Starship Asterisk*

The Maine Farmers' Almanac originally defined blue moon as an extra full moon that occurred in a season; one season was normally three full moons. If a season had four full moons, then the third full moon was named a blue moon. The popular definition of a blue moon as the second full moon in a month stems from a error in interpretation made by Sky and Telescope in 1946. According to the Maine Farmers' Almanac definition, the next blue moon is 2010 Nov 21, not New Year's Eve.

"What's a Blue Moon?", Sky and Telescope, May 1999

The trendy definition of "Blue Moon" as the second full Moon in a month is a mistake.

"BLUE MOON ECLIPSE", SpaceWeather.com, December 31, 2009

Blue Moons are rare (once every ~2.5 years). Blue Moons on New Year's Eve are rarer still (once every ~19 years). How rare is a lunar eclipse of a Blue Moon on New Year's Eve?

A search of NASA's Five Millennium Catalogue of Lunar Eclipses provides an approximate answer. In the next 1000 years, Blue Moons on New Year's Eve will be eclipsed only 11 times (once every ~91 years). So this is a rare event, indeed.

Happy New Year