The Pack of Nude Cards
One of the things McMurphy always holds onto in the mental hospital is his pack of playing cards with pictures of nude women on them. This little item tells us a whole lot about McMurphy's character.
For starters, he thinks of women as sexual objects, which we see when he shows the doctor one of the nude cards and casually asks, "Where do you suppose she lives?" This treatment of women reminds us of the fact that he's been convicted of statutory rape. The cards also show that McMurphy likes to gamble in every sense of the word, he not being one to shy away from risks.
Finally, McMurphy's attachment to the cards shows how devoted he is to playing games he knows he can win. That's why he gets so upset with the way Nurse Ratched always manipulates situations in her favor. As McMurphy tells one doctor, "She likes a rigged game." He symbolizes his dislike for her by loudly flicking through his playing cards while she's trying to speak.
The truth is that McMurphy likes a rigged game, too. He's just annoyed that someone is better at rigging the game than he is.