Why Polyhedral Dice On A Deck Of Cards Will Never Work… Or Will They?

A few months back, I was reading a post over on Tenkar’s Tavern ^[1] about one of Tenkar’s most/least favorite topics and I discovered a link to a kickstarter I had missed from back in 2015 (funded, but still unfulfilled from what I gather). It was for “Deck Dice” – a standard deck of playing cards that also act as a full set of polyhedral dice. I had two initial thoughts on this:

• That’s super cool!
• Too bad it will never work

So why did I think this concept would never work? Well, it boils down to the math. In order to properly simulate a polyhedral die, you need to have a randomizer with an even multiple of the number of sides of the die. So to simulate a d4 properly, for example, you need a deck with a number of cards that’s a multiple of 4. In order to do this for an entire set of polyhedral dice, you need to have a number of cards that’s a multiple of the Least Common Multiple of 4, 6, 8, 10, 12, and 20. If you can’t remember how to find that off the top of your head and don’t want to look it up, you have to find the product of the largest group of like factors across all the dice, which ends up being 2x2x2x3x5=120. So the only way to perfectly simulate an entire set of polyhedral dice with a deck of cards is to have 120 cards.

There are some ways around this, but each has its own issues or quirks:

• You can just get sort of close: put the numbers 1-20 on the deck twice, and then include 14 random numbers from 1-20 to fill out the other cards for example, but that’s not going to give you a very good distribution and you have to choose the distribution you’re going to create. Do you favor odds? Evens? High numbers? Low numbers? High and low numbers? Middle numbers? No matter what you choose here, you’re making a problem for someone.
• You can leave some die values off of some cards: 54 isn’t a perfect multiple of 8, for example, but 48 is. So, you could put the numbers 1-8 on the deck 6 times and then have 6 cards with no d8 value. What do you do if you need a d8 and the card you draw doesn’t have a d8 value on it? You keep flipping. Not so bad with that d8. 11% of cards wouldn’t have a d8. But for a d20, 26% of cards will be missing values.
• You can use multiple draws to build results, just like we do with d100s: 54 is divisible by 2 and 3, so all dice except the d10 and d20 can be built perfectly this way. Flip 2 cards, and you’ll always have a perfect d4 or d6 roll. 3 flips will give you a perfect d8 or d12. D10s and 20s still don’t work though. And who wants to flip 2-3 cards for every die roll?
• You can add some extra cards: a few extra cards will create different sets of factors to work with. but few of them work very well until you add 6 extra cards. That brings the deck up to 60 cards, which perfectly models all dice except the d8. But it also means that the deck of cards is now no longer a standard set of cards, which means you’ve lost whatever functionality you were hoping to achieve by having your dice on a standard deck of cards in the first place.
• You could use two decks of cards: This nets you 108 cards instead of 54, which means the 4, 6, and 12 all work perfectly, but personally I would never go this route. Why? Because if you have to go up to two decks to get a good distribution, that means you’re NOT getting a good distribution from a single deck. And it doesn’t matter where or how clearly you point out that you need to use all 108 cards to get the right distribution, someone somewhere is going to miss or ignore that, use only one of the two decks and then complain because the distribution isn’t right.
• You can mix and match parts of several of these methods: You could for example leave some die values off some cards, for 4s, 6s, 8s, 10s, and 12s, and then for 20s you flip till you get a d10 value, then flip again and add 10 if the second flip is red. There are plenty of ways to do this, some better than others.

The kickstarter that Tenkar had referenced combined two methods. First, they added 6 extra cards to a deck and they used two decks. That gave them 120 total cards, allowing them to perfectly simulate all types of polyhedral dice. Which is excellent. But it made the decks completely useless as an actual deck of cards, so what was the whole point of the product? And then you still have the “using only one of two decks” issue, although in this case, as long as each individual deck of 60 has a complete distribution of 4s, 6s, 10s, 12s, and 20s, at least only the d8 suffers for it, and not that badly.

^[2]

Click for larger image

But, after kicking it about a little, I think I have a better solution: make all the cards symmetrical, so it’s impossible to tell when it’s right side up and then put different rolls on the left and right side of the card, thus which side of the card is up when you draw it will give you different results. 108 cards means that only 4 or 8 blanks need to be left in for any given die, and since each card has two rolls on it, that’s 2 or 4 cards. Here’s what a sample card might look like:

So what’s all that extra junk at the top and bottom? Well, I had some leftover space, So I added a bunch of other fun stuff. There’s a generic fantasy class (Healer, Rogue,Warrior, Wizard) , a generic fantasy race attribute (Adaptable, Clever, Magical, Nimble, Savage, Sturdy), a general level (High, Mid, and Low), a reaction (30% Friendly, 40% Neutral, and 30% Hostile), a gender (M,F, ~2%Non-binary), a little rainbow symbol(~15%), and a random dungeon room.

So, there you have it. There’s my attempt at how I would make a set of Polyhedral dice cards, and as a bonus, it only took me about a month and a half – and everyone can download a free printable PDF below! On the other hand, the art is absolute crap, there are no faces on the face cards, and there’s no back, so you get what you pay for.

Of course, I could always scrounge up a few hundred bucks for some pro layout assistance and art, fund it with my own kickstarter and put it up in a print on demand venue. Anyone have opinions and feedback while I mull that one over? Don’t be shy.

^[3]

Click on this image to download the PDF Prototype

P.S. If you find the concept of dice on a deck of cards interesting, here are a couple other ones that are available. If you know of any others, put a link in the comments.

• Deck 100, which isn’t a standard deck, but which does have cool dragons and some other neat features ^[4]
• Dicecards, which is a standard deck, and which has a ton of cool randomizers on each card ^[5]