Linear Curve - - - Bell Curve
The Game - DMG.9 - DMG

As the DM, the tools of your trade are dice -- platonic solid-shaped or just about any other sort.
The random numbers you generate by rolling dice determine the results based on the probabilities determined herein or
those you have set forth on your own.
In case you are not familiar with probability curves,
there are two types which are determined by your dice:
    * linear (straight line),
        which has equal probability of any given integer in the # group, and
    * bell (ascending and descending line),
        which has greater probability towards the center of the group of #numbers# than at either end.

The two curves are illustrated thus:

Linear Curve

Linear probability develops a straight line of ascending probability when used as a cumulative probability as shown above.

Bell distribution, when used to delineate the probability of ceratin numbers appearing, develops a curved line like this:

Bell Curve (3d6)

A single die,
or multiple dice read in succession
(such as three dice read as hundreds, tens and decimals) give linear probabilities.
Two or more dice added together generate a bell-shaped probability curve.

Before any further discussion takes place,
let us define the accepted abbreviations for the various dice.
A die is symbolized by ”d”,
and its number of sides is shown immediately thereafter.
A six-sided die is therefore “d6‘, d8 is an eight-sided die, and so on.
Two four-sided dice are expressed by 2d4, five eight-sided dice are 5d8, etc.
Any additions to or subtractions from the die or dice are expressed after the identification, thus:
d8 + 8 means a linear number grouping between 9 and 16,
while 3d6-2 means a bell-shaped progression from 1 to 16,
with the greatest probability group in the middle (8, 9).
This latter progression has the same median numbers as 2d6,
but it has higher and lower ends and a greater probability of a median number than if 2d12 were used.
When percentage dice are to be used, this is indicated by d%.

The d4 can be used to generate 25% incremental probabilities,
random numbers from 1 to 4, with + 1 it generates a linear 2-5, etc.
It can be used to get 1 or 2 (1 or 2 = 1,3 or 4 = 2) or in conjunction with any other dice to get linear or bell-shaped probability curves.
For example, 2d4 = 2-8, 3d4 = 3-12, d4 + d6 = 2-10, d4 + d20 (as d10) = 2-14.
When rolled in conjunction with another die,
the d4 can be used to determine linear number ranges twice that shown on the other die, thus:
d4 reading 1 or 2 means that whatever is read on the other die is the number shown;
but if the d4 reads 3 or 4, add the highest number on the second die to the number shown -
so if d8 is the second die 1 to 16 can be generated,
if a d12 is used 1 to 24 can be generated. If a d20 is used either 1-20
(assuming the use of a standard d20 which is numbered 0-9 twice without coloring one set of faces to indicate that those faces have 10 added to the number appearing) or
1-40 (assuming that one set of faces is colored)
can be gotten by adding 0 if 1 or 2 is rolled on the d4 and 10 or 20
(depending on die type) if a 3 or 4 is rolled.
Linear series above this are possible simply by varying the meaning of the d4 number;
1 always means add 0, but 2 can be interpreted as add the value (highest number) of the second die,
3 can be twice value, and 4 can be thrice value.
Thus, a d4 reading 4 in conjunction with a d8 (linear curve 1-32) would mean 24 + d8, or 25-32.

What applies to d4 has similar application with regard to d6, d8, d12, and d20.
The d6 has 16 1/3% intervals, d8 has 12% intervals, and d20 can have 10% or 5% intervals.
A d6 is useful for getting a random number from 1 to 3 (1-2 = 1, 3-4 = 2, 5-6 = 3),
while 1 to 5 can be easily read from a d20 (1-2 = 1, 3-4 = 2, 5-6 = 3, 7-8 = 4, 9-0 = 5).

The d20 is used often, both as d10 and d20.
The bell-shaped probability curves typically range from 2-20 to 5-50,
i.e., 2, 3, 4 or 5d20 added together.
Also common is the reading as above with one decimal place added to the result to get 20-200, 30-300, etc.
In the latter case, a roll of 3 on one die and 0 (read as 10) totals 13, plus one place, or 130.

