Djinn power allows djinn to grant three wishes per individual. Also there is a fourth wish in the event the individual does not like the outcome of the wishes and can unwish the previous three. Also, it has been proven that djinn can offer three wishes to anybody; instead of having to be released from a confinement every time to bestow the wishes' to individuals. If djinn are released from a bottle by a member of their family, then no wishes would be exchanged.
Djinn can also give another djinn or human an emergency wish called a discrimen that allows them to avoid any kind of danger, usually the emergency wish is a very long word and the person can only remember and say it right in the event an emergency occurs, however two discrimen's would cancel each other out when activated. In the second book, it is shown that a creature called an optabellower or wish monster was spawned from the first Blue Djinn's mind from which it was created from the angry and thrown away wishes of mundane and djinn.