D&D Alumni
A Brief History of Dice
Steve Winter

Players who came to the game after the release of 2nd Edition missed out on a unique feature of the original editions -- the way dice rolls were expressed. In this month’s D&D Alumni, industry vet Steve Winter takes a look back at the bizarre mental math formerly required to determine exactly which dice to pick up and roll.


We're now accustomed to straightforward expressions such as 1d8, 2d10, 3d6+2, and so on. Up until 2nd Edition, however, that notation wasn't used. Instead, dice were indicated by their range of results. For example, what's now written as 2d6 was once expressed as 2-12; 3d10 was 3-30.

For the most part, this was straightforward. It even had some positive effects. Compare these two lists of weapon damage:

1d8 1-8
2d6 2-12
2d4+1 3-9
2d8 2-16
1d10 1-10

Scanning down the first column, looking for the 'best' weapon takes a bit of mental readjustment. In contrast, the second column gives an immediate impression. We recognize instantly that the weapons top out at 16 points of damage, and can rank them with no effort whatsoever.

It's important to remember that when D&D first appeared, hardly anyone was familiar with the "funny dice" used in the game. Few people had even heard of 4, 8, 12, or 20-sided dice, let alone seen them. That made results such as 1-8 doubly puzzling.

It didn't help that 20-sided dice at that time weren't numbered 1 to 20. Instead, they were numbered 0-9 twice. A 0 counted as 10, and a "control die" was needed to run the full range from 1 to 20. (The control die, usually a d6, was rolled along with the d20. So if the d6 showed 1-3, the 1-10 on the d20 was read straight-up. If the d6 showed 4-6, then 10 was added to this number.) Why go through all of that? Because the 20-sider needed to do double-duty as both a d10 and a d20. The d10 as we know it now didn't exist -- at least not as a die you could buy in a store. "True" polyhedral dice are based on Platonic solids, beautiful three-dimensional objects incorporating geometric perfection in their shapes. The d10 isn't such shape. It's a pentagonal trapezohedron, which is fancy math talk for an ugly, corrupted shape that has no business existing in the real world.

The 1974 "Blue Box" edition of D&D came with a full set of (badly made) polyhedral dice. Their use was explained on the last page of rules, in a section called Using the Dice:

Players need not be confused by the special dice called for in DUNGEONS & DRAGONS. By using the assortment of 4-, 6-, 8- 12-, and 20-sided dice, a wide range of random possibilities can be easily handled.

For a linear curve (equal probability of any number), simply roll the appropriate die for 1-4, 1-6, 1-8, 1-10, or 1-12. If some progression is called for, determine and use the appropriate die (for instance, 2-7 would call for a 6-sided die with a one spot addition). For extensions of the base numbers, roll a second die with the appropriately numbered die. For example: to generate 1-20, roll the 20-sided die and 6-sided die; and if the 6-sided die comes up 1-3, the number shown on the 20-sider is 1-10 (1-0), and if the 6-sider comes up 4-6, add 10 to the 20-sided die and its numbers become 11-20 (1-0). This application is used with the 12-sided die to get 1-24. If 1-30 or 1-36 are desired, read the 6-sider with the 20- or 12-sided die, with 1-2 equaling no addition, 3-4 adding 10, and 5-6 adding 20. This principle can be used to generate many other linear curves.

For bell curves (increasing probability of numbers in the center, decreasing at both ends), just roll the same die two or more times, roll several of the same type of dice, or even roll two or more different dice.

Is it clear now? (As a displacer beast.)

Oddly, the section closed with this statement:

In some places the reader will note an abbreviated notation for the type of die has been used. The first number is the number of dice used, the letter "d" appears, and the last number is the type of dice used. Thus, "2d4" would mean that two 4-sided dice would be thrown (or one 4-sided die would be thrown twice); "3d12" would indicate that three 12-sided dice are used, and so on."

