Mostly, these games are based on pretending to be Indians, trappers, cowboys, and so on. Johnny inevitably plays the main role and Bill usually plays the role that takes the most abuse.
Johnny calls himself Red Chief. The ongoing game he plays with Bill is Cowboys and Indians. When they first kidnap Red Chief, Bill plays the role of Old Hank, the Trapper. Old Hank is Red Chief's captive and he is to be scalped at dawn. Red Chief names Sam "Snake-eye the Spy" and he is also to be killed. Since Bill is his main captive, Red Chief punishes Bill (Old Hank) often.
The next morning, Johnny is still in character as Red Chief and he is threatening to scalp Bill. Red Chief takes this game of pretending much too seriously and too violently. Sam has to wrestle the knife away from Red Chief.
Later, Johnny decides he wants to play Black Scout and this means he will have to use Bill as a horse. Black Scout has to ride Bill to the stockade to rescue the settlers. This is the game that pushes Bill over the edge, so he tries to send Johnny home. However, Johnny returns and Bill reluctantly agrees to play a Russian in a Japanese war (another game of pretend). Surely, this will involve Johnny annoying and/or beating up Bill in some way.
Bill and Sam finally decide to accept Ebenezer's counter-offer to avoid any more trouble from Johnny.