The poker press routinely described the two pro players as grand masters, and endlessly parsed their styles. Mr. Ferguson, whose official first name is Christopher, was the mathematically minded Ph.D.; Mr. Lederer, the strategic Kasparov of Texas Hold ’Em. As the years went by, Full Tilt became a powerhouse in the cultish world of Internet poker. By 2010, Americans were gambling $16 billion a year through such sites, according to PokerScout.com.

But on April 15, players in the United States went to fulltiltpoker.com and found this message: “This domain name has been seized by the Federal Bureau of Investigation.”

Federal authorities had blocked access to Full Tilt and two other top poker sites, Absolute Poker and PokerStars, and accused all three of money laundering and fraud. In poker circles, April 15 became known as Black Friday.

But Black Friday was just the start. A bigger bombshell hit on Sept. 20, when prosecutors asserted that Full Tilt was, in effect, the biggest bluff in poker. In a civil complaint, the Justice Department said certain Full Tilt executives, among them Mr. Ferguson and Mr. Lederer, had defrauded players of hundreds of millions of dollars. Full Tilt, the accusations went, was not just a poker site, but also a vast, global Ponzi scheme.

However this scandal plays out — Full Tilt and its executives have denied wrongdoing — the Internet poker debate is now stretching from the tables of Las Vegas to the halls of Congress. (Absolute Poker and PokerStars are reimbursing American players; PokerStars denies that it broke laws, and Absolute said it would not be appropriate to comment on the case.)

In a bid for legitimacy, poker sites and players are pushing for the federal government to legalize, regulate and tax online poker. Big-name casinos, sensing opportunity, have thrown their weight behind the idea. Pushing back are conservative Christian groups like Focus on the Family, which argue that such a step would put a federal seal of approval on Internet gambling, with potentially disastrous consequences.

Could online poker go legit? It might sound crazy, given the uncertain future of online poker in general, and of Full Tilt in particular. (The French investment firm Groupe Bernard Tapie has agreed to buy Full Tilt, provided that the site’s legal troubles are resolved). And yet Big Poker and its fans say the best way to safeguard players would be to give Washington a piece of the action. Prying the game out of the dark recesses of the Web could yield many billions of tax dollars for public coffers, these people say.

The push to legalize the game comes despite a federal law that tried to curtail online gambling in 2006. Banks and credit card companies are basically prohibited from processing payments from online gambling companies to individuals. But many legal experts say the law is murky, and the industry is itching to expand.

Whatever the qualms about online gambling — nightmare situations, real and potential, are many — Uncle Sam is leaving a lot of money on the table. Over 10 years, legal online gambling could generate $42 billion in tax revenue, according to the Congressional Committee on Taxation.

An estimated 1.8 million Americans played online poker last year, and some make a living at it. Because of the legal issues in the United States, online card rooms typically base their computer servers elsewhere, in places like Costa Rica or, in the case of Full Tilt, in the Channel Islands.

Online poker fans, including some with money frozen in accounts at Full Tilt, are among the most vocal proponents of legalization. “It’s the only industry on earth that is clamoring for the U.S. government to impose regulations,” says Bradley Cole, an online poker player in Oxford, Miss. Mr. Cole said he had about $5,000 in his Full Tilt account on Black Friday.

Oddly enough, Internet gambling is already legal in the nation’s capital. Earlier this year, the District of Columbia became the first jurisdiction in the United States to legalize it. Officials there said they hoped the move would bring in $13 million to $14 million a year in tax revenue. But Washington may only be the start. Several bills now working their way through the House of Representatives would give online poker the run of the country.

IN five-card poker, there are 2,598,960 possible hands. A four-of-a-kind is dealt once in about 4,000 hands, a royal flush once in 650,000. And yet aficionados say poker isn’t really a game of chance. Instead, they argue, it is a game of skill — of mathematical probabilities and human psychology, played with artful direction and misdirection. The answer to this one question — chance or skill? — may well set the course of the multibillion-dollar business of online poker.

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