“Honestly? That’s so ‘Goodfellas,’ ” Travis Prescott, an executive at one of the more prominent sites, PerHead.com, said in a telephone interview. “With our setup, everything is streamlined and anyone can run their operation on their own.”

The best per-head sites are run like any large business and attract an increasingly diverse customer base, with demographics far beyond the stereotypical image of the mob-connected bookie. PerHead.com, for example, is based in Costa Rica and has nearly 100 employees working in a gleaming, modern office building. There are six full-time employees focused on I.T., working to ward off hackers and maintain the company’s servers. There is one person dedicated to increasing the company’s search engine optimization, which helps attract bookies of all experience levels, Prescott said.

Prescott said the surge in per-head start-ups began in earnest about three to five years ago — perhaps in response to government crackdowns on traditional online sports books. Although exact figures are unavailable, some estimates have the number of per-head sites operating to be “in the hundreds,” Prescott said.

“Younger bettors are used to ease and quality — they don’t want busy signals or guys who don’t answer their phone,” Budin said. “They want Web sites. They want a number they can trust where someone says, ‘How can I help you?’ if they have to call.”

Thomas, a longtime bookie in the New York metropolitan area who asked that only his first name be used because of the illegal nature of his work, said using a pay-per-head site had revolutionized his business. His customers can place bets at any time. It is a big change from the old days, when many bookies took bets only until 8 or 9 p.m. even though games on the West Coast began later. Those who want to place a complex parlay, or multiple-team wager, can call one of the Web site’s clerks, instead of him, to get an immediate reply on how much that bet will pay out if it wins.