Geralt of Rivia seldom shows his softer side. Because of his line of work, he's more comfortable by himself and hardly has any personal connections. Geralt wouldn't precisely do well at court—or at any social occasion for that matter—but he has more than enough qualities to set himself apart from others around him.
If he ever found himself in Westeros, chances are he'd make a name for himself in no time. However, the game of thrones is its own thing, and Geralt might find himself in over his head. He has everything to win the Iron Throne, but Westeros has plenty of dangers lurking in the shadows, and, as every Witcher knows, monsters come in all shapes and sizes.
Would Fall Short: He Has No Claim To The Throne
Lines of succession are vital in Westeros—or, at least, they should be. By the time Game of Thrones begins, the Baratheons have a somewhat firm hold over the realm, but there are still plenty of Targaryen loyalists hiding in plain sight.
As a foreigner from an unknown land, Geralt would be at the very end of the line. If he wanted the throne, he'd have to take it by force a la Aegon Targaryen. But, Aegon had dragons, and Geralt would have nothing, so he would first need to find a noble family to back him up. Alas, that would be almost impossible.
Could Win: He Isn't Afraid Of Getting His Hands Dirty
As a Witcher, Geralt isn't a stranger to killing. "The Butcher of Blaviken" had a reputation in the Continent, even if it was somewhat exaggerated. Geralt doesn't enjoy killing, but he does it if he has no other choice.
Considering his lack of lineage and influence in Westeros, the Witcher would have to take the throne by force. That means killing a lot of people, most of them soldiers. Unlike others who might be less experienced, Geralt wouldn't doubt himself when the time came.
Would Fall Short: He Has No Social Skills
Robert Baratheon was likable, and, had he been a more competent King, the Baratheons could've won the game. His charm allowed him to hold the Seven Realms in relative peace during his ruling. The Lords liked him, and the commonfolk admired him. Joffrey, Tommen, and Cersei lacked Robert's charm and ended up dead.
Geralt is loyal to his friends, but he isn't exactly friendly. He lacks charm and doesn't seem to have any interest in acquiring it. In other words, he wouldn't like the pretentiousness of court and wouldn't hide his contempt for it.
Could Win: He Knows The Value Of A Good Lie
Lying is a vital part of the game. Any player who wants to win or even stay in the running needs to be an expert liar. That's why the Starks didn't excel at the game; their honor prevented them from being deceitful.
Geralt may not be a treacherous liar, but he does understand the value of a good lie. For example, his name, Geralt of Rivia, is a fabrication. Wichers usually make up surnames for themselves to appear more trustworthy to potential clients. Geralt eventually adopts a Rivian accent to complement his new identity, showing his commitment to the lie.
Would Fall Short: He's Overly Cynical
One of Geralt's many flaws is his cynicism. Because he's lived for a long time and seen countless things, he lacks the drive of younger and more ambitious men. Geralt is not easily impressed and wears his heaviness on his sleeve. Indeed, Geralt's weariness prevents him from appreciating many of life's best things.
His cynicism would be a detriment during his time in the game. His lack of enthusiasm would be enough to derail him, but his faithlessness would also prevent others from believing in his cause because he would have none at all.
Could Win: His Experience Sets Him Apart
As a Witcher, Geralt is cunning and sharp. His advanced age also gives him valuable experience. Indeed, Geralt is not the most intelligent of characters, but he is worldly. He's the embodiment of "street smarts," having seen countless things.
It would take a lot to distract or surprise Geralt, and nothing the Westerosi nobles did would ever take him by surprise. After everything he's been through, Geralt is numb to shock, and not even something like the Red Wedding would get to him.
Would Fall Short: He Would Have No Allies
Game of Thrones nobles aren't trusting or foolish. They don't give their help for free, and they always doubt everything. In Westeros, kindness and selflessness are uncommon, and, if they exist, they never come freely.
Geralt would need to endear himself to at least one prominent family, and he'd probably fail at that. He could always use sellswords, but, even if he got enough money to hire them, their loyalties would never lie exclusively with him. There's always the option that many would follow him because of his skills as a warrior, but they would hardly be enough to call themselves an army.
Could Win: He Has Superhuman Abilities
Geralt is the best fighter in The Witcher, by far. He's also supposed to be among the best Witchers of all time because of the increased mutagens he endured at Kaer Morhen. He has increased strength, speed, and stamina—even more than his fellow Witchers.
His training also made him resistant to poisons and diseases and slowed his aging process. Geralt is also a skilled alchemist, strategist, swordsman, and combatant capable of performing several minor spells. Being a Witcher, he's an expert at killing monsters, meaning that not even Daenerys Targaryen's dragons could stop him.
Would Fall Short: He's Tired Of All The Fighting
As previously mentioned, Geralt is battle weary. After so much fighting, he's reached a point where he's no longer interested in it. Taking the Iron Throne in Westeros would mean going into fierce battles against pretty much everyone. Geralt would need to fight Cersei and her armies, Daenerys and her dragons, and every other would-be King that appeared, whether they be Robert's bastards or any other pretenders.
Being a King in Westeros means committing to a life with one hand in the sword and the other holding on to the throne. Geralt wouldn't be interested in spending what remains of his abnormally long life in an eternal war for the Iron Throne.
Could Win: He Wouldn't Want The Iron Throne
The Starks are the undisputed winners of the game of thrones, and a big reason why is their lack of desire for the throne in the first place. Ned never wanted to be King, nor Robb, nor Jon. Sansa was a brilliant politician, but her priority was always ensuring the North's well-being. Arya never had any desire to rule or hold any influence.
Geralt would be the ideal Stark. He'd have no interest in being King, which ironically might make him ideal for the role—at least in Westeros' eyes.