Why do the children make Boo's story into a game in Chapter 4 of Harper Lee's To Kill a Mockingbird? Who plays the part of Boo? Why? Is the game...

In Harper Lee's To Kill a Mockingbird, the children invent their Boo Radley game due to their strong curious drive to know the truth about their neighbor.

Their curiosity became piqued the summer prior to their invention of the new game, the summer they first met Dill. Dill is a very intelligent, creative child with an active imagination. Since Dill has such an active imagination, once Scout and Jem begin informing Dill about the mysteries and rumors surrounding their neighbor Arthur Radley, whom the children call Boo Radley, the more Dill hears, the more curious he grows about Arthur. Scout describes that Dill would stand, hugging the light-pole on the same corner of the street the Radley Place resides, "staring and wondering" (Ch. 1). Prior to meeting Dill, Scout and Jem had been content just staying as far away from their mysterious neighbor's house as possible; however, the more curious Dill grew about Arthur, the more curious Scout and Jem grew as well. It is during this first summer that Dill comes up with the idea to "try to make [Arthur] come out," an idea that fueled Jem's invention of the Boo Radley game at the start of the next summer. Hence, Jem invents the Boo Radley game because the children's curiosity has driven them to the point that they want to try and compel Arthur out of his house so that the children can confirm the rumors and myths they have learned.

All the children know about Arthur comes from Miss Stephanie Crawford, a very unreliable source of information since she is known as the "neighborhood scold" and gossip. Since their information comes from Miss Crawford, we can be certain that events the children are acting out in their game are not accurate representations of what happened in the Radleys' home. As the children act out the events, Scout is assigned to play Mrs. Radley; Dill is to play "old Mr. Radley, Arthur's tyrannical father; and Jem chooses to play Arthur (Boo) Radley. One can assume that since Jem invented the game and is essentially the group's leader, he chose to take the funnest, most active role for himself. Plus, Dill is best at playing the villain's part and is, therefore, assigned the role of the tyrannical old Mr. Radley.