Defeat Means Friendship with an instant Relationship Upgrade.
This trope describes a situation where a woman can or will fall in love only with a man who can conquer her. Her defeat may take place in actual physical combat (this obviously only applies to warrior women), or in a metaphorical sort of battle — giving way once she meets a man who can take charge and show her that he is the one who is making the decisions. In either case, once she is defeated by a man in this capacity, she will surrender her heart and/or body to him.
What forbids such a woman from loving a man who can't "master" her varies, but there is always some reason. She may have her own moral code telling her not to choose a mate weaker than herself. It may be an ancient custom or tradition of her people. It may even be religious or magical: there is a curse (or a blessing) on her that will not allow her to submit until she meets the man who demonstrates that he is worthy to have her.
The presence of some rule or custom is what establishes this trope. The woman who falls in love with her opponent after he defeats/stands up to her is not enough to qualify for this trope — there must be a clear injunction that she cannot love any man until he proves his mastery by defeating her.
Compare All Amazons Want Hercules. See also Slap-Slap-Kiss. See also Sex Face Turn and High Heel Face Turn. See also Red Sonja (the page for the former trope-namer). Contrast Love at First Punch, which lacks the explicit requirement either by the character themselves or their society.
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Anime and Manga
Shampoo and the rest of her Amazon tribe in Ranma ½. Specifically, if an outsider male defeats a female amazon, then she has to marry him (the outsider male has no say in the matter).
Also indirectly (and to her immense annoyance) Akane, after Kuno proclaimed that only he who could defeat her in combat was worthy of dating her. Cue the morning routine in which half the student body at Furinkan High (the male half) went out to fight her.
Amusingly enough, Kuno later reverses and applies this trope to himself, claiming that if the Pigtailed Girl (Ranma) can defeat him, he shall allow her to date with him.
Another variation is Akari Unryuu, whose grandfather wanted her to only marry a boy strong enough to defeat her giant sumo pig.
Miriya in Macross/Robotech is a borderline case. She fell in love with Max after he beat her, but there was never an explicit "rule" about it. (There was to be a female pilot in the never-produced Robotech II: The Sentinels who idolised Miriya and in an in-universe version of Misaimed Fandom vowed only to marry a man who beat her.)
Macross 7 arguably subverts this, as Max and Miriya have grown estranged from one another and Miriya is questioning whether marrying him was such a good idea.
It's rather un-subverted by the fact that they get back together in the end.
It was never subverted: the series strongly hints that Max and Milia grew apart because they couldn't mentally deal with normal married life, not for lack of love. Max and Milia are only good at fighting and sex (the pair had six children together, the second almost killing Milia during childbirth). Living together in harmony outside of those two activities is a major challenge for them.
Inverted in Steel Fist Riku: After she beats Chikara Toudou, Riku learns that he is now forbidden from setting foot on his family's property until he either defeats or marries her.
A less extreme version of this trope can be found in Bakuman。, where Iwase, the smartest girl in school, believes that she and Takagi are now a couple when he gets better grades than her. Too bad he thinks she was just making a friendly competition out of it.
As of recent chapters she's likely going to enter the field of manga in order to compete with him.
Note that Ku Fei doesn't require that the combat actually take place, she can tell that Negi could defeat her in an actual match, and that being able to defeat her is a necessary but not sufficient criteria. She's not romantically interested in Negi. Not yet, anyway.
Of course, he just beat her at arm wrestling (to minimize damage) and she joked that now they had to get married... and then Chamo started wondering why Negi's great-something-granddaughter looked so Chinese. Awkward timing there, huh?
Kumiko pulls this trope in Gokusen to get out of an attempted arranged marriage. However her tactics only make the prospective groom fall more in love with her and determined to win the fight and her hand.
Somewhat for Hinagiku of Hayate the Combat Butler. Hayate has 'conquered' her, in that he's taught her how to defeat her fears (or at least the knowledge how to), but when admitting it to Ayumu, she still wants Hayate to be the one to start the romance.
Unfortunately she's already seemingly given up on that, having tried a few times to confess.
