Updated: Oct 5, 2020
So why do we use all these dice anyway?
There's a game you likely know already, called Tic Tac Toe. Its rules are pretty simple. A grid of 9 squares (3 wide, 3 tall) represents some field or other location. An O represents one Player, an X represents the other Player, and they take turns "standing" in one square or another until one has moved through 3 squares in a row. You don't have to think of it as something so boring as standing in a field. Maybe the Players are rival Spies chasing each other through rooms. Maybe they're Knights on a battlefield. But the rules remain the same no matter what you picture in your head when you play.
So what happens, you might ask, if you're playing Tic Tac Toe and both Players want to "stand" in the same square?
Well, in that game, whoever goes first in the turn order chooses who gets the square. But consider if your battlefield Knights were to fight over standing room instead of chasing.
What might happen then?
How would you resolve that battle?
The answer is, you wouldn't. It's Tic Tac Toe. It has no rules, no mechanical way of representing a fight between the two Players. You could just imagine that the Knights do combat, but how do you decide who wins?
Who fights better, X or O?
To be fair in deciding, you need to look at the math of the fight.
If both Knights have the same level of skill, then we say that each has a 1 in 2 chance of winning, which is to say that out of 2 tries, only 1 will likely be a win. This can also commonly be represented as a fraction (½), or a chance out of 100, shown with a "%" sign (50%).
If you want to make a game that represents a 1 in 2 chance fairly, an easy way would be by moving and reading an object with 2 sides, and an equal chance of landing on each one.
Like a coin.
Flipping a coin, with one side meaning the victory of Player 1, and the other side meaning the victory of Player 2, would be one very fair way of choosing who wins. That is why we use coin-flips for so many things where two outcomes are possible, and equally desired, like who goes first in Football.
But, what if you have more than 2 Players? What if you need more than 2 sides?
This is why dice were invented.
The first dice we know of had 4 sides, and were Triangle shaped. Modern 4-sided dice still have this basic shape, and they can be used to represent any whole number from 1 to 4. This not only allows the deciding of 1 in 4 chances, but by doubling up (both odd numbers meaning 1 and both even numbers meaning 2 for example) the sides, you can also get 1 in 2 chances calculated with a 4-sided die.
Where things start to get more complicated is where two Players don't have the same ability to do something as each other, or where the chance of doing something can't be calculated with simple math. When that happens in a game, we do one of 5 things:
Create personal Scores for each Character which affect the outcome of the die roll, making it a higher number or a lower number.
Roll a die with more sides, so there are more possible outcomes.
Roll more than one die and add the results together, so the Probability Distribution changes.
Roll more than one die and compare the results against each other, so the Probability Distribution changes in a different way.
Create uneven probabilities, like 3 in 4 or 7 in 20 by deciding that multiple sides on the die represent the same outcome.
Most Role-Playing Games (The Elf Game included) use all of these strategies in complex ways to make lots of different situations have different Probability Distributions from one another, each fitting that specific scenario.
For example, a Character has a Strength Score, and it is generated by a roll of three 6-Sided Dice added together (“3d6”). This gives a number from 3 to 18, which will have a Bell Curve (because the curve is shaped like a large bell), or Normal Distribution, meaning most Characters will end up with a Strength Score somewhere in the middle, while only a few will end up with a very high or very low score. On average, most people are of Average Strength. (That’s what’s known as a Truism, something which has to be true even to be said, or else it wouldn’t make sense to say.)
Say a Character wants to push a boulder up a hill. The Strength Score, generated by 3d6, is compared to the roll of a single 20-Sided Die, which of course gives a random number from 1 to 20, each having a 1 in 20 chance of appearing, a Linear Distribution. If a 7 is rolled on the 3d6, then a 7 or lower must be rolled on the D20 in order to succeed at the Strength task. This means only the 1, 2, 3, 4, 5, 6, and 7 are “success” numbers in this case, so the chance of success is 7 in 20.
In this example, we have combined 4 ways of changing Probability, and that is just one of many ways of doing things. In another example, the Character might want to simply lift the boulder and throw it to the top of the hill. In that case, you might want a Normal Distribution (3d6, for example), as the actual likelihood of doing such a thing is distributed on a Bell Curve.
So dice, then, are just standing in for something real happening in the world of the game. Whether it's an entire battle being decided by the flip of a coin (D2), or 47 dice of various sizes being added together and compared against each other (with adjustments from Ability Scores!), the goal is to have the chance of the mechanic match the chance of the outcome.
That is to say (and this will be another Truism) things have exactly as much chance of occurring as there is probability that they will happen. So the thing you use to represent chance should likely match the probability of that chance.