You may also be looking for Dueling, the activity in Red Dead Redemption and Red Dead Revolver.
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Duels was one of the two game modes available in Red Dead Redemption: Gunslingers. In Duels, opponents were matched up with the player based on similar level and experience. By winning duels, players could level up and gain in strength, which would eventually allow the player to become a top-notch gunslinger.
Twenty remaining stamina points were required to participate in a Duel.