#Dice math

[dice-wizard]

So I have a pretty basic question

what’s the benefit of a dice pool rpg system over just rolling a d100 or something?

Okay so, a single die (but also d% even though this is rolled as two dice) has a flat distribution. There is an equal chance of all results on the die. When you roll a d20 your odds of a 1 are the same as the odds of a 20. The d20 was intentionally used for attacks in D&D because of the swinginess of that probability.

When you use a dice pool, it creates a bell curve instead, broadening and stabilizing your results. This is why PbtA is built around the 7-9 mixed success result - this will happen with much more stable frequency than rolling 10+ on 1d20. Similarly, Exalted uses pool math that allows the player to estimate every 2 dice generating one success, around which all the base difficulties are structured. When you start fucking with things like ones taking away in classic World of Darkness, you destabilize the nice curve and get into bad swinginess again.

The smaller your single die, the tighter (andore difficult) the framework for where you can adjudicate failure. My butthole clenches when I see people using single d6 resolution and have failure on 3 or less.

I don't really think people understand the importance of mathematical stability underpinning your basic resolution, if you're going to do something with randomization at all.

When someone says "We'll just roll a d20" I ask, is it because you want that level of swinginess? Usually no. Usually the answer is because that's what that person is familiar with - which fuels some of my distaste for WotC's stranglehold on the ttrpg zeitgeist.

Anyway, the difference is all in the control you want to have over success, failure, and your system's ability to predict and adjudicate that.

[zigmenthotep]

I was trying to find an answer to some more complicated dice probability and I thought that the AI summary was just being shit as usual, but then I found a whole Quara thread full of people who were very confident that the odds of getting all matching results on Xd6 is equal to (1/6)^X. Which is very incorrect.

Person after person after person was just going, "Let's see, the probability of rolling a 6 is 1/6, so the odds of rolling two 6s is 1/36, and three 6's 1/216. So the odds of rolling three matching numbers on three dice is 1/216!"

Mind you, a few people did actually understand that a die has multiple numbers, but most people basically invented a sub-problem—the odds of rolling three of one specific number—solved that problem, and then just walked away, confident in their own intellectual superiority, without considering the original problem.

Actual explanation after the break.

Okay, so yes, the odds of rolling any number on a d6 are 1/6, and the odds of rolling one specific number on 2d6 is 1/36—there are 6×6=36 total results possible, only one of which is that specific outcome.

But we want to know the odds of rolling matching results of any number, not just one specific number, and the math here is actually incredibly easy, if you remember what the problem is.

On 2d6 we have a 1/36 chance of rolling two 1s, a 1/36 chance of rolling two 2s, a 1/36 chance of rolling two 3s, and so on, and so on. So we have 6 possible matches in our 36 results, meaning the actual probability of rolling any matching numbers on 2d6 is 6/36, or 1/6.

Now let's expand that to 3d6. We have 6×6×6=216 possible outcomes, but once again 6 outcomes where all the dice match, since we still have 6 numbers. So 6/216 odds of rolling three matching dice, or 1/36—are ya catching on yet?

So all those very smart people on the Internet would have had to do to have the correct answer is remember that there are six different results on a d6, and multiply their result by 6.

And as you may have noticed, since each die added divides the probability by 6, and to get the correct answer we multiple the probability by 6, the very easy formula for determining the odds of all dice matching when rolling XdY is (1/Y)^(X−1).

(And yes, technically that even works for a single die)

Also, I wasn't intending for this to be a promo, but if you want to learn more dice math, check out my upcoming math zine, The Goblin Guide to Advanced Dice Rolling.

[ribstongrowback]

hi, french person here. I wasn't born then, so I can't speak for earlier iterations than INS/MV (as we call it here, as In Nomine Satanis is rarely spoken of without its angelic counterpart Magna Veritas).

however I would like to point out that the text does not ascribe an order, what it says is "use one as the ones, the other as the tens" which in context is not providing an order and more pointing out that you should interpret those separate dice in different ways rather than roll in a peculiar order. interestingly, in the following d666 roll they change this to make it ordered in hundreds, tens, then ones in the explanation.

i digged a bit though, because INS/MV was made by one of the (if not arguably the single) most influential french ttrpg author, Croc, a guy whom wikipedia credits as importing in france the concept of making games where you can give your character flaws in exchange for more advantages. i find dubious, he wasn't the only french nerd able to read in english, or interested in game design, but i do think it is fair to describe him as part of the very first french game designers.

all this to say that i think you can rest assured that it doesn't get much older than this where france is concerned, we didn't contribute much to game design until i was born [/j]

Here's a tabletop RPG history question, and also an etymology question if your nerdery bends that way.

d66 tables – as in "roll a six-sided die twice, reading the first roll as the 'tens' place and the second roll as the 'ones' place, yielding a number in the range from 11 to 66" – have been around at least as early as 1977, when the Starships book for classic Traveller used them to randomly generate trade goods for players to buy. However, the term "d66" wasn't yet being used to describe them – the book's text simply describes in detail how to roll on them each time such a table appears.

Conversely, we know the term "d66" was being used to describe this type of random lookup table no later than 2004, because several popular Japanese indie RPGs which came out in that year use it. However, none of these games seem to have originated it – the way they're using it suggests they're dropping a piece of jargon that was already well established at the time.

So the question is: what's the earliest tabletop RPG that specifically uses the term "d66" or "d66 table" to describe this type of random lookup roll? i.e., not "d6/d6" or "d6,d6" or any alternative verbiage, but "d66" specifically? It has to have been published in or before 2004, and (probably) not earlier than 1977. No speculation about which games might have used it, please; if you're going to suggest a candidate, be prepared to cite a specific title and page number.

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[berensreverie]

been experiencing Baldur's Gate 3 lately

[swordscomic]

Buy some dice! We have so many. Order Swords: Cut the Deck dice on BackerKit

[halhys]

Cloudkill

[tetedurfarm]

blockbuster's babies are big enough for their first vaccine, and if someone doesn't take these from me i will cry

[cake-crumbs]

Bibliophile :: Available here sold

[jamieylnn]

sometimes you just have to match your dice to the ship you're manifesting 🕯️💙💚🕯️

[zigmenthotep]

OMG, it's live and pulsating! Check it out and back the most important dice-related math zine of 2025!

[prokopetz]

Why do games so often model a d3 with "1d6, divide by 2 and round up" rather than the neater-feeling "1d6 mod 3"? [Not particularly about CAIN, but it's an example]

The modulo operator isn't particularly intuitive for folks without a math background. In practice, nobody's really doing the math at the table every time they roll a d3 – both the divide-and-round-up formula the mod-3 formula serve simply as mnemonics to help remember which faces to read as which values, and 1/2 = 1, 3/4 = 2, 5/6 = 3 is just plain easier for a lot of folks to remember than 1/4 = 1, 2/5 = 2, 3/6 = 3.

[felixisstimming]

troy lougferd (jrwi: wonderlust) stimboard

❄️ with snow and red + orange things

🛷 requested by @t4tlintrollerjrwi

x - x - x // x - ❄️ - x // x - x - x

[sapphicdemi]

Bought my first dice today!

[cutiepieautistic]

Shape stim toys

×/×/× ×/×/×

[pourovergaming]

“Sick Starter Jacket, Bro!”

90’s Dream Jacket

When I was 6, there was one thing I wanted more than anything - an Anaheim Mighty Ducks Starter jacket. I asked for it every birthday and holiday from 6 to 10 before giving up all hope I’d ever don the turquoise and purple.

While I never got my dream pullover, you can take a piece of my childhood and play ttrpgs with it.