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The sum of two dice rolls will not have uniform distribution. Never realized...

Is there an easy way to cheat?

Will this work? 1st die roll, 1-6... 2nd die roll, if 1-3, add 0 to first die, if 4-6, add 6 to first die.

Is this sum uniformly distributed?

ps... inspired by "How to generate a random number between 1 and 10 with a six-sided die?"

Shing Lau
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    Yes, this is uniformly distributed between 1 and 12. You can do even better: use the first dice roll plus 6 times (the second dice roll minus 1), which is uniformly distributed between 1 and 36. –  Jun 08 '15 at 19:37
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    What Rahul is doing is using one die to choose the "ones" place and the other die to choose the "sixes" place. This uniformly chooses a two digit number represented in base six. Then we convert it to base ten for our convenience. – Ian Jun 08 '15 at 19:57
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    Another way to put it is, relabel the second die so three faces have six dots each, and the other three faces have none. The first die corresponds to the polynomial $x+x^2+\dotsb+x^6$, the second to $3+3x^6$, and the product of these two polynomials is $3(x+x^2+\dotsb+x^{12})$. – Gerry Myerson Oct 01 '23 at 06:24
  • @GerryMyerson That’s a cool way to put it. Can you recommend any resources that develop that kind of approach? – Josh Keneda Feb 02 '24 at 01:30
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    @Josh, I don't know any resource specifically devoted to analyzing dice this way, but more generally the topics to look for are generating functions and polynomial factorizations. – Gerry Myerson Feb 02 '24 at 01:48
  • @GerryMyerson Thank you! – Josh Keneda Feb 02 '24 at 02:43

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Yes, this will give you a uniform distribution on the numbers from 1 to 12.

Zardo
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