The calculus of tipping
Actually, the way it works is, if a 22% tip is automatically added to the bill, there's now a new total, so you ought to add a 22% tip to that. But now there's another new total, so you have to add a 22% tip to that, meaning of course that you will have to add a 22% tip to the new total thus created, which then you will have to add a 22% tip to ... Eventually, you will have asymptotically given the bell hop everything you have.