What Makes A Star Bill Valuable?

Very quickly: each year, as the bills are printed, some are rejected because of errors in the printing process. Those bills are destroyed, but new bills are printed to replace them. These replacement notes have a seven digit serial number and a star, to indicate to the accountants and auditors that they are replacement notes and that the bureau did not print more bills than it was authorized to print.

Star notes are more valuable only because they are relatively scarce, representing (typically) 1% to 5% of the total run for any year.

Notes are printed for each of the regional federal reserve banks (Chicago, Atlanta, etc.) Those banks are identified on the note by a letter (B for New York; K for Dallas, and so on). The numbers of bills printed, and the number of star notes for each reserve bank will differ; so a star note from one may be much more rare than a star note from another.

It's pretty cool. Nothing quite like it in coinage.

a star note is also used for the 100,000,000 note in a series b/c numbering machines cannot print over 8 digits

Revision- hockingzig, I found 3 star notes out of a hundred bills that morning. They are usually harder to find than that. The post above made it sound like that was a common occurence.

Another valuable star note is when you find a succesion of notes with serial numbers next to each other. i.e. last number 1,2,3,4.. I still find it exciting to find star notes and will keep the lower denominations. Definitely don't want to get you and your daughter dissuaded from collecting them.