AP Photo

Dr. Edward Thorp doesn’t look like one of the world’s most notorious gamblers. At 79 years old, he sports braces and large, wire-rimmed glasses.

But on a recent Saturday night in suburban Las Vegas, 70 of the world’s best card counters—people who memorize cards on the blackjack table to determine the probability of a good hand—nervously fluttered around Thorp inside a banquet hall. There were real-estate investors, television producers, even a group of evangelical Christians. Some donned swishy track pants and fake names like “Diamond Mike.” Others wore suits and arrived with beautiful women....