There are many different (and perhaps more practical) criteria than average coins per transaction. For instance, I don't like a lot of coins in my pocket at onc

There are many different (and perhaps more practical) criteria than average coins per transaction. For instance, I don't like a lot of coins in my pocket at once. And, I always want to get rid of coins when I use them! So, what are the least number of coins I can carry to guarantee that I come back with at most the number of coins I started with (after change is given)? On the other hand, sometimes I only carry coins to get rid of them! With the current system, I need to carry nine coins to guarantee exact change -- what system maximally reduces this?