Abstract
The concept of jointness for guessing principles, specifically lozenge(kappa) and various Laver diamonds, is introduced. A family of guessing sequences is joint if the elements of any given sequence of targets may be simultaneously guessed by the members of the family.
While equivalent in the case of lozenge(kappa), joint Laver diamonds are nontrivial new objects. We give equiconsistency results for most of the large cardinals under consideration and prove sharp separations between joint Laver diamonds of different lengths in the case of theta-supercompact cardinals.