The present invention contemplates methods and systems of conducting wagers, such as parimutuel wagers. In one exemplary embodiment an event, such as a horse race, dog race, a combination of races, etc., is identified for which a plurality of bettors may each place at least one wager. Each bettor of the plurality is enabled to provide input regarding at least one portion of their respective at least one wager prior to the event. At least one other portion of each bettor's at least one wager is randomized prior to the event. The wager then comprises the combination of the bettor-selected portion and randomized portion. In one exemplary embodiment, the player-selected portion may include selecting bettor-preferred participants of the event while the randomly selected portion may include randomly assigning a finishing order to the player-selected participants.