Suppose we roll \(3\) fair, standard six-sided dice. Any dice that show a \(6\) are removed, after which the remaining dice, (if any), are rolled again. As before, any dice showing a \(6\) are removed, and any remaining dice are rolled again. We repeat this process until all \(3\) dice have been removed.
###### Image Credit: Wikimedia Walter J. Pilsak

The expected number of rolls needed until all \(3\) dice have been removed is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a - b.\)

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