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Balanced Die / Dice (updated)

by RarelyEvil, published

Balanced Die / Dice (updated) by RarelyEvil Sep 8, 2013
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Summary

This die has the same amount of material missing from each side. It makes this die more balanced than regular dice. In theory. ;-)

Update: some users tested the first version of the die for fairness. Turns out: it wasn't very fair at all. This could be caused by the rounded edges amplifing any imbalance. So, the new die, version 2, has sharper edges.
I've tested the new version and it seems to perform much better. Also, the rotated print gave better results than the regular one did. See the comments for more information on how others and I have been testing the dice.

Created with Tinkercad.

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So I printed one with supports. It came out pretty cool, but not so smooth. It might not be perfectly balance, my husband thinks it tends to roll 3's. Anyways, I decided to print it again without supports, hoping that it might turn out smoother on all the sides. Unfortunately, the base it creates this way is so small that it came unstuck 3 times and had to be aborted. Is there a way I can have it create a bigger base?

Sweet! I'm going to run the print and give feedback!

Thank you cymon and teejaydub for testing the die. I'm working on a new version to get better results.

I am doing a similar experiment, tho not to the degree you are. I've found similar things, these rounded corner dice are bad. I'm going to start making flat sided dice and see what difference that makes.

I'm also not sold on the boring deeper as a way to remove the same amount of material that this dice does. I'd rather have the dots get progressively bigger or smaller.

Cool! I did another 6,000 rolls of this one, printed upside-down in case filament droop around the pips was causing trouble, and got middling results again - 4.2% chance the die is fair by the chi-squared test.

If the pips got bigger in diameter, that would at least give you a visual indication that the die was balanced! Diamond-shaped pips would also provide more reliable printing - they wouldn't get as squashed at the top.

But I think the fairest 3D-printed dice may always be ones with the pips just inked on, OR printed with a double extruder so they can be filled in with a contrasting color. (But: I also want to try packing [balanced] holes with oogoo or Sugru!)

http://joesmakerbot.blogspot.com/2013/10/testing-3d-printed-dice-fairness-chi.htmlhttp://joesmakerbot.blogspot.c...

My test wasn't as extensive as yours, but this one ended up being one of the least balanced of all the 3D printed dice I tried. Ironically the so called "Worthless" dice was one of the most. And it turns out printing it solid makes it less balanced.

Thanks for testing it you guys. Too bad it didn't fare too well. I've made a new version with sharper edges by combining 8 dice-shapes. I also made a rotated version, which is standing on a corner. I figured that since the die is made in layers, the structure of the sides, top and bottom could all be different, influencing the chances. Starting from a corner should minimise the effect, as all sides are printed at the same 45° angle.

I tested the new versions using the Angular Dice Tower: http://www.thingiverse.com/thing:88518http://www.thingiverse.com/thi...

I rolled both dice 144 times. Which gave me the following Chi-squared values: Normal: 5.17 out of 11.070 (for 0.05) Rotated: 2.50 out of 11.070 (for 0.05)

With this they are well within the limit of 11.070 and give a 40% and 78% chance the dice are fair respectively.

I hope you are willing to test the new versions, to see if you get similar results. (I use an PP3DP Up Mini for printing.)

Angular Dice Tower

I like the 45-degree idea! I'm printing it now and will try it in my machine.

I thought the layers thing would matter, too. And maybe it does if you print lower resolution than I did. I printed 0.15mm, so the layers blend pretty well. What layer height did you print at?

My layer height is 0.20mm, that's the smallest height my printer will do. But I think the big difference is not in the layer height or how well they fuse, but in the way the sides are printed. When printing a die on one of its sides, the sides that are at the bottom and top are printed in just a few layers, while the other sides are made of many stacked layers. That makes them structurally different. Printing with a corner facing down will make print all sides in many layers. I don't know how much influence this will have to fairness, but in my (limited) test the rotated version did outperform the 'flat' version. I'm really interested to see other people's results.

Shoot - for me, the rotated version totally flunked both the chi-squared and Kolmogorov-Smirnov tests at 6,000 rolls. It also didn't print very prettily - the sides were rougher and there were some drooping filament bits - so maybe that's part of it. I'm testing the non-rotated v2 now, for comparison.

I've noticed that, for a lot of my own 3D-printed dice that don't perform well, the most-frequently-occurring face is the face that was on top when the die is printed. This suggests to me that filament droop in various places could be the culprit - lowering the center of gravity. I also don't like the way my Cube printer does top faces, so I'll be trying to subvert that (it's closed software so hard to hack).

I'd be wary of using a chi-squared statistic to compare two dice, especially with low numbers of rolls. The only thing that statistic is designed to do is to disprove the null hypothesis "the die is fair" - that is, it can give a clear result of "the die is unfair" with 95% confidence (1 false positive in 20), but the alternative is not "the die is fair"; it's "the die is fair OR it's unfair but we got lucky OR it's unfair but not by enough to distinguish from random variation with this number of rolls."

Assuming its printed with 100% infill, does it favor any numbers when rolled, or does it actually get an acceptable spread of randomness?

If this could be printed perfectly, it shouldn't favour any number by a statistically significant amount. It's balanced by removing the same amount of material from each side: the 'one-hole' is 3mm deep, the 'two-holes' are 1.5mm deep, 'three-holes' are 1.0mm deep, four-holes are 0.75mm, five-holes are 0.6mm and six-holes are 0.5mm. All 3mm in total. There may still be a very small spread because the holes are not in exactly the same location on each side. Though, the error margin of the average 3D printer will be a much larger factor in changing chances than the location of the holes.

worked well until it got to top layer which ended up being very messy

I found printing it on its side (45 degrees turned, so an edge faces down) gets a slightly better print result for my Up Mini.

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