The "arm loss" mentioned at the start happened in Chapter 3, Pages 12-14. They were facing a giant armored beetle and Uber Brat threw a projectile from across the map.
That said MC truly has laid the groundwork properly. The rules are clear stated in book and he ensure everyone, especially nobles, to understand it, and they give their consent. So any nobles caught to be cheating or not playing by the book will be shunned among community by a public shaming.
The only thing I can think that can mess things up is if someone pitching in gambling.