Less of giving up, more of realizing that Hayate is just that stupid.
She took a more literal interpretation with that bokken duel fiasco.
Subverted in Pokémon Special. It is heavily hinted that the reason why Winona broke it off with Wallace was that having the regional champion as her boyfriend made her insecure of her own abilities.
The Gurren Lagann manga Guren Gakuenhen has Nia's split personality showing signs of this.
In the Sorcerer Hunters manga, Gateau's younger sister Eclair once vowed that she would never fall in love with any man who couldn't beat her in a fight. Since Eclair is about as strong as her brother, this disqualified most men in the world. Deconstructed when she becomes attracted to the (first) Big Bad Sacher Torte who easily stops her frequent attempts to avenge her parents' deaths. She later falls in love with him after agreeing with his ideals and has him erase her memories so she doesn't have to feel conflicted about her feelings anymore.
Deconstructed in Record of Lodoss War. Shiris was bested by Parn in the first episode of the TV series, and after that, she was quite adamant that she was in love with him; however, her partner Orson pointed out that she was really resentful of Parn beating her and desperately wanted to replace that resentment with another emotion, namely "love", in order to regain her lost pride. She was so angry by Orson's remarks that she hit him.
The formerTrope Namer here is Red Sonja, originally(-ish) from the Conan the Barbarian comics (and later a movie starring Brigitte Nielsen). Red Sonja lived with her family in a humble house in the Western Hyrkanian steppes (modern Ukraine/Russia). When she had just turned 17 years old, a group of mercenaries killed her family and burned down their house. Sonja survived but she had been raped by the leader of the group, leaving her in shame. Answering her cry for revenge, the red goddess Scathach appeared to her, and instilled in her incredible skill in the handling of swords and other weapons on the condition that she would never lie with a man unless he defeated her in fair combat.
Though Wolverine's not thrilled with the initial situation. After he beats Sonja, she basically gives up and waits to be raped. Wolverine walks away, telling her "Sorry, darlin', that ain't my style." She's both perplexed and slightly insulted so she follows him. (Apparently, she had never even considered the possibility that her eventual defeat would come at the hands of someone who wasn't interested.) It's only after their next meeting that he warms up to her. (Keep in mind, the stories in What If take place in Alternate Reality settings, and as such, the characters and situations in these settings are dfferent than those in the mainstream Marvel Universe. The "real" Red Sonja may not have reacted this way at all.)
Kalidor had previously implied that he thought the condition was silly, saying that it meant, basically, she could only love a man who had tried to kill her. (Possibly a valid point.)
In issue 15 of the current series, she and two friends take on a god—a weakened god, but still a quasi-deity at least. He quite naturally trounces them. Whether that counts as a fair fight, which is what has to be waged for it to work, is somewhat moot: he doesn't invoke the trope—she does. Because, the writer said, she was using the loophole wherein someone who's beaten her isn't necessarily someone who has to have sex with her, or whom she even has to let, but whom she can allow to do so if she wants...and the writer decided she did want, some time after the fight was over and they were allies. It's notable that in the new series, at least, the portrayal seems to be romantic love with someone who hasn't beaten her isn't forbidden—just physical affection.
This was further spelled out in issue #31, where it is revealed that Sonja did share a romantic, but non-physical relationship with a king who hired her as his bodyguard and grew to want her as his queen. Sonja refused, fearful of killing the man she loved if he pressed the issue of being able to consummate their love and challenged her to single combat. Seeking guidance from her goddess, Sonja was told that she could abandon her oath but that she would lose the superior skills she had been blessed with. Deciding this was acceptable, Sonja went to the King's bed chamber to tell him her decision, just as a group of assassins with magical weapons showed up. Sonja was able to repel the assassins but knew the only reason she was able to do so was because of her blessed skills. Her sense of responsibility to hold to her oath to fight evil at the expense of a normal life held and she resigned her post the next day.
