## Introduction: 3D Printed Spinning Percentile Dice

I've been designing and printing various odd parts on 3D printers ever since I convinced my wife to let us buy a 3D printer in 2012 after seeing them demoed at Maker Faire. My son grew up seeing printers in action and all the things you can make them. So I shouldn't be surprised when he casually suggested I could make a two part spinning dice based on a dreidel.

Below is the story of how this crazy contraption came to be.

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## Step 1: Taking a Design Further, Way Further...

A while back I designed a spinning die with five possible rolls (0-4) for an ancient board game (the Royal Game of Ur) I was making. It was inspired by a dreidel and designed to be easily 3D printed. I showed my son the die since he is really into D&D and thought he would appreciate it, which of course he did!

With both of us being makers as well as engineers (well, he’s still in school studying engineering…) we couldn’t leave it well enough alone and began to contemplate how to take the design further. Of course, he wanted me to make a complete set of D&D spinning dice which at this point didn’t seem that difficult and he agreed. Though, after making one (a D10) we decided they wouldn't be practical since they would spin so long you'd get impatient waiting for them to stop. The idea was too cool though, so we continued to brainstorm.

After discussing various types of dice we could make this way, my son threw down the challenge gauntlet and suggested a 2-part percentile version. A what? My son explained that percentile dice in D&D and other dice games are used for certain actions described in percentages such as if your character has an ability that has say, a 65% chance of succeeding, you need to roll a 65 or lower to be successful (a very simplified explanation). Usually this is done rolling two D10 dice. One for the 10s and one for the digits. “Wouldn’t it be cool if you could use one dice instead of two for this?!” he says… I, not really understanding what he was talking about said, “Oh yeah, of course!”. But how would you do this? Apparently there is such a thing as a dice within a dice, I was informed. The inner dice freely moves inside a larger hollow faceted dice. That’s it! I already made a spinning faceted top like dice, just add another spinning faceted top like dice inside it.

## Step 2: How It Was Designed

So, the problem seemed straightforward to solve - dice within a dice, easy peasy. I began laying out the 10 sided spinning die in Fusion360 the same way I created the other spinning die. Start with a 10-sided polygon, extrude it vertically. I gave the polygon a 1 inch radius and extruded it the same amount. Next, chamfer the top edges all at once with a 45 deg chamfer. There’s your basic shape, a flat faced diamond. On the 5-side die I added a post in the middle and numbers on the flat side lining up with the facets. When the spinning dice slowed down it would come to a stop on a faceted side. For the percentile die, I needed to hollow out the main die and insert another smaller die inside it. To do this, I used the shell command on the main shape. I left about a .375” thickness to allow enough space on the flat to number the larger die. I added a stem to the main die ending flush with the face. The inner die has a hole a bit larger than the stem so it can spin freely about it. The hole has the added benefit of shortening the inner die so it has plenty of vertical space to spin about. It is faceted too, so it will bounce and land on an inner facet of the main die.

I didn’t want to have a convoluted support system to remove when I printed this, so I had to make it a multi-part print and assemble the final die. To do this I added an over-fitting top stem that slipped over the stem on the main die and glued in place. The inner die spins about the base stem and the top stem keeps it from falling out.

## Step 3: This Is Where It Got Real or "Don't Pull That Thread!"

**Editors Note: If you don't care about the physics and mathematics of randomness in dice please proceed to the next step for the 3D files and have fun printing and playing with this cool dice.

After I made the D10 spinning die we were playing with it and reveling in out success when we realized we were getting an unusual amount of the same number. Something wasn't adding up so I decided to do a “little study”. I’d spin the double die fifty times marking down the results of each roll to see if our fears were true. Unfortunately they were. A very large percentage of the rolls landed on either 30 or 40 on the main die. What was happening? I designed the die in CAD, it was perfectly symmetrical. I then checked the 10-sided spin die I made. It too seemed off, favoring the 1 or 10.

Ok, seeing a pattern here. Both dice favored two numbers right next to each other. Obviously they were weighted on the opposite side, but how. Both dice were printed on their side. I had designed them with 45 deg sides so they would all print easily in one piece and you'd get nice legible numbers. Each had 3 perimeter wall thickness and both had 10% hex infill. That’s it! The infill printed vertically, but the dice were positioned at a 45 deg angle. When you stand the dice up straight, the infill is now at an angle. The infill was throwing the weight off!

