(AP) — Whether the New York Yankees want to celebrate it or not, there seems to be a decent chance for Alex Rodriguez to move into sole possession of fourth place on the all-time home run list Thursday night at home.

Rodriguez has an excellent history against Baltimore Orioles starter Chris Tillman as they match up in the opener of a four-game series.

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General manager Brian Cashman said over the weekend that the team won’t pay a $6 million bonus to Rodriguez for his 660th home run, which he hit Friday in Boston to tie Willie Mays for fourth.

With that in mind, it’s unlikely there will be any special tribute in the Bronx if Rodriguez hits No. 661. He is 5 for 10 with three homers against Tillman.

Tillman (2-3, 6.23 ERA) went 1-1 with a 1.98 ERA in four starts against New York last year when Rodriguez was out of baseball. That included a seven-inning effort in an 8-0 road win June 22 after he went 2-3 with a 9.62 ERA in his first six outings at Yankee Stadium.

The right-hander lost his second straight start Friday when he yielded two runs with seven strikeouts over seven innings in a 2-0 loss at Tampa Bay.

Tillman has also has trouble facing Mark Teixeira, who is 7 for 21 against him. Brett Gardner is 6 for 27 in this matchup.

Gardner sat out Wednesday’s 5-1 defeat at Toronto with a stiff neck, though he could return Thursday. Chase Headley went 0 for 4 after missing one game with a sore lower back.

Second baseman Jose Pirela went 2 for 4 in his season debut after being out with a concussion. Stephen Drew moved to shortstop, with struggling Didi Gregorius getting the night off.

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Baltimore (12-13) could welcome shortstop J.J. Hardy for his season debut Thursday. Hardy has been out with a strained left shoulder and manager Buck Showalter said it’s possible he could play in the series opener.

The Orioles make the short trip to the Bronx after totaling three runs in losing twice in Queens to the New York Mets, including Wednesday’s 5-1 defeat.

Adam Jones was 1 for 7 in the two games. He went 5 for 11 with two homers in the first series between these teams when Baltimore took two of three April 13-15.

The Yankees (17-11) dropped two of three to the Blue Jays after going hitless in six at-bats with runners in scoring position Wednesday while Toronto was 2 for 9.

“That’s the difference in the ballgame,” manager Joe Girardi said. “We didn’t get the hits with runners on, they did.”

New York has captured the last three starts by Nathan Eovaldi (2-0, 3.81), who allowed two runs over 6 2-3 innings to earn Saturday’s 4-2 win at Boston.

The right-hander made his lone career start versus Baltimore on April 15, allowing two runs and striking out nine in five innings as he did not receive a decision in a 7-5 road loss.

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Eovaldi’s .328 opponent batting average is one of baseball’s worst marks.