A bearded Carmelo Anthony was photographed with a fat cigar in his mouth at a New Year’s Eve party, though there was no word on his 2014 resolutions.

Thursday night he can start making a statement on the most important new year of his career. After missing the past three games, Anthony makes his return as the Knicks start their Texas Triangle trip in San Antonio.

There are valid reasons why Anthony might decide 2014 will be his last calendar year as a Knick, with the club crashing and burning.

On Christmas, Stephon Marbury sat four rows behind the Knicks’ bench — his first visit to the Garden in three years.

Anthony sat on the bench in a brown suit, missing his first game with a sprained left ankle. Marbury and Anthony are products of Brooklyn — Coney Island and Red Hook, respectively. Marbury became such a pariah among Knicks fans the Garden didn’t have the heart last week to put him on the scoreboard for a “once-a–Knick-always-a-Knick” introduction.

“He saw Marbury get heckled by some fans on Christmas,’’ one source told The Post. “He doesn’t want to be the next Marbury. He’s very sensitive.”

Anthony proved that sensitivity Tuesday when a fan heckled him on Twitter after he promoted the release of his new shoe , writing Anthony should care more about winning a title and it’s “disappointing” rooting for him.

Uncharacteristically, Anthony responded, “I didn’t ask for your glazed donut face ass to root for me anyway!!!!” The tweet was later deleted.

Anthony doesn’t want to be a poster boy if the Knicks spiral into a losing era, and it could influence his thinking when he makes his decision come July. Though still undecided, there’s part of him that may want to bail if he thinks the Knicks’ ship completely sinks. He does not want to be the scapegoat.

Anthony wants to play for a winner, but desperately wants to play in a big market because of his business ventures — his Jordan Brand sneaker line, his PowerCoco energy drink, his watch deal.