At SXSW Tuesday afternoon, Peter Thiel, the entrepreneur, venture capitalist, and contrarian thinker, told the story of the day Mark Zuckerberg decided to turn down Yahoo's $1 billion offer to buy Facebook.

"The most important moment in my mind in the history of Facebook occurred in July 2006," he began.

At the time, Facebook was just two years old. It was a college site with roughly eight or nine million people on it. And, though it was making $30 million in revenue, it was not profitable. "And we received an acquisition offer from Yahoo for $1 billion," Thiel said.

The three-person Facebook board at the time--Zuckerberg, Thiel, and venture capitalist Jim Breyer--met on a Monday morning.

"Both Breyer and myself on balance thought we probably should take the money," recalled Thiel. "But Zuckerberg started the meeting like, 'This is kind of a formality, just a quick board meeting, it shouldn't take more than 10 minutes. We're obviously not going to sell here'."

At the time, Zuckerberg was 22 years old.

Thiel said he remembered saying, "We should probably talk about this. A billion dollars is a lot of money." They hashed out the conversation. Thiel said he and Breyer pointed out: "You own 25 percent. There's so much you could do with the money."

Thiel recalled Zuckerberg said, in a nutshell: "I don't know what I could do with the money. I'd just start another social networking site. I kind of like the one I already have."

Thiel described the argument Zuckerberg finally came down on like this: "[Yahoo] had no definitive idea about the future. They did not properly value things that did not yet exist so they were therefore undervaluing the business."

Thiel told this story to make a larger point about how the most successful entrepreneurs operate. He said that the best entrepreneurs, like Zuckerberg, have a definitive view about the future (in this case, an enormous, profitable social network) and plan for it; they don't willy-nilly chase luck--using statistics, probability, and iterative processes--to stumble upon something, anything that flies.

"All of us have to work toward a definite future…that can motivate and inspire people to change the world," he said. In this scenario, "luck is something for us to overcome as we go along the way, but not something that becomes this absolute dominating force that stops all thought."

Thiel doesn't subscribe to what he calls the start-up "religion" of a-b testing every tweak (until you run out of money) or incrementally-iterating at every step--to be so systematically chasing some random success that it strips out all conviction and creative ideas about the future.

The Yahoo-Facebook decision made Thiel a "little worried." He went along with Zuckerberg because, he said, the framework at his Founders Fund investment firm is to "always back the founder."

Immediately after they turned down Yahoo's offer, there were a large number of stories questioning the decision. Thiel recalled the naysayers said stuff like: "How could you have a CEO who didn't know you should sell the company?" "This is what you get when you have a CEO who is only 22 years old."

His only partial rationalization at the time was that in the history of Yahoo, it had made two $1 billion offers that were also turned down. And those were to eBay and Google. "At least I could actually make a pseudo-scientific argument that in every case Yahoo offered $1 billion and it was rejected, it was the correct thing to do," said Thiel.