Why roll 2D6 when you can get the same result with a properly numbered D36? Okay, don't answer me. This is not a practical solution, but it is an educational one, if you're studying probability. Rolling 2D6 gives 36 distinct outcomes, even though the possible results (if you're adding the dice) run just from 2 to 12. If you instead subtract one die from the other, or the high from the low or vice versa, you get a different range of results, with the same probability curve, and of course the same number of distinct results on the dice making it up. These different D36s demonstrate those different results, and let you view them physically.

I made the first versions of this, with just 2D6 represented two ways, a couple of years ago. But the recent Stand-up Maths video on D6 with advantage vs √(D6) made me think it was worth posting them on the Educational contest. 

Provided are 

• 2D6 with the results shown as numbers (that is D6+D6)
• 2D6 with the results shown using hex code (D6+D6, but 10=A, 11=B, 12=C) for the Traveller RPG players out there.
• D6 roll twice pick the higher. D&D calls this “D6 with advantage”.
• D6 roll twice pick the lower. (“D6 with disadvantage”)
• D6-D6 where the positive die is determined in advance, yielding results from -5 to +5 (Traveller calls this “flux”)
• D6-D6 where you subtract the low die from the high die, results from 0 to 5, with low numbers more likely ("good flux")
• D6-D6 where you subtract the high die from the low die, results from -5 to 0, with high numbers (closer to zero) more likely ("bad flux")
• for completeness, a straight D36, numbered 1 to 36.
• edit: added blank version for remixing

Note - I don't expect these dice are really equal-probability for each side. The construction process in Fusion was painful, and didn't let me adjust them to optimize for full fairness.

Update 11 January 2025: By request from @Phelix_2804152 I am uploading a blank version of my D36 model for them and anyone else to modify with their own numbering. 

Backstory:

I am a longtime fan of the Traveller role-playing game, going back to the little black books in the late 1970s. Traveller eschewed the set of polyhedral dice D&D had made so popular, and used only D6s. For the character stats and a LOT of other rolls, the roll is 2D6. I loved the probability curves for the D&D 3D6 stats, and the 2D6 curve is a lot less pretty, but it is also a lot more commonly encountered, in gambling and all kinds of boardgames. It is ubiquitous, but a lot of people only understand it somewhat vaguely. Knowing it was built from 36 equally likely possibilities, I had always wanted to see a 36-sided die numbered 2-12 with correct 2D6 probabilities. But even with the proliferation of inventive dice in the world these days, I had not seen one available commercially.

So I set out to figure out how to make a regular-enough-to-be-rollable D36, and how to model it with my rudimentary Fusion 360 skills, and designed this. I only made the 2D6 with numbers and 2D6 with hex at first, but Matt Parker's video (linked above) made me expand that to include Advantage and Disadvantage. And then I had to include Traveller T5's “flux” dice combinations as well. 

PRINTING NOTE: The STLs provided are very big, as a result of the process I went through to make them. When I actually print dice for rolling, I print them at 50% scale, adjusted in the slicer. The full-size dice might be useful for demonstrations and classes where you're discussing probablility.