I did a little figuring and by all rights, the 2 dollar bill should be the most prevalent in circulation. To give out change from 1 to 19 dollars using the least number of bills, a $1 bill would be used 18.2% of the time, a $5 or $10 bill would be used 22.7% of the time, and a $2 bill would be used 36.4% of the time. Here's a chart:
Change Bills
1 1
2 2
3 1,2
4 2,2
5 5
6 1,5
7 2,5
8 1,2,5
9 2,2,5
10 10
11 1,10
12 2,10
13 1,2,10
14 2,2,10
15 5,10
16 1,5,10
17 2,5,10
18 1,2,5,10
19 2,2,5,10
Can we use this information somehow to convince people to use $2 bills? I don't like how the $2 bill has gotten short shrift in recent decades. Why did usage die out in the first place?