: How to defeat a strategic mastermind without throwing the idiotball? My antagonist is a "strategic mastermind", similar to the one discussed in How to prevent seeming like a Marty Stu-ish villain

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It isn't what you don't know that hurts you, it's what you know that ain't so. --Mark Twain.
I think the best way to defeat a mastermind is to plant a seed and do it early; no matter how smart somebody is, there can be things they believe to be true that are false. They can be mistaken. They think somebody is dead, that isn't. They think they are the only one that knows something, but they aren't. They think they weren't seen doing something, but they were. They think a crime of their youth went undetected, but it is quietly found out and clues there reveal something about them that can be used against them. They killed somebody to protect a secret, but the person anticipated that might happen and the secret was cleverly preserved for somebody else to receive.
Their downfall lies in what they know that ain't so, which means they are not prepared for the attack (whatever form it takes) and this can plausibly be their undoing.
This way they don't make a new mistake that looks like a deus ex machina: The mistake was made long ago, the longer ago the better, and the more difficult it is for the hero to find this weakness the better; make them work for it.

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There are several ways a strategic mastermind can be realistically defeated.

A mastermind can only take into account what he knows of. The opposing side can come up with new technology or new magic, that changes the situation. Consider, for example Japan in WW2: leaving aside whether their strategy from the beginning was good or bad, there is no way they could have accounted for nukes. There was simply no way for them to know that such a thing could exist.
There might not be a way for the mastermind to win, no matter what they do. Consider Bowie and Travis at the Battle of the Alamo: they were outnumbered and outgunned to such an extent, that no matter what they did, there was no way for them to win. Your villain too might get outnumbered and outgunned.
Some ways of acting are so "crazy", your mastermind might not even consider them. Those would be very costly, and very different from what the mastermind would do. Napoleon routed the Russian army, and conquered Moscow. He did not consider that the Russians might burn their own capital city, refuse to surrender after their capital has been taken, and instead leave Napoleon's troops to starve. As far as Napoleon was concerned, taking Moscow should have been the end of it. Instead, it was the end of him. Similarly, in the Lord of the Rings, Sauron fails to consider the possibility that someone would attempt to destroy the Ring rather than use it. It offers great power, which is what he seeks, so to refuse power doesn't enter his thoughts. Also, the Ring is quite persistent at torturing the bearer's mind and offering him power, so it should be impossible to destroy.
Finally, a mastermind can be betrayed by someone they trust. Consider Julius Caesar - by all accounts a military genius. Betrayed and murdered by Brutus, whom he considered a friend.

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