The Gambler, The Chess Master, The Master Planner, The Mastermind, The Xanatos, etc, etc. There are lots of tropes for characters to essentially be incredibly smart. Now, this intellect can come in different ways. Some are just that good at reading people. Others are just that perceptive. There are even those who break down the entirety of the world into math, and figure it out that way. The thing they all have in common? They're smarter than you, smarter than your Players, and at some point or another you're very likely going to end up with one in your game. So, how do you handle it while still being fair? Let's take a look.
Smarter Than Me
Playing someone smarter than you is hard. For some - like me - playing someone dumber than you is hard too. Not using some of your mental faculties is just...weird, and damn near impossible for me. However, I can't even imagine what it is like to have more mental faculties. Not because I think I'm that smart, but because I've never experienced it from the inside. Oh sure, I could tell you some of the outward signs: appear to know things they couldn't know, massive intuitive leaps, ability to process things ridiculously fast. But I have no experience with them, and so I have nothing to draw on to present that. Luckily, you can cheat.
One of the best ways to play the super smart person? Pre-plan ahead of time. Now, as a GM this means putting a lot more time into planning, but it is worth it. Take your week or so, and take what you know of your players - not just their characters - and really think about what they're going to do in certain situations. You have advantages here. You know what the situation will be, you know where all the pieces are, and you aren't under a time limit. Exploit this. Redundant plans within plans and cover every possibility that you can think of. Now, odds are you won't cover everything (that's perfectly fine, and if the players find that gap reward them for it. After all, you worked hard to close it) but you will have a lot more than you'd expect.
This method isn't even really technically cheating. One of the aspects of the smart villain is that they plan for all the eventualities. The only difference here is that they are under a time limit and duress in game, whereas you are doing it relaxed and with full knowledge of everything. However, those advantages you have are how you are simulating the higher intellect. Now, if the players play into one of the things you planned for, you can use your best judgement on whether or not the villain pre-planned for it, or will just react, but having something ready will mean that you can roll with the punches. It's a lot better than being stopped dead in your tracks, believe me.
This is generally a big no-no, even for the GM, but sometimes when playing a super smart person you have no way of knowing it. Sometimes, the PCs will say they are doing something, and your brain will just immediately click "Oh, the villain would have thought of that, but I didn't...it's so obvious though!" Now, in some situations (like when you spent time planning out every eventuality before hand) you may want to just give this one to the PCs. However, other times, just hand wave and say they would have thought of it and react accordingly. The person thinks on a higher level, and would be accounting for things your mortal brain can't really be expected to.
You want to be careful with this one though, do it too much and your PCs may get suspicious as to what is happening, or feel they are being punished for being creative. My recommendation is to either flat out warn them - a simple "this villain is so smart, I need to metagame a bit with them" - or just be very careful not to do it too much. Either way, on occasion let the players find something the villain missed, or otherwise do something to topple the villains intellectual superiority.
Just Flat Out Cheat
This is a method I don't recommend doing unless absolutely necessary. If you can't do anything else, you had no time to plan, the PCs didn't discuss their plan, and you have to do something. You can just cheat. Honestly, if you do this well, the PCs may never even know you are doing it. You will though, and it isn't a crutch you want to get used to having. Just keep track of what you say and what information you give out. When talking as the GM you don't want to get caught in a lie, or contradicting yourself. Still, there are other ways to do it, and I'm sure you'll figure something out.
I just want to reiterate that playing people at different intellectual levels is very hard, at least for me. Of those, the characters that are smarter than the player are the hardest. You need to be able to improvise, and you need to be able to plan ahead and make the plans look like improvisation (but genius improv) in order to sell it. If you do sell it, your players will very likely thank you for it. There is a reason that Xanatos was such a popular villain on Gargoyles, popular enough to have several tropes named after him, and it was't just his money and being voiced by Reiker (however you spell his name).
Do you have other tips for playing super smart characters as a GM? Let us know in the comments below.