MINNEAPOLIS — Jake Cave came up through the minor leagues hoping to play in big games like Monday night’s ALDS Game 3.

The day dreaming just usually included Cave in pinstripes, not playing against them.

But the Yankees’ 2011 sixth-round pick was back in the Twins lineup Monday night, trying to help them live another day against a handful of players he used to call teammates.

“I think it’s really cool that you can go out there and compete against somebody and hate them, and then after the game you can talk to them and have a beer with them,” Cave said before batting ninth and playing left field for Game 3. “I think that’s what’s beautiful about the game. So it’s been really neat to be able to play against some of my buddies at this level.”

Cave spent seven years as a Yankees minor leaguer before getting added to the 40-man roster after the 2017 season. But he didn’t last long there, getting designated for assignment the following March so the Yankees could make space for Neil Walker. It opened the door for a trade to the Twins in exchange for Luis Gil, now a 21-year-old right-handed pitcher who is currently the Yankees’ No. 4 prospect, according to MLB.com.

The trade has worked out well for both sides. Cave got the opportunity he couldn’t find in New York, playing 163 games for the Twins over the last two seasons and batting .262 with a .795 OPS and 111 OPS-plus. After a late-July demotion to Triple-A this year, Cave came back up to the Twins and got hot at the right time, posting a .940 OPS in his final 37 games to help clinch the AL Central.

“I think I proved I can play at this level in any capacity that’s needed,” said Cave, who went 0-for-2 in Game 2. “I feel like I can play left, center and right. I can bat anywhere in the order they want me to bat. I’m just going to go out there and compete and keep that reputation.”

Cave shared the outfield often with Aaron Judge on his way through the Yankees’ minor league ranks — in 2014 at Single-A Tampa, in 2015 at Double-A Trenton and in 2016 at Triple-A Scranton/Wilkes-Barre. While they never got to be teammates in the big leagues, Cave believes he still ended up in a good spot.

“It is cool to be able to go out there and look across the field and see my buddies and see the Yankees and be like, ‘Hey, you know, I made it on to a really good team and I got to play for a really good team,’ ” Cave said. “So maybe if I never got to make it with the Yankees, I showed that I could play at this level.”