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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
This might work as a scam, but I'm not sure it's the scheme referred to in the show. Dennis' lines about how they "always just took the difference from [Dee's] purse" also implies she's stealing from the bar.
I think the scheme might work more like this:
Two tables have a similar order
Dee gives one table their bill and they pay in cash
She pockets the cash (and the tip)
She delivers the same check to the second table
The second table pays and she puts that amount in the till (and keeps the tip)
This scheme would not work if the till has inventory tracking, but given the gang's poor understanding of technology and finances, such as Mac's "Irish honor system" being considered, and every character drinking beer from the bar's inventory without paying for it it, they clearly have no inventory tracking system
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!