Obviously, if you have just three dice left to roll, and what to know what the probability is of rolling a 3-of-a-kind is, the answer is going to be different than if you had 4, 5, or 6 dice. Probably the easiest way to determine this (for me) is to write a quick and dirty program to loop through all possible ways to roll six dice, and then ...

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3d6 would mean "roll three six-sided dice." Commonly, these dice are added together, but some systems could direct the player use them in some other way, such Rolling three or more dice gives a probability distribution that is approximately Gaussian, in accordance with the central limit theorem.