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Sword over Head: At the climax of Part II, when he has Chozen at his mercy and asks him, "Live or die, man."
The So-Called Coward: Chozen and his goons repeatedly call Daniel a coward throughout Part II because of his reluctance to fight them. But when a typhoon hits the village, Daniel and Miyagi risk their lives to rescue Sato when he is trapped inside his dojo, and Daniel further tempts fate by going back into the storm to rescue more villagers. Chozen, on the other hand, cowers in the shelter and refuses to help, even when ordered by Sato to do so. Sato is so impressed with Daniel that he offers to oblige Daniel any request, and he is so disgusted by Chozen's cowardice that Sato disowns him in front of everyone.
Training from Hell: Especially what Terry Silver puts him through in Part III, which is more like torture disguised as training.
Retired Badass: A martial artist and a World War II veteran (who was even awarded the Medal of Honor).
Heartbroken Badass: While Mr. Miyagi was serving with distinction for the United States in World War II, his wife and son died due to complications during childbirth in the Manzanar Japanese Internment Camp. Decades later, Mr. Miyagi is still haunted by the loss.
Fish out of Water: In The Next Karate Kid, he proves to be a little out of his element dealing with Julie. For example, he accidentally walks in on her once, freaking her out. He immediately apologizes, citing that he and Daniel used to enter each other's rooms all the time and it was no big deal. He also has some trouble trying to buy her a prom dress, since he has no idea what she would like and can't ask her because he wants it to be a surprise. All of that said, he gets a handle on things fairly quickly.
My Greatest Failure: It turns that he has a few in the first sequel: he left the girl of his dreams behind to go join the war, he didn't visit his father enough before he died, and he left his brother on bad terms.
Nice Guy: Mr. Miyagi is an unambiguously good person. He is kind, forgiving, thoughtful, and he only uses violence as an absolute last resort.
Papa Wolf: Snaps into action whenever Daniel is outmatched in a fight.
Parental Substitute: As time goes on, Mr. Miyagi becomes more and more of a father figure to Daniel.
Defeat Means Friendship: Though he doesn't appear again after he gets berated by Kreese for losing at the beginning of Part II.
Even Evil Has Standards: When Kreese orders Johnny to target Daniel's wounded knee by performing a leg sweep, Johnny appears shocked that he's being ordered to do something so dishonorable (even though leg sweeping is a perfectly legal move in competitive Karate).
Ordered to Cheat: He instructs Bobby to take out Daniel's knee, even though doing so will result in Bobby's disqualification. Then Johnny also uses "unethical" moves that target the injured knee. Was originally the Trope Namer.
Minion with an F in Evil - When Johnny first gets jealous of Daniel with Ali, Bobby tells him to forget it. The third time Johnny beats up Daniel, Bobby tells him to leave Daniel alone, despite Johnny's insistence that an enemy deserves no mercy. During a sparring session he hesitates to hit Robertson while he's down. And when Kreese tells him to injure Daniel in the tournament, he does not want to at first, and apologizes to Daniel when he does.
Corrupt Corporate Executive: He's a wealthy industrialist whose supertrawlers have greatly depleted the local fish population, forcing the former fishing village to scrape by via small farming. He also owns all the land in the village and forces its residents to rent from him.
Even Evil Has Standards: Despite being a real bastard, it's shown that Sato does possess a sense of honor by giving Miyagi time to mourn and honoring the bet that Daniel could break more ice blocks than Chozen.
Break the Haughty: Nothing went well for him once Daniel arrived in Okinawa. His uncle shut him up at every turn, Daniel caught him cheating the villagers with false weights, Kumiko falls for Daniel, Daniel bested him at breaking ice blocks (earning him a huge wager that Uncle Sato forced him to honor), Miyagi curbstomped him when he and his friends attacked Daniel, then he got exposed as a coward when the storm hit, and Sato disowned him . That was just the prelude to the big showdown at the end, which he lost.
Cruel Mercy: When defeated by Daniel. Daniel offers Chozen the choice "Live or die?" Chozen chooses death, but Daniel instead tweaks his nose and drops him to the ground, shaming him in front or the entire village.
Dirty Coward: On only one occasion does he face Daniel unaided, and even then he has Daniel cut off any help.
Dragon-in-Chief: He bullies Daniel throughout the movie, mirroring the rivalry between Sato and Miyagi. He also is disowned by Sato after his Heel-Face Turn for refusing to save the bell-ringer girl during the typhoon, which leads to him being the Final Boss in the story.
Never My Fault: Chozen blames Daniel for dishonoring him. Daniel 1) accidentally revealed that he was cheating the villagers 2) fairly won a bet that Chozen forced him into and 3) helped save some of the villagers from the typhoon while Chozen was doing nothing.
Mighty Whitey and Mellow Yellow: She's surrounded by Asian men she doesn't show the slightest bit of interest in, but as soon as Daniel shows up at the front door... Then again, the other suitor with a chance was Chozen of all people.
Plucky Girl: She gets points for trying to help Daniel against Chozen, despite knowing how dangerous it is.
Put on a Bus: Daniel mentions in Part III that she chose to take a job with a dance company in Tokyo instead of coming back to the United States with him. He seems less bitter about it than Ali though, possibly because he knew how much she wanted to be a traditional dancer as opposed to just dumping him for another guy, therefore he knows she's following her dream.
Unkempt Beauty: Try as she might, she can't quite keep her hair out of her face.
May-December Romance: Even though their characters were about the same age in the movie, actress Robyn Lively was 11 years younger than Ralph Macchio in real life, and it showed.
Put on a Bus: She goes back home to Ohio midway through the movie, and is never seen or mentioned again. Probably because the producers realized the aforementioned May-December Romance just wasn't working.