"The Bet" opens at a dinner party in which the banker is the host and the lawyer is one of his guests. The topic of discussion at this party is capital punishment and, specifically, whether it is better to die than to spend one's life in solitary confinement.
For the banker, the answer to this question is simple: the death penalty is "more moral" and "more humane" than imprisoning a person for the duration of his life. In contrast, the lawyer believes the opposite and argues that it is better to live some life than to have no life at all.
It is this difference in opinion which provides the context for the bet. Feeling confident, the banker proposes the bet to the young and ambitious lawyer who is keen to enrich himself, regardless of the emotional sacrifices involved.