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The remainder of a smoked joint that is much larger than the average "roach" and has been disposed of, on the ground, by a smoker who has had reason to dispose of it. A "papa roach" is minimum one-third of a full joint. Papa roaches are often found at the initiation site of a police chase as the person smoking the joint may likely attempt to dispose of the "evidence" by throwing the partially smoked joint out the window of a car.
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