It's worth noting that the traditional interpretation of Sonja's blessing/curse may have missed the mark. The reality appears to be that Goddess granted Sonja powers that she could only lose by voluntarily lying with a man, like the traditional oath of chastity. The "unless he defeats you in combat" may simply be a rape exception, so that Sonja doesn't lose her powers if she is defeated and taken advantage of. After all, she was given her powers in the first place to kill a rapist, so it would be a good idea to make sure she wouldn't be depowered & could get revenge again if it happened again. Of course, Scathach asking for an oath of chastity in the first place is an artistic liberty, since the goddess in question is an aspect of the Morrigan, a war goddess known for, among other forms of Karmic Justice and Kick the Dog, raping male heroes and villains (with or without offering a Sadistic Choice between sex or death first) as punishment or a symbol of the horrors of war.
Parodied by the character Blue Opal in the Phil Foglio comic XXXenophile, for whom this was more a curse than an oath. After the sexually-frustrated warrior out-drinks and out-fights every man in the bar, the only one left is a meek man who invites her to play a strategy game with him. The curse is lifted after he beats her at the game—which, as they realize later, has a name that translates as "Battle". Joyful sex ensues.
Subverted in furry parody comic series, Red Shetland. At one point, the titular character and a chivalrous and handsome stag knight end sharing blankets on a wintry night in a cave. The setting created too much temptation for Red to resist and she has passionate sex with her new lover. Later, Red is convinced that her goddess has removed her boons because of this and is despondent, until the Stag proves to her that she has lost nothing once she regains her confidence.
Viciously parodied in Wonder Woman vol.3 #24, where the producers of a Wonder Woman movie have her make this vow, and get defeated by Hercules. The real Wonder Woman is not impressed. Not least because in the DCU, Hercules raped Wonder Woman's mother.
Earlier, Power of Shazam had an inversion: Billy Batson has a dream about arm-wrestling Wonder Woman in which he throws the match because the Wisdom of Solomon tells him she needs to defeat him before they can "get together".
Parodied in Cerebus as Red Sophia. Her father hires Cerebus to torture the man who besmirched her honor. During the journey her logorrhea is too much, they fight, he wins, she pledges service. The eventual torture is forcing the blackguard (who saw her naked) to marry Sophia. Years later she marries Cerebus.
According to Marco Polo, Aiyaruk, the daughter of a nephew of Kublai Khan, said that she'd only marry a man who could defeat her in a wrestling match. She never did find a husband. Demanding that every suitor bring her one hundred horses that would be forfeit if he lost, Aiyaruk came to own ten thousand steeds. Eventually, a handsome and especially strong prince came and offered a thousand horses instead of a hundred, to show his confidence. Aiyaruk's parents begged her to let him win, but she refused. In the Hollywood version, he'd probably have been the one to get the girl — but according to Polo's account, after an especially long and difficult match, she was able to defeat him, too. Aiyaruk never did find her match, and instead became a skilled warrior (which was not unheard of amongst Mongolian women, regardless of the accuracy of Polo's specific account).
Nearly inverted by the Scythians, a nomadic civilization whose women were warriors. Greek accounts would have it that before they could get married, Scythian women had to defeat three men in combat. (However, not full inversion as they married others of their tribe rather than the defeated men, who were often dead.)
In Curse of the Ring, Queen Brunhilde wears a magical belt that makes her stronger than just about any man. She will only wed the man who can outpower her or best her in combat. There is one such man, but he is not interested in her due to a spell put on him. But he is the only one she wants, and is after his love.
Mystique in X-Men tries to seduce Logan/Wolverine in the second film because he defeated her in combat in the previous one, complimenting him that "nobody ever left quite a scar like you did". Logan is not interested. Later films show that Mystique is capable of having loving, if not necessarily intimate, relationships with other mutants even if they didn't actually beat her (Charles Xavier, Magneto).
In the Nibelungenlied, a 12th-13th century German verse epic, the Icelandic queen Brunhilde declared that she would only marry the man who could defeat her in three contests of strength, one of them direct combat with her. Only one man alive was capable of this, the protagonist Siegfried; however, Siegfried had his eye on Kriemhild, sister of King Gunther, and so he agreed to aid Gunther using his incredible strength and magical artifacts, one of which let him become invisible so he could create the illusion that Gunther won the contests while Siegfried did the hard work.
