Sheldon Adelson is really into lists. On a visit to Fortune yesterday, he spent several minutes reeling off the (impressive) academic and other accomplishments of his two daughters--much to the embarrassment of one of them, Sivan, who was sitting next to him.

Before that Adelson (the "ad" is pronounced like advertising, not lemonade) had named all the countries whose populations he expects to draw on to fill the spectacularly immense new hotel/casino/shopping/entertainment complex his company, Las Vegas Sands, is building in Macau, the former Portuguese colony near Hong Kong. He listed the populations, too: Japan, 128 million. South Korea, 44 million. Taiwan, 24 million. And so on.

Adelson paused after mentioning India's 1.1 billion inhabitants--whom he said he really isn't counting as part of his potential customer base. My boss, Eric Pooley, started asking a question. "No, I'm not done yet," Adelson interrupted. "I was having a sip of coffee." He continued: "I forgot about the 1.3 billion in China."

Then it was time for the punch line. "Do you know how many people I need to come each year to make my 20,000 rooms 100 percent occupied? Two million." That's if they stay an average of three-and-a-half nights. Then Adelson started going through the other permutations: What if people stay two nights? Or one night?

"The numbers of people I need to make it work are almost infinitesimal," he said. "It's almost a no-brainer. What bewilders me is that no one else could see it."

This is the third and biggest of the "no-brainer" bets that has made Adelson, 73, perhaps the most spectacular late bloomer in the history of business. The first was his idea that the nascent computer industry really needed a trade show, which led him to launch Comdex in 1979 (he sold it to Softbank in 1995 for $862 million). The next was that Las Vegas's future was in conventions, which led him to to buy the Sands hotel and casino in 1989 and build a huge private exhibition center next to it. (He later blew up the Sands and replaced it with the much fancier Venetian.) And now Macau.

How big is the Far Eastern Las Vegas Adelson's company is creating? Here's the Adelson rundown: The Pentagon is 6.5 million square feet. The new Venetian Macau will be 11 million square feet. Add in the other hotels Adelson is building on the newly filled-in space between two of Macau's islands that he has dubbed the Cotai Strip, and you get 50 million square feet. "That's eight-and-a-half Pentagons," he said, displaying a rare lapse in arithmetic.

Later in the conversation, Adelson went through all the confirmed and potential future sites for Sands-built casinos--Singapore (confirmed), Japan (likely), England (unlikely), Pennsylvania (likely), and somewhere in Southern Europe (way too early to tell).

Then he started talking about his aim to transform medical research by doling out huge grants that require researchers to collaborate and communicate far more than is now the custom. And of course, he listed the affiliations of the 40 researchers he and his wife, a physician, have signed up so far for their first such project, the Miriam and Sheldon Adelson Program in Neural Repair and Rehabilitation: Harvard, Rockefeller U., UCLA, Johns Hopkins, etc., etc.

This is the Sheldon Adelson experience, and it's hugely entertaining--if also tiring. I'd never heard of the guy until Rik Kirkland profiled him in Fortune last fall. But now he's everywhere: The Wall Street Journal put him on page one a few weeks ago, and he just leapt to No. 3 (from 15 last year and 60 in 2004) on some other business magazine's list of the 400 richest Americans. He'd taped an interview with Charlie Rose earlier yesterday, and appeared to be greatly enjoying his late arrival as one of the world's business giants.

We didn't get around to what is said to be one of the most entertaining, if frightening, Adelson experiences: Seeing how he reacts when you say nice things about his better-known competitor Steve Wynn (who is also building in Macau, but on a much smaller scale). But it may be that Adelson is interested in a new rivalry now, with the two guys ahead of him on the Forbes rich list: Bill Gates and Warren Buffett.

"People ask, 'Do you want to be No. 1 or No. 2 now that you're No. 3?'" said Adelson, whose 70 percent stake in Las Vegas Sands was valued at about $17 billion this morning (and who has a couple billion dollars more on the side). He left the question alone for a while. But then he returned to it later, after extolling the uniquely profitable and reliable nature of the gambling business.

"They talk about, 'Can you become No. 1 or No. 2? ... It seems to me that it's kind of in the cards."