Here's the idea. This guy is a genius and he's super rich. He traveled the world doing all sorts of stuff and facing challenges (before the story began.) At the start of the story, this guy says he's conquered every earthly challenge worth conquering, so he decides to go bigger. He looks into the supernatural and finds this god. First face off neither can win or lose, so they get stuck in this feud that gets progressively more complex and dangerous. The guy can out think the god, but how do I get him on the same level when they are fighting physically?
We don't know, you haven't explained the rules or powers of this god. Presumably, this mere human would have to use some sort of supernatural or artificial means.
God of what? In Greek myth humans were always coming up with challenges to the gods and almost winning, because, you know, Ancient Greeks. In the Iliad, Menelaus (I think) hits Aphrodite with a spear, who was protecting Paris, causing her to retreat from the battlefield. It came back to bite him later, because again, Ancient Greeks, but certain gods in mythology did have certain weakness. My first thought, though, considering he's rich, is a Batman/Iron Man hybrid. ETA: Maybe it was Diomedes?
My recommendation actually comes from along the same lines of the show Supernatural. The god is just that a god. They have strengths and weaknesses just like humans do so have the human fight him in a way that doesn't allow the god to exercise their powers to their full potential. Another book I read had a teenager that was facing off against a high level devil who could easily tear him apart but because the devil was a lawful creature he challenged it to a game of chess and beat him like that. Most gods tend to be lawful beings as well (minus a select crazy few) so that alone could provide an avenue to go down.
Yeah, it was Diomedes. Not only did he wound Aphrodite, but he defeated Ares as well. Honestly, the Iliad was the first thing I thought of when looking at the title. You've got lots of mortals and gods going head to head there. Achilles fights a local river god all on his own (Diomedes was empowered by another Olympian--Athena maybe?--when he attacked Aphrodite and Ares). I'm gonna have to agree with the first poster. We need more info to give a good answer. First you have to answer the question "what is a god?" Those cargo cults out in the Pacific are effectively worshipping American airmen. Their "gods" are just as mortal as they are. Some historical deities in polytheistic pantheons aren't omniscient. Some only have power in their sphere of responsibility. Then you get the monotheistic creator god that no human could ever match. You probably need to rule out omniscience and omnipotence in order to have a story. Since you want neither to win or lose, having the god be immortal and your hero deifying himself--as Homer suggested--seems like your best bet.
Cheat . Snoke was omniscient but there was this one little thing he didn't get quite right ... There's always something you, the writer, can include that would give your hero an advantage.
There was a great story I read recently that kind of delved into this. Here's the link: http://creepypasta.wikia.com/wiki/Ascension
With the exception of monotheistic (eg Judeo-Christian tradition) gods who are basically the best at everything because they're the best at everything, gods have limits in...nearly every pantheon I can think of. Sure, gods are stronger than mortals, but they're not unlimited amounts of strong. And a sufficiently smart mortal could work around his own physical limitations. Sure, gods are bigger/faster/smarter/whatever, but they've got limits. A sufficiently smart mortal could work around those limits--not by going beyond them himself, but by organizing the situation such that it falls outside their limit...and into his. For example: -Hercules can't pierce the skin of the Nemean lion; he finds a way to kill him without piercing his hide. -The above Snoke reference. He's not omniscient (last I checked, maybe I'm wrong), but he's absurdly confident and...hubridous? Full of hubris? He knows the exact actions that (spoiler] will take; he knows exactly what (spoiler] is feeling. He just happens to be very, very wrong about what *precisely* is about to happen. (spoiler] can't outmaneuver Snoke with normal force powers or in a fair fight, so s/he has to use Snoke's hubris against him. Snoke's problem wasn't that he didn't understand (spoiler], or that (spoiler] was smarter than Snoke. He just got outplayed, blinded by excessive pride and confidence in his own abilities. -Hippomenes (greek mythology) knew he couldn't beat Atalanta in a fair race; he also knew she had a thing for golden apples. She slowed down to pick them up, and he beat her by a dick-length. And that's just off the top of my head. EDIT:: I am really, really sorry about the formatting. It wasn't supposed to be in spoiler tags, I forgot the forum autocompletes. In any other situation, that would have been awesome.
In Greek literature (or many stories involving super-powerful beings) the gods are limited to a specific set of rules by a much more powerful entity. For example, in The Odyssey, Neptune controlled Odysseus' journey because he controls the sea. But Odysseus made a deal with Hippotes who controlled the winds, which allowed him to sail back to Ithaca. If it hadn't been for his crew opening the jar, he would have bested Poseidon. In another popular story, two guys encountered The Reaper, who was bound by higher rules to let them go if they bested him in a game. By reducing the terms of engagement to Battleship, Clue, and Twister, Bill and Ted easily bested The Reaper.
Have you ever read Neil Gaiman's American Gods? I would highly recommend it if you're doing a modern spin/take on gods as people. It's been adapted by Starz as a series if you like TV, and is following fairly closely through the book in season one.
