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I think I finally wrapped my mind around how Dee's Double-Drop works! Am I missing anything?
(files.catbox.moe)
...and then Dennis comes along and takes the $4 from Dee's purse and puts it in the cash register anyway.
My previous explanation that is probably incorrect: https://litter.catbox.moe/iblc2r.jpg
That makes more sense! I agree that my explanation is a viable scam, but not the one depicted in the episode. I updated the OP. Thanks!