The character in "The Player of Games" experiences a gradual realization of the intricate and complex mental model he has built regarding the game's contest. This model is layered and rich, reflecting the multifaceted nature of the competition he is involved in. As he examines this model more closely, he begins to perceive the depth of the game and the various strategies at play.

With his newfound awareness, he manipulates the structure of his thoughts and perceptions, which leads to a transformation in how he engages with the game. The changes in his understanding alter the dynamics of the contest, suggesting that a deeper insight into a challenge can significantly shift one's approach and the outcome itself.