if you are trying to roll damage, like in our initial example, on a d6, you will typically do 4 damage. However, if you are trying to accomplish a task by rolling a d20, and the difficulty to complete that task is considered to be equivalent to a 10 out of 20, then more often than not, you will succeed at the task since the average of a d20 is above a 10.
If you’ve gotten lost so far with all the numbers and explanations of what types of numbers there are, no worries. The main thing to consider is that each dice has an average roll. If you are trying to see if your chances of doing what you want to do are good, as long as the chance of success is at or below the average of the dice, you have a good chance at succeeding.
If you find yourself in a situation where you are trying to roll a number that is above the average, then the chance of your success now becomes a bit more of a math problem for each roll. The average of a dice is defined by the number of faces and assumes they count up by one. The chance of rolling above a certain number on a die, on the other hand, is a matter of determining what the chance of rolling a specific number on that die, and then counting how many of the faces are above that number.To give an example of how to determine the chance of rolling higher than a specific number, let’s consider the d10, to make things simpler.
In the case of a d10, the chance to roll any single number is 1 in 10, also known as 10%. Knowing that each face represents a 10% chance of rolling that specific number, the chance to roll above a 5 can be determined by counting the number of faces that are above 5: 6, 7, 8, 9, 10. With 5 faces being higher than the number 5 and each face being a 10% chance, you have a 50% chance of getting above a 5. Similarly, if you are trying to get above an 8, the only numbers above 8 are 9 and 10, so you only have a 20% chance of getting above an 8.
The chance of rolling above, or below, a certain number is always representative of your chance to succeed on this roll. By rolling again, you don’t inherently gain the chance from the last roll. For example, if you have a 20% chance to roll above an 8 with a d10, and you roll a 5, by rolling again, you still only have a 20% chance on your second roll of getting above an 8. The number doesn’t increase by 20% each time you roll.
If you truly wish to know the impact of increasing your chances by rolling multiple dice, I would highly recommend you look into the probability of dice and the effect of increasing the number of dice included in the chance of success. There are a few videos out there that go into significant detail and a few that cover the general application but show a concise summary of the data collected over time. My favorite example of one of these videos is this one here: The unexpected logic behind rolling multiple dice and picking the highest. where the “Stand Up Maths” channel goes over the probability of rolling multiple dice and rounds out the video with discussing the formula for why the average of a d6 is 3.5.
With all that said, I hope you’ve learned a bit about the world of chance when it comes to rolling dice. Each shape and size has its purpose,, and if you know your way around the rolls, you’re one step ahead of the rest. Next time you’re in a battle of wits or maybe even trading blows with the friendly neighborhood ogre, you’ll know whether the odds are in your favor!
About the Author
My name is Josh, I have been playing or DM-ing DND campaigns since 2016 and have spent almost all of my time on 5e. Outside of DND, I have spent some time in other roleplay (RP) spaces on various multiplayer games like Conan Exiles as well as some Military Simulation games like Ghost Recon and Arma. I enjoy telling the story of things and building characters that feel like a part of the world.
RPG Counterpoint 
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