A federal judge had previously ruled Ivey and companion player Cheng Yin Sun didn’t meet their obligation to follow gambling regulations on four occasions in 2012 by having a dealer at the Borgata arrange Baccarat cards so they could tell what kind of card was coming next.

Last week the judge ordered the pair to return $10.1 million to the casino. The order by U.S. District Court Judge Noel Hillman essentially returned both sides to where they were before Ivey and Sun began gambling at the Borgata.

The sum includes money that Ivey won playing craps with some of the money he won at the card table.

“This case involves the whims of Lady Luck, who casts uncertainty on every hand, despite the house odds,” Hillman wrote in his opinion. “Indeed, Lady Luck is like nectar to gamblers, because no one would otherwise play a game he knows he will always lose.”

He added that deciding the case involved “voiding a contract that was tainted from the beginning and breached as soon as it was executed.”

Ed Jacobs, the attorney for the nine-time World Series of Poker bracelet winner, stressed that the judge affirmed that Ivey had followed every rule of Baccarat and did not commit fraud.

“What this ruling says is a player is prohibited from combining his skill and intellect and visual acuity to beat the casino at its own game,” he said, adding Ivey will appeal the ruling soon. “The casino agreed to every single accommodation requested by Phil Ivey in his four visits because they were eager to try to win his money.”

The judge rejected a request by the casino to use a formula for calculating damages that could have seen the restitution go as high as $15.5 million. That method, assessing how much the casino could have won had Ivey and Chen not engaged in a style of play known as edge-sorting, was deemed too speculative.

The Borgata claimed the pair exploited a defect in cards that enabled them to sort and arrange good cards. The casino says the technique violates state casino gambling regulations. But Ivey asserts his win was simply the result of skill and good observation.

The Borgata claimed the cards used in the games were defective in that the pattern on the back was not uniform. The cards have rows of small white circles designed to look like the tops of cut diamonds, but the Borgata said some of them were only half-diamonds or quarters. Ivey has said he simply noticed things that anyone playing the game could have observed and bet accordingly.

The judge noted that Ivey and Sun instructed dealers to arrange the cards in a certain way, which is permitted under the rules of the game, after Sun noticed minute differences in them. But he ruled in October that those actions violated the state Casino Control Act and their contractual obligation to abide by it in gambling at the casino.

Neither the casino nor Ivey’s lawyer immediately responded to requests for comment Monday.

The judge rejected a request by the Borgata that Ivey repay nearly $250,000 in comps — listed only as “goods and services” — the casino extended him while playing there.