By setting the action up as a bet, this story necessarily ends up being a contest between the two men involved. The one-upmanship is the reason for the bet, the reason for the raised confinement length ante, the reason for the banker almost committing murder, and maybe even the reason for the lawyer's final twist of an escape. In the end, though, "The Bet" refuses to in any way rule on the wager at its center, leaving the reader to decide whether anyone won or lost, and whether the competition between the banker and the lawyer was the strongest motivator for the actions of each.
The story's ending is an elegant solution in which both men emerge from the bet victorious.
The entire competitive aspect of the story is purely in the banker's mind—the lawyer couldn't care less about the banker and has no interest in any of the jockeying for position that the banker seems to be obsessed with.