They throw a mean “check” right hook. 

It’s April 18 and Max Medley is having an amateur sparring session at the inaugural Interclub chess boxing event at the iconic Gleason’s boxing gym in Dumbo, Brooklyn.

As is common with this paradoxical pursuit, the scrimmage had come down to a contest between brains and brawn.

As the superior chess player, the 26-year-old architect knew he could excel in the strategy game component — provided he could survive the boxing round.

However, his opponent, the more skilled fighter, had “come out swinging.”

“I’m not going to have to win in the boxing….I just need to play better chess than you,” Medley recalled to The Post. “So the whole time I’m boxing, I’m thinking about just getting through this so I can win in chess.”

Thankfully, brains prevailed that day. Medley triumphed via checkmate despite, as he put it, “getting my a-s beat.”

“It was very difficult,” recalled the relieved athlete, who showed up to his white-collar gig the next day bearing the bruises like something out of the movie “Fight Club.”

But this was not an officially sanctioned tournament bout with cash prizes or belts on the line, but rather a duel fought purely for the fun and challenge.

Medley is one of a growing contingent of regular professionals embracing the hybrid pastime, which combines speed chess and live boxing sparring, no experience in either required.

The hour-and-a-half classes that combine “high intensity cardio, technical ring work and strategic chess training” take place every Sunday morning at Gleason’s in partnership with Chessboxing NYC, and cost $40 for a drop-in, $20 for Gleason’s members or $60 for unlimited.

As the name suggests, contests alternate between 11 rounds of chess (six rounds) and boxing (five rounds), 3 minutes each.

When time expires, contestants pause their match, don boxing gloves and step into the ring before it’s back to the game board.

Victory is achieved through knockout, checkmate, time forfeit on the chess clock, resignation in either discipline or referee stoppage.

Ironically, Medley believes that boxing is more important, quipping, “It’s kind of like you’re asking who would win in chess boxing Prime Mike Tyson versus Prime Magnus Carlson.”

However, Alex Selden, who runs Chessboxing NYC with his wife Cassandra Angelini-Vazquez, told The Post that the match is more “dictated by chess.”

“I would say 70% of matches end with checkmate or losing on time [for the chess game],” said Selden, a three-time Nassau County chess champion. However, he noted that chess players need to be fluent enough in fisticuffs “so they don’t get potentially knocked out in the first boxing round.”

The somewhat subterranean pastime dates back to a 1992 comic by French graphic novelist Enki Bilal, before Dutch performance artist Iepe Rubingh staged the first live chess boxing match in Berlin in 2003, before it gained popularity around Europe.

“Putting them together makes you a pretty unique character,” Selden said.

He first saw a clip of the sport in 2013 while attending college in Syracuse and thought it was uniquely suited to Gotham, given the city’s legendary boxing and chess scenes.

During spring of 2020, Selden was awaiting a call from Rubingh to discuss the future of the brains and brawn biathlon.

But the phone never rang. He learned later that Rubingh had died that morning.

“That was kind of a lightning bolt moment where it was like, ‘We’re going to do it no matter what,’” declared Selden. 

After the COVID-19 pandemic, he devoted six months to learning boxing with various trainers while simultaneously starting a chess club called Bushwick Chess so they could “make connections” in that world before splicing the two pastimes.

Despite Bruce Silverglade, the owner of Gleason’s gym, helping accelerate the craze, die-hard boxers didn’t know what to make of the activity at first.

“They were like, ‘Why are those people hitting bags and then playing chess?” Angelini-Vazquez pointed out.

Today, NYC boasts three major chess boxing clubs — Chessboxing NYC, ITC Chessboxing and Manhattan Chessboxing.

Angelini-Vazquez said the sport attracts a highly “eclectic crowd,” ranging from finance to tech guys and even people hailing from jiujitsu and other martial arts.

“We also have a bit amount of women that are interested in it because for them it’s like, ‘Oh, if there is chess, maybe the boxing is more accessible,” she said.  

What’s the appeal of this somewhat incongruous pursuit? “Being just fit is overrated, being the smartest is overrated. Being good at both is fun. I think also it’s cathartic to do both things at once,” Angelini-Vazquez explained.

“For me, it’s kind of like a mental triathlon,” she said, adding that it offers a fun, lighthearted respite in a city where people often take everything too seriously.

However, mastering this hipster-sounding activity is no mean feat.

Along with his weekly chess-boxing training, Medley competes in weekend chess tournaments, does private lessons throughout the week, and even wakes up at 6 a.m. to practice boxing at his local gym.

“It’s not just how good you are at chess, how good you are at boxing,” he explained. “It’s how hard can you dig through and reach and hold on to that chess player when you are in that primal zone because you’d be surprised how much your chess ELO (rating system for chess players) drops after one boxing round.”

A 2019 study of boxers and Muay Thai fighters found that just three 3-minute sparring rounds resulted in memory problems and impaired communication between the brain and muscles. 

Then, of course, there’s the head trauma concern.

Even Medley admits that the sport is “kind of contradictory” given that chess is viewed as “good for your brain” while boxing is, well, the opposite. 

However, he adds, “Your brain and your body are actually just decaying every day,” he said. ”And none of us are getting out of this alive.”

Selden emphasized that organizers are taking a responsible approach to the pastime. “It’s real punches to the face, this is real boxing, this is real chess,” he said. “There’s no gimmick about it. Safety first is the most important thing.”

Because chess boxing is not sanctioned by the New York Athletic Commission, bouts are relegated to exhibitions and amateur showcases.

He hopes that being battle-tested in NYC’s notoriously strict combat sports scene will help legitimize a pastime that’s often viewed as some underground bloodsport. 

“Our goal is to get cozy with USA Boxing in such a way that we can start having regular competitions here,” he said. “But also having copycat clubs pop up, maybe in the greater New York area or in the Tri-State area. I think there are a lot of possibilities.”