Currency distribution about the bill size.

A research report:

The distribution of the Dutch currency circulation by denomination is related to the requirements of efficient payment, i.e., payment involving a minimum number of coins or banknotes for any amount.

A trivial rule, minimize redundancy, maximize entropy.

Transaction sizes and transaction rates are coherent between the currency channel and the goods channel. This seems trivial but it implies that the price standard is not as strong as we think. Consumers and retailers will snap to about the $20 bill, and by ignoring the price deviation to within a standard uncertainty, the retail chain gains efficiency. Dollar Tree for example.

Look, if currency bill size and purchase value have this relationship, then there is a definition of the median retail purchase, and a definition of money.