[fanagra32]

> If we were talking about 1 restaurant, or even 100, that would mean that 1 in 4,096 orders (or 1 every 40 days) are getting swapped due to this efficiency.

Not really.

For swapping to occur, two orders have to be sitting there at the same time with the same last 3 digits and the wrong one has to be picked. So thats one in 2x4096. Every time there is only one order sitting there, the propability drops to 0%. And once there are more orders sitting there, it increases beyond one in 2x4096.

Where the total ends up is heavily dependent on how often multiple orders are sitting there, waiting. It's hard to quantify, but qualitatively we can certainly conclude that the more busy a place and time is, the more likely this is to occur.