The next section of the Guide to GreedFall contains a walkthrough of the side quest Dangerous Bets commissioned by Petrus.
Where to start the quest?: Talk to Petrus' father - he will tell you if he needs help.
Petrus will tell you all about his plan and direct you to the bookmaker. He's right at the entrance to the arena in the inn - talk to him about the next fight. You will be directed to Candy Cane - he's only out at night, so you might need to sleep over. You can ask him to set up a fight or use charisma to convince him.
Now you need to wait 24 hours. Go and use the hideout to speed up the time quickly. Then go to the arena and fight and defeat the champion. You fight alone, so be careful.
Now go to a meeting with Mother Cardinal and complete the mission. You will get 1300 XP and +3 rep with Petrus.