This might not be the year and Max Player might not be the horse. But Linda Rice believes, with increasing opportunities, a female trainer eventually will win a Triple Crown race.

“There’s a lot more women training horses now than there were 100 years ago,” Rice said on Wednesday after the post position draw for Saturday’s 152nd running of the $1 million Belmont Stakes. “Chances are, given a little more time, sooner or later a woman will win this race.”

The Rice-trained Max Player drew 15-1 morning-line odds and Post No. 3 — Rice wanted to be more toward the middle of the 10-horse field — but has just three career starts and has not raced since winning the Grade 3 Withers at Aqueduct on Feb. 1.

It will be the Wisconsin-born, New York-based Rice’s second Belmont Stakes entry and third in a Triple Crown race. In 2003, Rice’s Supervisor finished fifth in a six-horse field as Empire Maker ended Funny Cide’s Triple Crown bid at the rain-soaked Belmont. Rice’s Kid Cruz finished eighth at the Preakness in 2014.

Rice, 56, led NYRA’s winter meet with 40 victories at Aqueduct, the second straight year she’s been the meet’s leading trainer. She became the first woman to win a New York training title with 20 wins at Saratoga’s meet in 2009 and that marked the first training title for a woman at a major racing venue.

She earned her 2,000th career win at Aqueduct on Jan. 12, becoming the third female trainer after Kim Hammond and Kathleen O’Connell to reach that mark.

Last year, she was ranked 251st among the world’s trainers.

But only three of the world’s top 100 trainers are women and there are just five U.S. women among the top 500 trainers.“Horse racing right now, we’re just happy to be racing,” said Rice, a third-generation trainer. “Horse racing has gone through some difficult times, just like any other business in this economy with the pandemic. I’d like to see more women get the opportunity and, hopefully in time, they will.”