Given how often we complain about sequels, reboots, and a general lack of originality in Hollywood, we shouldn't really be surprised that coincidences are used as often as they are, even in great films. And it makes sense -- coincidences are a convenient screenwriting tool. That said, we've reached a point where both Hollywood and audiences unquestioningly accept certain hilariously improbable events. For instance ...
6The Hero And The Villain Inexplicably Have The Exact Same Skills
Forget all the father-son mumbo jumbo for a minute, and let's look at the Darth Vader / Luke Skywalker relationship. At the age of nine, Vader was building his own protocol droid, kicking ass in podraces, and well on his way to becoming a(n evil) Jedi. By the time he was in his 20s, he was a highly skilled pilot and up for a potential promotion to Jedi Master. Luke's training, on the other hand, consisted of some vague bullshit from an old man in a mud hut and a few hours with a clearly senile Yoda in a swamp. There is no goddamned reason that Luke should have defeated his father with that kind of training.
And yet he does, because apparently the only way moviegoing audiences can understand good triumphing over evil is if they are competing in the exact same arena, even though this is rarely the case in real life. (Al Capone was arrested for tax evasion, and not all the blackmail, murder, and extortion he masterminded.) Luke should've beaten Vader by rallying subjugated planets to rise up and topple the Empire with sheer numbers, not through a one-on-one sword fight against a lifelong master of the weapon.
To be fair, that mask gives him a -3 in Perception.
Okay, so maybe that could be chalked up to the mysteriousness of the Force and an overly confident Emperor Palpatine. So let's examine The Karate Kid. Danny is, as we've come to learn, a bit of a prick. Rather than do the smart thing and pick up a skill that a) would impress Ali and b) Johnny could never hope to learn, he marches straight into Johnny's dojo and agrees to a challenge in Johnny's sport. Danny should have had his ass handed to him on a silver platter. But instead he got handed a four-pillar trophy, because he inexplicably learned karate and surpassed Johnny's level of skill within the running time of the movie. It probably would've been less of a hassle to simply plant drugs in the evil karate bully's locker, but then the movie would've been called The Plant-Drugs-In-Your-Locker Kid.
"In The Plant-Drugs-In-Your-Locker Kid: Part II, he convinces the bully to apply for his GED, only to ... well, you'll have to find out!"
There's a pattern here across a lot of movies. If the hero fights with swords, the villain will too. If bad guy is going to be a crack shot, so will the good guy. Sometimes, like in Batman Begins, the hero and villain will have similar backgrounds, so it makes a little more sense. Other times, it looks like this:
How is it possible that Sherlock Holmes, a detective, and Moriarty, a professor, have the exact same training in hand-to-hand combat? That'd be like if an interior decorator and a professional snowboarder teamed up to build a military-grade submarine. Nobody seems to be using their exact set of strengths as a character, and instead have to rely on a final battle that involves a skill shoehorned in for them to make things look more badass.