The protagonist is the main character of a story in the sense that they are expected to make important decisions or deal with challenges. A story mostly revolves around a protagonist and the circumstances they are in. The antagonist, on the other hand, is also an important character who challenges the protagonists. The antagonist may also initiate events that force the protagonist to make important decisions that determine their future or show their strength or weakness.
To determine the protagonist and the antagonist of a story, it is important to avoid the hero/villain bias. In some stories, the hero, who is expected to be the protagonist, may actually be the antagonist. Thus, in my opinion, the distinction should be made based on who presents the challenge and who deals with it. In The Bet, the young lawyer merely expresses his opinion, but it is the banker who presents the challenge. The decision by the lawyer to accept or decline the challenge presents the first important decision of the story that propels the story forward. The young lawyer accepts the challenge, and his tribulations begin. He remains resilient, and right before he earns his prize, he makes another very important decision for the story and deliberately opts out of the bet. In addition, the lawyer’s last decision might also present the moral of the story.
Based on the definition, it is clear that the young lawyer is the protagonist because he deals with the challenge and makes most of the important decisions in the story. The banker, on the other hand, is the antagonist who presents the challenge and even attempts to end the lawyer’s life before the bet is complete.