I don’t think he can beat katakuri but instead, they can escape mama’s territory alive. Luffy’s power is so behind these monsters, yet. I guess they will head back to you and train there for quite some time. there may be a special room where they can train like son Goku and Vegeta did in DB.
Luffy vs Son Goku shirt
Like Law said, Remember what happened to those who underestimated the Strawhats, since in Grandline who would be thought that Luffy beat Crocodile, there is very large gap between them when it comes to power and status and yet Luffy beat him, and in Enies lobby they all learned and develop new technique to beat their enemies, Luffy 2nd&3rd gear, Sanji Diable jambs, Zorro Asura, Nami illusion, Chopper Monster point and Ussop Kabuto, it can happen again when they faced an extreme battle again. Luffy vs Son Goku. Sorry definitely underestimated Luffy in the fight between him. He just didn’t kill him at the right moment because he wants to Trash talk. but that’s the manga and it was a great fight.
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He will get stronger like Goku during the fights and will beat Karakuri. when he fights Kaido (probably with many help), he will get stronger again, well luffy will level up and observation haki. luffy just need to stay calm and focus like katakuri and luffy will do it. he can see the future a little bit like katakuri. because if he can’t beat katakuri in this act. it is imposible to see luffy fight kaido or it will be strawhat lose.