I modified the dice and printed them flat on their faces resulting in the model printing perfectly vertical. The double percentile die, with it’s 100 possible rolls, was taking too many spins to get a pattern of the randomness, so I focused on the plain 10-sided spinning die. It still has 10 possible rolls, but figured fifty spins should show the range of randomness possible. Well, not so much. The flat printed version still seemed to favor one side. I upped the spins to 100 and the pattern was more obvious. It definitely favored one side. (See the radar charts above which conveniently show how the the dice seem "weighted" to favor certain sides.)

I tried many different options from varying the infill amount to printing with numbers and without. There didn’t seem to be the level of randomness needed for the spin dice to be considered fair. So I tried a standard D10 polyhedral die from my son's D&D set. After 100 throws even it didn’t seem perfectly random - closer, but not perfect. Now I was really at a loss.

I took a step back and did some research on fair dice. If you want to jump down a very large rabbit hole start with a great video on YouTube by Numberphile called "Fair Dice (Part 1) - Numberphile". In it they give a good definition of “fair” and go into a lot of interesting aspects of dice including platonic solids, symmetry and the physics of rolling dice. Pretty heady stuff, but it got me thinking. How would a D6 cubic platonic solid die perform in my impromptu study. After 100 throws I was amazed at it’s near randomness. Maybe there is something to this platonic solid thing.

I was nowhere near an answer except that in figuring out the fairness of my dice you can only go so far. True randomness doesn’t occur except at infinity, and even then, it’s random. By making my spinning die as symmetrical and accurate as possible in its construction and limiting it’s roll (or spin in this case) to one plane (vertical as it spins), the die has as much of a chance of landing on one face as it does another and therefore is more or less fair.

## Step 4: In Summary...

To print your own spinning percentile die, download the attached files. Be sure and print with the face of die flat on the build plate. You will need to glue the top stem into place - a bit of superglue or epoxy should work. Depending on how your 3D printer's first layer is calibrated you may need to trim any flare in the hole for the stem and the top stem as well for it to fit. To assemble the percentile die, slip the smaller inner die over the stem on the main die, then glue the top stem into place . I've included versions with numbers and without in case you want to paint your own numbers on the dice.

For printer settings, I used 3 perimeters for wall thickness and 10% infill. Also, I scaled the original file down by 30% when I printed it. That seemed like a more reasonable size to play with....scale at your own preference.

So, put as much into this as you like. I think this dice design is unique and fun. It will never meet the standards of Vegas, but should provide an interesting addition to your next dice game adventure.

Participated in the

3D Printed Contest

## 32 Discussions

4 weeks ago

Love the idea and the work gone into making it work. But I noticed you made a 5 sided simple version for the Royal game of UR.The correct odds for the Royal Game of UR are not equal.

0 and 4 are 1 in 16.

1 and 3 are 1 in 4.

2 is 3 in 8.

Therefore

using a modified one of these percentile dice with 8 sides, 2x0s, 2x2s

and 4x1s on each ring would give the correct odds. I specified 8 sides

instead of 4 or 16, as 4 sides would probably restrict the inner ring too

much as well as bounce a lot when it fell over, and 16 would roll too

much.

Also by having 2 of each result (4 of the 1's) the resultant dice should be 'fairer'.

Reply 4 weeks ago

Interesting concept. How did you come up with the number odds? Not doubting them, just curious. Is it from the originally found 4 - 4 sided dice that a lot of the current remakes use? This is basically 4 bi-numeric (?) dice or for the 4 sided dice with 2 sides marked and 2 not marked. You roll 4 dice and roll is the count of marks up.

Making a multi-sided dice with multiple numbers present representing their odds is interesting. Be fun to make one and roll the odds to see how they play out.

Reply 4 weeks ago

O.K. The tetrahedral dice gives either a 1 or a 0, as there are 4, think of it as a 4 bit binary number from '0' 0000 to '15' 1111, there is only 1 number with no 1's (0), only 1 number with 4 1's (15), 4 numbers with 1 1 (1,2,4,8), 4 numbers with 3 1's (7,11,13,14) and 6 numbers with 2 1's (3,5,6,9,10,12). I got my numbers for two rings by doing the same thing with 2 bits.

This is important for the Royal Game of UR as the odds affect the strategy, which is why it was the top strategic game for approximately 3000 years.

Reply 4 weeks ago

Ok, now I get it. I did have to have my son simplify it a bit! ( he just took a probability and statistics class...) and you're right, the odds aren't truly random in Ur, that's what makes it challenging.

