MASHANTUCKET, Conn. — For gamblers skilled at counting cards, it can be especially risky to play at America’s tribal casinos: Those who have gotten caught tell stories of seized winnings, wrongful detentions, or worse.

Casino bosses everywhere have ways of making so-called “advantage players” feel unwelcome, regularly tossing and blacklisting them. But gamblers have limited options to press claims of mistreatment at Native American-owned properties, which generally are shielded from lawsuits in outside courts by laws recognizing tribes’ sovereignty.

Now, a pair of lawsuits in federal courts is testing the principle of tribal immunity in cases involving allegations of abuse and bias in tribal justice systems.

The cases, in Connecticut and Arizona, involve crackdowns on advantage players who say they use card-counting or other methods that shift the odds in their favor, but generally are not illegal.

“You do not have a level playing field,” said Stanford Wong, a Las Vegas-based gambling expert who advises readers of his newsletters to be aware that tribal properties are governed by their own laws. “In a tribal casino, there’s no recourse whatsoever. You can’t sue them in regular court. The odds are all stacked against you.”

At the country’s largest Indian casino, Foxwoods in southeastern Connecticut, three gamblers from China claim the casino wrongly seized $1.6 million deposited as “front money” and $1.1 million in winnings after accusing them of cheating at mini baccarat during a graveyard shift on Christmas Eve 2011. The gamblers said they used a card-monitoring practice called edge-sorting, which involves players being able to tell the difference between some cards because of imperfections on their non-playing sides.

The gamblers including Cheung Yin Sun, a woman known as the “Queen of Sorts” for her card-monitoring skills, said they were denied the lawyer of their choice in tribal proceedings that ended with a ruling against them by the tribe’s gambling commission.

When the gamblers filed suit in federal court, the casino’s owner, the Mashantucket Pequot Tribal Nation, argued it had immunity, and a federal judge in early June dismissed the suit. The attorney for the plaintiffs has asked for the case to be reopened and is considering an appeal.

In the United States, there are 493 Indian casinos and 1,262 commercial casinos. In 2013, tribal casinos generated $28.3 billion in revenue while commercial properties had $37.7 billion, according to the Casino City research firm.

The options available to gamblers who want to press a claim depend on the contracts between tribes and the host states, which typically grant rights to operate locally in exchange for a share of revenue. The state of Connecticut, which does not require the tribe to waive sovereign immunity, has seven gambling regulation officers assigned to Foxwoods, but their role is limited to testing of the slot machines whose revenue is shared with the state. The state has no oversight of table games.

While tribal gambling commissions answer to the same tribes that own the casinos, National Indian Gaming Commission spokesman Michael Odle in Washington said they operate independently. He said those alleging a lack of impartiality could make the same argument about federal courts handling cases involving the U.S. government.

George Henningsen, chairman of the Pequot gaming commission, said it’s difficult to dispel allegations of bias because it’s typically only losers who speak out about their experiences with tribal justice.

A handful of lawyers around the country with expertise in gambling disputes say the worst horror stories are at tribal casinos. While some hope to bring pressure to put tribal properties on the same legal footing as commercial casinos, one attorney, Bob Nersesian, said he is more focused day to day on helping the clients who call with claims of abuse.

In the Arizona case, advantage players filed suit after they were detained on suspicion of cheating in 2011 at the Mazatzal Casino, owned by the Tonto Apache Tribe. A federal judge in Arizona last year ruled that sovereign immunity did not apply because tribal officials involved were named in their individual capacities, but a federal appeals court is now weighing whether tribal immunity should apply.

One of the plaintiffs, Rahne Pistor, said the officers who detained him did not identify themselves as police and grabbed his genitals as they assaulted him.

“I simply had won more money than they liked,” Pistor said, “so they kidnapped me, handcuffed me, forced me into an isolated back room in the casino and physically stole whatever money they could out of my pocket.”

Nersesian, the plaintiffs’ attorney in the Mazatzal case, said such disputes do not discourage advantage players from visiting tribal casinos. If anything, he said, they draw them out in greater numbers by showing the games can be beaten.

“It’s more like somebody dying from a hot shot of heroin,” he said. “As soon as that happens, the market goes up, not down.”