Dice roll odds for table top games

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The way I've worked it out so far is that if I roll 2d6, there's a 1/6 chance of rolling a pair since whatever number the first die rolls, the other has a 1/6 chance to match it.

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I'm trying to determine what the theoretical odds are of rolling a set number of six-sided dice (#d6) and getting at least one matching pair of dice among them. Hi! I know the title makes me sound like a middle schooler asking for homework answers, but I'm actually a tabletop game designer!

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