So with that as a baseline, I see two ways of making a spinning dice that is "equal" in odds to the 4 binary dice normally used. #1 is to make a 16 sided single top (no need to make a double like the percentile) and put 1- 0, 4-1s, 6-2s, 4-3s and 1-4 on it like you suggested. I don't think it would matter on placement around the circle if we assume the 16 sided spin dice is equally random for each facet.

#2 would be to make a weighted 5 sided dice that gives you the same odds. I did a rough calculation and since 2 is the highest odds at 6 out of 16 chance that would be baseline at 100% weight of a side, then 0 & 4 would have 1 in 16 chance so by running the proportions those sides would need to be 16.66% of weight of the 2 side. One would have 1 in 4 chance to would be 66.6% the weight of side 2. I thought it would be easier to calculate it by volume, to take the volume of the #2 side at 100 and reduce the others by their percentages keeping the dice with equal shaped sides and facets, just take out the volume required instead of making different shaped side/facets which wouldn't make it as fair landing on the smaller sides I would think. This would be a much more difficult way of designing it but would be interested in seeing if I could pull it off!

So, challenge accepted! I'll start playing with both options and see if I can successfully print them. Then I'll spin them and see what kind of odds I can get from them. Cool! Another project to work on....

Reply 4 weeks ago

Have fun. The problem I see with a weighted spinner is stability, if the spin axis is not through the center of gravity, it will probably dance around the table a lot.

Reply 22 days ago

So I've been working on the challenge and have it mostly done. Interesting results, so I'm writing another Instructable to document it properly. Hopefully have it up in a day or so. Thanks for the motivation!

On the weighted spinner, I was able to distribute the weights around so it actually spun pretty nicely....results, not so much.

Reply 16 days ago

So finally finished and got it posted (https://www.instructables.com/id/3D-Printed-Dice-for-the-Royal-Game-of-Ur/ ) Results were pretty predictable. Thank you for the discussion and motivation to further explore these dice. It's been great seeing where it goes.

22 days ago

Very interesting, nice work!!

My only criticism is with the distribution of the numbers. Normally on dice, the sum of the opposite sides is tried to be twice the average. On a D6 die you have an average of 3.5, so the sides add up to 7, 1 + 6, 2 + 5 and 3 + 4. And the same on a D10 die, 5.5 on average, 11 is double, so 1 + 10, 2 + 9, 3 + 8, 4 + 7 and 5 + 6.

I think this distribution, 1234509876, would increase randomness. Of course the numbers could be moved, but keeping their opposite partner. 1637205849 for example.

Reply 22 days ago

Holy cow, why didn't I think of that.... That's a really good point, and I think it would improve the randomness. I did include a version without numbers, so you could always just print your own numbers. Great observation, thanks!

22 days ago

Nice one! Printing with 100% infill to see if the solid construction minimises the bias created by misaligned in fill etc...

4 weeks ago

This is really cool! I loved step 3, and I'm so glad you included it. It's just the right amount of info to satisfy my curiosity without compelling me to start down the rabbit hole myself.

A couple questions:

1. Does the internal die ever get "stuck" to the external one, or is there enough clearance to always make it spin freely once the main body stops spinning?

2. Since there seems to be a wee bit of difference with and without numbers on the dice (and to over-complicate things, 'cause that's what I do), what would happen if you printed the numbers as a separate part (kinda like a 10-sided washer), and then also cut the number from the opposite side of the of the die out of the underside of the ring? Stand by... I need to doodle... OK, I've whipped something up to try to explain - please see attached picture. TL is looking at the top of the ring, TR is same with hidden lines to try to show alignment of "bottom side" numbers, BL is the bottom and BR is same with hidden lines. You'd want some kind of alignment feature so attaching it to the body would be easy, but I didn't want to go overboard. (Did I just hear someone say, "too late!"?)

Reply 4 weeks ago

So glad you like the nerdy Step 3! It was very edited down from I originally had. I almost didn't put it at all, but I think that section is such a big part of the project. Not everything goes the way you plan. I'm a firm believer of owning your mistakes and issues. It's the only way we grow.

For your 1st question, best way to answer is to watch the video with sound on. The inner die does nest down and lock into place. It's the same faceted bottom as the inner facets on the main die. When it's spinning its immobile, but once the spin breaks and the main die starts bouncing about (on those facets) it throws up the inner die and it's momentum continues it's spin until the facets stop it's motion too. I kept widening the hole of the inner die until I felt it was large enough to allow for free bouncing!

