If Yuuta were to act more confident than before, there's a huge chance that Brooks would catch wind of his antics and reject the bet. If that were to happen, then Yuuta wouldn't be able to punish Brooks for his actions. That's why, for the first time in his life, he decided to act like a normal teenager as a front so Brooks would take the bait.
"T-t-twenty levels?" That's ridiculous! Are you sure you're willing to lose that many levels in a single duel? There's no going back once we a-a-accept the conditions," Yuuta forced a smile on his face, totally getting into character. He'd have to do at least this much to trick Brooks once again, and then after that, humiliate him for a second time while everyone is watching.
Hopefully, everyone is watching, so he could further destroy Brooks's reputation.