It did not end well when Kriemhild blabbed out the truth when she got in a dispute over precedence with her new sister-in-law.
Chaucer's Wife of Bath describes having several husbands whom she doesn't seem to care for in the slightest; that is, until she marries Jankyn, the first man who seems to have an ounce of power over her.
Of course, given the content of the Wife of Bath's tale and the fact that she asks that Jankyn give her mastery over him/their relationship this may be more of a desire for a challenge than a desire to be "conquered."
Bradamante, the daughter of Duke Aymon in Ariosto's epic Orlando Furioso, escapes the specter of arranged marriage by getting Emperor Charlemagne to promise that she won't have to marry any man who can't endure a duel with her from dawn to dusk. Her motivation for this is that she's fallen for a Saracen knight named Ruggiero and been tasked by Merlin's ghost with converting him and founding a lineage of great Italians.
Britomart (an expy of Bradamante) in Edmund Spenser's poem The Faerie Queene is another example, with pretty much the same vow as Red Sonja's if for completely different reasons. She is an allegorical figure of the virgin Knight of Chastity.
Brienne of Tarth was set up for an Arranged Marriage with a noble who made it clear he would 'chastise' her if she persisted in wearing chainmail and training in swordplay. Brienne stated that she would only allow herself to be chastised by a man would could defeat her in combat. Deciding to teach his future wife her place, he accepted the challenge and ended up with several broken ribs from a tourney mace. After that Brienne's father gave up the idea of marrying his daughter off.
The Marat in Codex Alera are a subversion. Marat women do give potential suitors a challenge that they must complete to win their affection. However, the challenge isn't necessarily against the woman herself, and either way the woman chooses the challenge. This means, as Tavi notes, if the woman doesn't fancy that particular suitor, she need only choose a contest he's likely to fail at. Kitai's challenge to Tavi: Defeat the Big Bad.
The ancient chinese tale Hua Guan Suo Zhuan speaks of a Bao Sanniang, a young girl who was both immensely beautiful, and immensely strong. With countless suitors, she declared that she'd only marry the one who could beat her in a duel, and proceeded to beat up every last man who came for her hand. Eventually, Guan Suo - third son of the incomparable Guan 'The God Of War' Yu - heard of this, and went to challenge her. He beat her, and she instantly fell in love with him. (By all accounts, he was quite the Bishōnen, and known to wear flowers in his hair even upon the battlefield, so that probably helped too...) From then on, she followed him everywhere, and even fought alongside him in his remaining campaigns.
There is some debate as to whether Bao Sanniang is a wholly fictional character, or a romantization/dramatization of a historical individual, mind.
In The Hundred-Thousand Kingdoms, the Darre tribe is a matriarchal society where the female leader wrestles against a male. If the female wins, he dies and doesn't marry her. If he wins, he rapes her in front of the entire village.
Live Action TV
Saffron from Firefly tried to con Mal at the end of the episode "Our Mrs. Reynolds" by pretending to be this type, but Mal didn't fall for it and responded with a Dramatic Gun Cock instead.
In Dark Kingdom The Dragon King (a.k.a. The Ring of the Nibelungs) Kristanna Loken plays Brunhilde the Queen who will lose all her strength if she marries a man who has not defeated her in battle.
In Game of Thrones, Jaime Lannister guesses that boys had tried to force themselves onto the gigantic Brienne of Tarth and suspects that she secretly wanted to find a man who could overpower her. She declines to confirm this, saying only that no one ever could.
In Chinese Paladin, Yue'Ru's father despairs of finding a man for her (and is personally fed up with her bratty behavior), and offers to marry her to anyone who can defeat her in a kung fu contest. In something of a subversion, after seeing the quality of the contestants who do show up, he privately advises her to go for the kill. She subsequently falls in Love at First Punch with the hero.
Atalanta, who would only marry a man who could defeat her in a foot race. The losers were executed. Eventually, Aphrodite got sick of Atalanta's attitude and gave the next competitor three golden apples with which to cheat. Every time Atalanta got ahead, he threw one out in front of her and broke for the lead while she was distracted, giving him the win.
