NEW YORK -- It was the gamble of a lifetime for Aaron Judge, turning down a substantial Opening Day contract extension, then posting a historic season that set a new single-season American League record with 62 homers while leading the Yankees to the postseason.

General manager Brian Cashman was on the other side of those negotiations, unable to convince Judge and his camp to agree to a pact that would have been worth $213.5 million over seven years. After a year that likely will end with Judge winning the AL’s Most Valuable Player Award, Cashman knows that the price has gone up.

“He’s a great player who bet on himself. It’s the all-time best bet,” Cashman said. “The way he navigated the season; he was healthy, and you know what he’s capable of when he’s healthy. He’s always put up huge numbers when he stays healthy, and now he’s stayed healthy for a number of years. It was a remarkable accomplishment; it was very special to watch.”

Judge led the Majors in runs (133), homers (62), RBIs (131), on-base percentage (.425), slugging percentage (.686), OPS (1.111), OPS+ (211) and total bases (391), pacing the AL with 111 walks. His .311 batting average was second in the American League behind the Twins’ Luis Arraez (.316), leaving him just shy of a Triple Crown.

Cashman said that Judge’s home run chase “captivated the entire baseball world” and “was a great gift that he gave to the industry and our fanbase.”

When Judge turned down the Yanks’ Opening Day proposal, he said that he would prefer to delay any further negotiations until after the postseason. By all indications, he and agent Page Odle have not altered that stance, and Judge appears primed to test free agency after the season.

The Opening Day proposal would have made Judge the highest-paid position player in franchise history, in terms of a $30.5 million average annual value. Could the next offer be worth $40 million per season? Is, as Alex Rodriguez speculated, $50 million a possibility?

“There’s a pot of gold there,” Cashman said. “It’s yet to be determined how much it weighs, but it’s a pot of gold, no doubt about it. So good for him. It was already a big pot, and obviously it’ll be bigger. He’s put himself in an amazing position to have a lot of choices. Obviously, we’d like to win the day on that discussion. If you need to hear it again, I’ll say it again: of course we’d love to have Aaron Judge back as a New York Yankee.”

Assuming no deal is struck before the free agency period opens, the Yankees will be involved in the bidding, but so too could the Giants, Dodgers, Mets, Red Sox and others.

“I think that history since the ‘70s, and the advent of free agency, shows that players have changed organizations,” Cashman said. “We always compete to try and keep what we’d like to keep. In some cases we’re successful; other cases, we’re not. We always try to compete and try to take free agents from elsewhere. Sometimes we’ve had a lot of success there, other times we haven’t. It’s part of the market process. That’s all for another day.”