The bet between the lawyer and the banker is a relatively simple bet. It takes a long time to complete, but the set up itself is straight forward. The banker believes that capital punishment is better, and the lawyer believes time in prison is more humane. The two men make a bet. If the lawyer can tolerate 15 years in solitary confinement, then the banker will pay him 2 million rubles.
Most of the story is told from the banker's perspective, so the reader gets a good insight into his conflict. The lawyer's conflict is a bit harder to pin down. Of the plot types that teachers emphasize, the lawyer is experiencing a man vs. self conflict. He is in his prison all by himself. He is well provided for with food, drink, books, and music, but he has almost zero contact with humans of any kind. He is not in danger from any outside force or person, so man vs. man and man vs. nature do not apply. The lawyer's struggle is within his own mind. Can he remain sane and positive during the 15 years? I would argue that he failed. He comes out despising just about everything in human life, and he no longer wants the money. Perhaps that is a victory, but I see him as a broken man.