In Chapter 4, Jem and Scout argue about Jem's retrieving their tire from the Radley yard. Jem gets the tire, pretending not to be afraid, and shortly thereafter announces that they will now play another game, "Something new, something different." He calls the new game "Boo Radley." Scout thinks he made up the game to prove that "he wasn't afraid of Radleys in any shape or form."
In Jem's game, the children staged a little play born of the gossip they had heard about Boo and his family and their own vivid imaginations. Scout was Mrs. Radley, Dill was Old Mr. Radley, and Jem played the role of Boo. As the summer wore on, they "polished and perfected it." Looking back, Scout the narrator recalls it was "a melancholy little drama."
Atticus interrupts them playing their game one day, wanting to know if it had anything to do with the Radley family. Jem denies it, knowing his father would disapprove. After Atticus goes into the house, some discussion ensues among the children about continuing to play. Jem thinks they might, since Atticus might not know what they actually were doing and had not forbidden their playing. Scout disagrees, vehemently. She wanted to quit the game anyway, based on what she had heard when she had rolled into the Radley's yard inside the tire.
They play the Boo Radley game in where they pretend to be Boo Radley and try to guess what happened to him. Within this game Scout, Jem, and Dill go through different scenarios and when Atticus catches them he informs them of how terrible the game is and how he never wants anyone to play the game again and warns them.
the kids name the game the "Boo Radley" game.