ChicagoImprovAnarchy can't be accused of exercising undue advantage over its audiences in this clever fully improvised murder mystery. Though, as usual, we must guess whodunit, so must the troupe's detective--TV pitchman Billy Mays in the current version of the show (previously it was Columbo). After our suggestions have determined the characters, we vote on the victim, who then chooses his/her killer and tells the cast--except for the sleuth--who it is. We too are kept in the dark, and the murderer's name is sealed in an envelope entrusted to a spectator. Whether or not the investigator correctly deduces the identity of the culprit, the intricacies of the hour-long police procedural are sure to delight fans of the genre. Strawdog Theatre Company, 3829 N. Broadway, 773-419-4606. Through September 26: Fridays, 11 PM. $9. Then at Stage Left Theatre, 3408 N. Sheffield, 773-419-4606. October 17-November 15: Fridays-Saturdays, 11 PM. $9.