Break out the Gekkeikan, it's Kagami Biraki! Over 300 years ago, the fourth Tokugawa Shogun, Tokugawa Ietsuna, first held this ceremony with his daimyo, breaking open a cask of sake before going into battle. The outcome of the battle was successful, and the opening of a cask of sake is now a wish of good fortune for the celebration or event being held. In modern Japan, the celebration falls on 11 January (11 being an oddnumber and attributed to luck), though the tradition of Kagami Biraki can be seen at weddings, business launches, and other important events. It is now highly tied to New Year celebrations in the Gregorian calendar where households will set out round mochi balls (gelatinous rice cakes) during the holidays to take and eat them on the eleventh (Kagami Mochi).
The breaking of the mochi is symbolic of breaking the cask of sake. Many martial arts dojos use the tradition of Kagami Biraki and Kagami Mochi to signify the first practice of the new year. Kigami Mochi can be simply the rice cakes found above or they can be seen with more elaborate, decorative elements.
If mochi isn't available in your area, your liquor store is sure to have a bottle of sake somewhere. Just ask, sit back, and pray that the gods bless you with luck this year (and to wake up without a hangover).