When playing with a partner, you will be able to eliminate four of the five types of bets. The last one will be the bet that is active for the game. The five bets are Abilities Used, Enemies Killed, Headshot Count, Critical State, and Duel. Follow the instructions for the bet and come out ahead of your partner to win a bet.
Abilities Used - Use the abilities.
Enemies Killed - Kill more enemies than your partner.
Headshot Count - Get more headshots than your partner.
Critical State - Die fewer times than your partner.
Duel - Win the duel against your partner (deathmatch).