Peleus had to defeat the immortal and shape-changing Thetis to be allowed to marry her. Their son was Achilles.
A set of Dungeons & Dragons trading cards from the mid-90s included a variation, with a Lawful Good priestess who was prophecised to leave the sisterhood in order to wed a great hero, and vowed only to marry a man whose virtues exceeded her own.
Shakespeare's A Midsummer Night's Dream had the Amazon Queen Hippolyta marrying Theseus, the Duke of Athens, after he defeated her forces.
The Taming of the Shrew could be argued to be an example of this, as Kate 'defeats', or at any rate sees off all other potential suiters until Petruchio manages to break her through sheer horrendous treatment and stubbornness.
Discworld has a Red Sonja Expy, who had the standard oath regarding laying with a man who could defeat her. Later on in the game, she notes that she was finally defeated by a man who challenged her to a game of tiddlywinks. It seems her goddess didn't stipulate that she had to be defeated in armed combat. Rincewind learns of this, much to his regret, as he is really good at tiddlywinks.
Curiously, completing the Handmaiden's romance sidequest in Knights of the Old Republic 2 requires defeating her in three unarmed duels. Where both participants are wearing underwear (the player's covers more than the Handmaiden's does, though).
Ditto for the sidequest with Visas, though hers is more of a Defeat Means Friendship blossoming into something more.
Jeanne, of World Heroes seems to be of this type, as her endings usually have her lamenting her victories as a still-single woman.
Uthgerd the Unbroken in Skyrim will only marry you if you can defeat her in a brawl.
Non-canon sidequests in Dynasty Warriors games often involve male characters needing to prove they are worthy of their love interests by defeating them.
In Izuna: Legend of the Unemployed Ninja, the fisherwoman Ichika spends a lot of her time looking for a mate who's as strong as her. By the end of the game, she eventually finds him, and the sequel begins with their wedding.
One of the campaigns in the RTS Blood and Magic, called "Matchmaker Mayhem," revolves around this plot. Princess Roxana proclaims that she will only marry a man who can best her in a contest of martial skill, although the suitor is allowed to pick the specific contest. She defeats several would-be suitors in jousts and duels, before facing Bryan the Bold, who chooses open war as his specific conflict. You, the player, can choose to lead Bryan's forces or Roxana's.
In Captain SNES, the wife of Cid from Final Fantasy IV is said to be this.
The unnamed Mongol warrior from Get Medieval falls hard for the alien gladiatrix Rylede after she defeats him.
Yatta-Ta is convinced that the title character of The Challenges of Zona is this and so far, no amount of evidence to the contrary will convince him otherwise.
Parodied in Insecticomics: after being beaten by Flamewar, Grimlock assumes he has to marry her. Flamewar questions the logic of this, asking if she has to marry Jazz because he once shot her in the back. Being Grimlock, he agrees, and it only gets better from there. Jazz even refers to it as a "Red Sonja-kick".
Inferno: Hey, Grimlock, ya didn't win the lottery last week.
Grimlock: Then me Grimlock must marry...the LOTTERY!
A character by furry artist, Linno, falls under this trope (at least at one point). His Kangaroo babe, named "K.O." is a professional boxer, who uses both her fists and her tail to box with. Of course, this would seemingly make her quite tough to beat in an actual match; so for anyone who does beat her in a one-on-one challenge gets a very special prize. Believe it or not, there was even an adult flash game made out of it (no, this isn't made up).
The If I Am Ever The Heroine list (similar to the Evil Overlord List) strongly warns against agreeing to this practice.
Tetramands in the Ben 10 Universe have their courtship working that way. Notably, Tetramands possess natural Super Strengh, and females are naturally stronger than males, so this actually is an uphill battle for males. Ben 10 Omniverse reveals that Kevin defeated Tetramand princess Looma when he was 13, though he was only interested in the engine her family would give him as a wedding gift. When the time to marry her came, he pulled out a Batman Gambit to trick Ben into defeating Looma in a duel, leading him to become her fiancée instead.