The bet evolves from McMurphy's apprehension that Nurse Ratched oppresses the men in the ward with her insulting questions and intimidation.  For instance, in Chapter 4 Nurse Ratched asks the men to "Let out those old secrets"; however, when they refuse to talk, she turns to their records and asks them, "Must we go over past history?"  She then gets the men to shout over each other with their terrible secrets, and she nods at each confession.  Further in the meeting she leads the other men to tear into Harding's sexual problems, leaving him humiliated.

Afterwards, McMurphy talks to the men, asking why they let the Nurse brow-beat them so.

"Look at you here:  you say the Chief is scared of his own shadow, but I never saw a scareder-looking bunch in my life than you guys."

The men tell McMurphy that Nurse Ratched usually beats them because she gets their "goats" by making them "crack in some way"  such as in cursing her or breaking a window. Unfortunately, after having committed such an action, the men are sent to the Disturbed Ward or Electroshock Therapy. But, if they maintain control, the Nurse can do nothing.  Hearing this, McMurphy challenges the others:  he bets them five dollars a man that he can disturb her and "get the best of that woman" without her doing the same to him.  Telling the men he has yet to see a woman who thinks she is more man than he, he expresses his confidence in winning the bet.

Then, in Chapter 5 as the men play cards with McMurphy, he becomes annoyed at the radio that plays incessantly. He threatens to tell the orderly to turn it off, but he is cautioned by Harding,

"Friend, that is exactly the kind of statement that gets one branded assaultive. Are you so eager to forfeit the bet?"

He further teases McMurphy about losing his stoicism with which he tries to defeat Nurse Ratched. So, McMurphy reflects upon this, takes up his cards and recommences his blackjack with an air of insouciance.