What makes this comment odd is that the notation isn't used anywhere in the rulebook! In the vast majority of cases, the standard ranges are used. The one exception occurs on a table listing the different types of giants. Under Special Characteristics, their damage is spelled out as such: The frost giant "Does 2 die + 1 damage per hit," while the fearsome storm giant could smack you down for "3 dice + 3 damage." (If you find those damages surprisingly low, remember that this was a time when all weapons, regardless of type, caused uniform 1-6 damage. Not even exceptional Strength gave you a bonus. Only a magic weapon could do that.)

Despite its whimsy, this system worked well 95% (1-95) of the time. Things sometimes got interesting, however, when the nomenclature was applied across the board. Sometimes it was just a question of dividing things in your head, as in these examples (remember that in earlier editions, the number of a given monster appearing per encounter was a listed line in their stat block):

Gorgosaurus -- no. appearing: 7-28
Platinum Dragon -- no. appearing: 6-48
Earth Elemental -- no. appearing: 4-32
Whales -- no. appearing: 3-24 or 6-24, by size

Sometimes it was a case of confusing jargon:

Black Pudding -- no. appearing: 1 to 1-4
Caveman -- no. appearing: 10-100 (120)

And sometimes it was a case of multiple choice answers. The classic example of this was 3-12. Does that mean 3d4 or 1d10+2? In terms of probable results, those are quite different. The same goes for the huge ranges that occurred frequently in the "no. appearing" entries of the Monster Manual:

Nixie: 20-80
Orc: 30-300
Buccaneer: 50-300
Dwarf: 40-400

If the party encounters orcs, is the DM supposed to roll 30d10? 1d10 x30? 5d10 x6? Or something else of his own concoction? Especially disturbing was that mention (in the Blue Box edition) that you could "roll two or more different dice" in certain cases. In other words, 1d4 + 1d6 was OK. That particular example would give 2-10 -- not impossible to figure out, but it slows you down. Consider what happens when confronted with 2-16. That probably meant 2d8, but it could also -- not likely, but possibly -- mean 1d6 + 1d10.

This issue was amusing enough that, for some game groups, it became a game in its own right. During slow points in play, someone would call out a range of numbers -- "3 to 16" -- and the race was on to see who could be first to find a legitimate way to generate that range, using only real dice (no d9s or d7.5s).*

Where did this system come from? Obviously, the "#d#" style of notation had been thought of. Why wasn't it used originally?

The first likely suspect is tradition. D&D grew out of military miniatures games. Looking back through the rules for pre-D&D miniatures games published by Tactical Studies Rules (or its predecessor, Guidon Games), one sees that die results were almost always listed as ranges. That is, instead of noting a roll of 4+ or "4 or higher," the rules would call for a roll of 4-6, as in this table showing the likelihood of desertion by infantry units, from Cavaliers and Roundheads:

Turn Die Score
First 1-5
Second 1-4
Third 1-3
Fourth 1-2
Fifth 1

More modern games would not use that structure. Instead, it's likely they would ask for a roll greater than the turn number. In those days, if it could be put in a table, it probably was.

The second and more important reason was that the ranges weren't always meant as dice rolls. Where weapon damage and hit points were concerned, dice rolls were appropriate. When talking about the number of orcs in an encounter, however, "30-300" didn't necessarily imply a dice roll of any kind. It was more appropriate for the DM to consider the situation and choose a number. The range simply gave the upper and lower bounds that should be considered. And even those could be ignored at the DM's option.

Of course, gamers being what they are, any excuse to roll dice is generally seized upon, even when it's not clear exactly which dice should be rolled.

* 2d6 + 1d4 works. How many more can you think of? Here's a harder one for advanced players -- 8-26. Think you're an expert? Find a way to get 4-66. Yes, solving these sometimes requires a bit of algebra, but if you played D&D in 1975, odds are good that you were either acing algebra (because you were a genius) or flunking it (because you were spending all your time playing D&D).


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