On 2, that's exactly how I was going to redo the dice! Once I realized it needed to print face down, I wanted to print the face and stem separately, mostly to get a better print of the numbers. That's why I designed the original dice with a 45 deg bevel to it would print on it's side and get the best surface for the facets and the numbers. I couldn't figure out an easily printed way of matching the top and bottom so just left it as is. You could draw out and print a "face plate" in paper with nice numbers and design then glue it on..?

If you always print the main and inner dice up to where the numbers print, then switch filament colors for the rest or just a few layers in a contrasting color for the numbers to show better. I've done this before (on nicer printers...) and it really makes a design pop.

thanks, for the comments, really appreciate the dialog! patrick

Reply 22 days ago

You could print the numbers in the contrast colour on the bed, 1-3 layers, then overlay the dice print using a z-hop of 1mm to clear the existing numbers print to enable the 'insert' of the colour and also address any extra bias from the different weighting of the numbers.

Question 4 weeks ago

Great instructable. Is there a recommended 3d printer that you favor or a few important things to look for when buying one. Looking to start after a long time interest in this area. Thanks!

Answer 4 weeks ago

That's for the comment. If I was in the market for a 3D printer now (which I kind of am...just gotta get the wife to be as well!) I would get the Prusa Mk3. I think it's the best printer on the market right now, period. That being said, you really can't go wrong with the Creality printers. I haven't used one, but for less than $400 and with everything I've seen and read these are the best printers to start with. Simple machines, cheap, awesome fidelity, and open software/slicers. If you don't like it or use it as much as you thought, you're not out that much money. Yeah, the parts are cheap, and things might not last as long as more expensive units, but its a very inexpensive way to see if you like the hobby. The Prusa is $1200 (which is still just over half what I paid for my Makerbot Rep 1 in 2012) so it's still "cheap" compared to the high end printers like Ultimaker and Makerbot, but you really aren't getting much if any benefits or better results by spending twice enough for these two.

Sorry, don't get me started.... This is just my opinion, your mileage may vary. Good luck!

Reply 4 weeks ago

Great response that was just the suggestions I was looking for. Gonna start my research and hope theres some left of my stimulus check!!!

Thanks!

Reply 22 days ago

The Ender 3 Pro is a great starting point, lots of help with tuning it in and the few upgrades needed to improve printing aren't hugely expensive either. Most 'upgrades' are printed on the machine itself. The Ender 3 V2, if you can wait a bit, would be my 'newbie' starting point today, much of the Ender 3 Pro and upgrades plus a few more things.

The New CR-6 SE has many of the 'upgrades' and more out of the box, probably the printer to start with, though this is very new. Check out the reviews by Naomi Wu and 3D Printing Nerd on YouTube for a better look. https://www.creality.com/art/cr-6-se-crealitys-fir... this has the details and Naomi's review.

Looking at the duel extruder options, it is cheaper to replace the main board and extruder on the Ender 3 Pro than it is to pay for the CR-X which is 3 times the price, but you need to be reasonably confident you have the skills to do the conversion.

Have fun!

22 days ago on Step 2

Very cool. I love tops and dice. Great job.

4 weeks ago

This is a really cool concept, for me this would not be practical as it's spinning takes to long, and the Guys I RPG with would all start complaining very quickly at how long it takes (this is kind of an interesting contrast to the way it was when we played as kids. To mix it up a bit, how about considering putting this die set mounted firmly on a support and put bearings on the spinners and use it like a roulette table type of Die set, the platform wouldn't have to be large at all, and could still fit in your pocket.....hey I might try making something like this too, except my printer is on the fritz, but I really like this concept! You could make it with a center pin like you have now, only have two gear rings on it and the inside of the Spinners and you could also make it so that the center pin needs to be pulled up for it to engage the gears on the bearings' inner races. after spinning the pin would simply fall down and then they can free wheel at the speed which friction will slow them down the two spinners would slow at different rates because of spinning mass being different and also the quality of the bearings would also be a factor. Just a suggestion, I have a 3D printer myself but I'm having serious problems with it and I'm not optimistic about getting it working. Anyways, great instructable. And a really cool concept for rolling percentile! Keep up the work my friend (ha! As if this is work LOL).

Reply 4 weeks ago

Wow, that roulette like dice sounds fascinating! Pretty complicated, but very cool. As for the spinning problem with mine, that's the main reason we decided not to make a full set of D&D dice. As for the Percentile dice, for the video I shot, I got it spinning really well since I was doing it all myself. I got pretty good at spinning it just enough to turn a few times before it started tumbling. You should just make one and try it yourself!