Non-platonic solid-shaped dice are available in some places.
The most common of these is a ten-sided die numbered 0-9.
As with the d20, this can be used for many purposes,
even replacing the d20 if a second die is used in conjunction to get 5% interval curves (1-20).
Also, the die can give 0-9 linear curve random numbers, as the d20 can.

Other dice available are various forms of ”averaging” dice.
The most common of these has six faces which read: 2, 3, 3, 4, 4, 5.
The median of the curve it generates is still 3.5, that of a normal d6, but the low and high numbers,
2 and 5, are only half as likely to appear as 3 or 4.
There is a 33%% chance for either of the two latter numbers ta be rolled,
so the probabilities of absolutely average rolls are far greater.
Other such dice have zeros on them, several low numbers, and so on.
These sorts of dice, along with poker dice, ”put & take” dice,
or any other sort can be added in order to give you more flexibility or changing probabilities in random selection or event interpretation. For example:

The author has a d6 with the following faces: SPADE, CLUB, CLUB, DIAMOND, DIAMOND, HEART.
If, during an encounter,
players meet a character whose reaction is uncertain,
the card suit die is rolled in conjunction with 3d6.
Black suits mean dislike,
with the SPADE equalling hate,
while red equals like, the HEART being great favor.
The 3d6 give a bell-shaped probability curve of 3-18,
with 9-12 being the mean spread.
SPADE 18 means absolute and unchangeable hate, while HEART 18 indicates the opposite.
CLUBS or DIAMONDS can be altered by discourse, rewards, etc.
Thus, CLUBS 12 could possibly be altered to CLUBS 3 by offer of a tribute or favor,
CLUBS 3 changed to DIAMONDS 3 by a gift, etc.

Q: What does "1d10" mean?
What does "d%" mean?

A: "1d10" means roll one 10-sided die.
"5d10" means roll five 10-sided dice. That
is, the number before the "d" is the number
of dice and the number after the "d"
indicates the number of sides each die has.
The abbreviation "d%" indicates percentile
dice: that is, roll two ten-sided dice, reading
one die as tens and one die as ones in
order to get a number between 1 and 100
(00 = 100). The term "d%" is also
expressed as "d100".

Howdy John,

Indeed, the best advice I can give is design to please yourself and your trusty gaming comrades so as to maximize the enjoyment generated by playing the campaign.

I do indeed get a bit fed up with disputes about which game is "best," for it is a matter or personal/group taste.
The same with niggling over mechanics and rules. The RPG is a bloody GAME, after all is said and done.

As random events occur all the time in actual life, I am a firm believer in having the same thing happen in the role-playing game. Whether the probabilities for various random things are relatively equal as with a linear curve, or wildly disparate, as a bell curve with multiple dice delivers, no matter...aslong as the resulting event is approproate to the likelihood of it occuring when compred to the class of other such events in which it appears.

I do prefer the 100 possibilities of the d% roll to most others, and one can have additional rolls if needed to reflect decrasing probability of the indicated result.


Re: Wow - still here?
Originally posted by Caedrel
How have the dice (number of sides, etc) evolved in D&D? Other games I've seen tend to use multiple d6s with maybe a different value on one side, but I love the number and variety of dice in D&D, as well as rolling them (even if some do get a bit lonely - I feel especially fond of the d12 in this respect ). Were there always the d4, d6, d8, d10, d12 and d20 in D&D?

Indeed, from the inception of the game with OD&D, the Platonic solids were included. There were no d20s per se, then. They were numbered 0-9 twice, so you had to color in half the faces for 10 plus the number, or else roll another die with that one to get a 1-20 range.

Now I include a d30 in the LA game, although it isnt' used much. I also have a d7 that's useful but not caled for in the rules. A d7 and d4 in conjunction give you the day of the lunar month, of course Also handy for random determination of something when there are seven characters involved.


