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I don't particularly like D4 dice since they can't roll well, so I was thinking about using a D12 since mathematically, if you do modulo 4 + 1 you should still have an even distribution among the numbers.

I was then looking if anyone had made a 12-sided dice with only numbers 1-4 but did not find anything. Is this mathematically incorrect or is there just no demand?

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Mathematically, this idea is quite sound. Twelve-sided dice marked 1-4 exist, although they are not exactly commonplace. They were created as part of a Kickstarter project, which was mostly about twelve-sided dice marked 1-6. You can buy them here, as "Triplefours."

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There is little demand for these kinds of dice from my knowledge. Another way you could do roll dice to save money and to get the same results is to just roll a d8 and do 1-2=1, 3-4=2, 5-6=3, and 7-8=4.

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Little demand, probably.

The only die I’ve seen printed like this is a cubic d3 (1,2,3,1,2,3), once, and I’ve been gaming since ad&d 2e.

Mathematically you should be fine using a d12, or anything whose number of sides is a multiple of the die you want to use. d10 for d5, d12 (or d8 or d20) for d4, etc.

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