Originally Posted by Jehosephat
Thank you kindly Gary. I remember those dice from my early D&D and Gamma World boxed sets.
Actually, for reasons of nostalgia, it wouldn't be bad to have a set of those right now.
I remember the 4-siders actually had a pretty sharp point on them.
You know if you attacked someone with them, I'll bet they would do 1d4 damage. :P (sorry I couldn't resist that corny joke).

As it happens I have quite a number of the old low-impact dice around here somewhere.
The points on the d4 were very sharp but wore down quickly.
Rob had a d20 that would stand on a worn point about one roll in 50

Somewhere I lost my d20 with half the faces colored gray.
It was my "killer die" that rolled an idnordinate number of 20s, and the players really hated it


Originally Posted by Grazzt
I have one of those myself (a "killer die"). Yeah- the players really, really hate it.


Right Rob was always looking to get one for himself to get even with me when he was DMing for my PCs.
One encounter Robilar had when he was about 9th level and AC -4 was with an Evil Cleric and his gnoll guards.
The latter managed to hit Robilar so many times because of my 20s that he had only about 10 HPs left when he finally offed the cleric and was able to concentrate on the gnolls.



It is good to learn that there is at least one other person who isn't superstitious about his dice being touched by others, particularly players from the group.

That said, I would be none too happy if my favorite ones were absconded with.
I hate it when the opposition I am represenring can't find the pointy ends of their swords, or use their natural weapons to effect.
No challenge to the characters at all when that happens...and it does happen!


Originally Posted by Silver Moon
Treasures indeed! A week ago I had been doing some cleaning in our gaming room and accidentally misplaced the mug-full-of-dice that we put out on the table for everyone to game with. This brought things to a standstill at the beginning of the game until I remembered that there might be some in the back of a drawer inside the figure case. Wouldn't you know, it was the old chipped-up soft plastic bunch listed above that we had started out with. So some 23 years after we were first rolled them we were using them again!

There's much to be said for results, and those old low-impact dice do generate random numbers
Not much to look at but they deliver.

Of course I do prefer a d20 numbered 1-20, and in all the contemporary high-impact plastic dice are a boon, I have an odd mix of old and new, but my d30s and d7s get a fair workout in most game sessions,


Originally Posted by MerricB
Happy new thread, Gary! (wow, part 8... where does the time go?) 

Gary, thanks to D&D you have introduced many of us - of not most of us - to an unforgettable experience:

The use of the d4 as a caltrop.

Many has been the time that I've got out of bed at night, only to suddenly feel something sharp and painful digging into my foot. If my mind worked faster at such times, I might have been calling down imprecations on your name, but as it doesn't the most I can normally manage is "Ow!" (or some choice swearing).

Could you please tell me if you had any idea what you were unleashing on the world when you included the d4 as part of the standard D&D game (and whether you've ever experienced this exquisite sensation yourself)?

<big grin>

Best wishes,

Hi Merric

As the real old timers know, I was always an active gamer since I discovered there were fanzines offering a forum for one's gaming thoughts, opinions, and play offerings.
In short, I've been balbbering thus for about 40 years, so it's no wonder a lot of my fellows are familiar with my name.

The d4 was one of the five Platonic solids sold by the school supply company in California from which I obtained the first of the new milti-sided dice that were introduced in the first edition of the D&D game, I have indeed stepped with stocking feet on one of those yelow caltrops--also a d8, that being back in the early 1970s.
Thereafter I made a point of picking up all of my dice and keeping them off the floor.

Cats seem to love to play dith d20s, BTW, and a few were lost that way to various felines that resided in my house.

When I'd leave my dog "Bowser" (a bull mastiff) alone he would get revenge that included shredding my dice bag and leaving a minefield of milti-sided dice in my bedroom and in the kitchen...the devil know where I was sure to go :\


Originally Posted by BOZ
hey, if you can find an actual d46 that might be worth some money!

D4 followed by d6 gives a range of 1-24 <EEK!>