This is something I read in the mid-to-late 1980s, probably in a thick collection of short stories.
"Second Game" is a novelette by Katherine MacLean and Charles V. De Vet, the first story in their Kalin Trobt series; originally published in Astounding Science Fiction, March 1958, available at the Internet Archive. The "thick collection" you read it in could be the one I'm looking at: from 1980, weighing in at x+768 pages, The Arbor House Treasury of Great Science Fiction Short Novels.
A man who is acting as a spy or maybe just a researcher goes to an alien planet. The aliens of this planet are human-like (or possibly a human colony planet), but are very xenophobic and do not allow what they consider aliens in their society.
They are very humanoid aliens:
Earth's colonies had expanded during the last several centuries until they now comprised a loose alliance known as the Ten Thousand Worlds. They were normally peaceful--and wanted peace with Velda. But you cannot talk peace with a people who won't talk back. Worse, they had obliterated the fleet bringing our initial peace overtures. As a final gesture I had been smuggled in--in an attempt to breach that standoff stubbornness. This booth at their fair was my best chance--as I saw it--to secure audience with the men in authority. And with luck it would serve a double purpose.
The protagonist has become fairly expert at a game that they play on the planet, which for some reason I am thinking had similarities to go (aka weiqi, igo, or baduk), and has decided to participate in a large regional or global competition.
The alien game is more like chess:
Several Veldians gathered around the booth and watched with interest as my opponent and I chose colors. He took the red; I the black. We arranged our fifty-two pieces on their squares and I nodded to him to make the first move.
The Earthian protagonist explains how he learned the alien game:
"I learned it before I came. A chess adept wrote me, in answer to an article on chess, that a man from one of the out-worlds had shown him a game of greater richness and flexibility than chess, with much the same feeling to the player, and had beaten him in three games of chess after only two games to learn it, and had said that on his own planet this chesslike game was the basis for the amount of authority with which a man is invested. The stranger would not name his planet.
"I hired an investigating agency to learn the whereabouts of this planet. There was none in the Ten Thousand Worlds. That meant that the man had been a very ingenious liar, or—that he had come from Velda."
Much is made about the fact that in a critical game against one of the planet's masters, the protagonist attempts a kind of three-pronged attack (called a "triple push"?) when normally even a double-pronged attack is considered nearly impossible to pull off.
Is "triple decoy gambit" close enough?
The following evening when we began to play I was prepared to give my best. I was rested and eager. And I had a concrete plan. Playing the way I had been doing I would never beat Yondtl, I'd decided after long thought. A stand off was the best I could hope for. Therefore the time had come for more consummate action. I would engage him in a triple decoy gambit!
I had no illusion that I could handle it—the way it should be handled. I doubt that any man, human or Veldian, could. But at least I would play it with the greatest skill I had, giving my best to every move, and push the game up the scale of reason and involution—up and up—until either Yondtl or I became lost in its innumerable complexities, and fell.
The only other thing I remember is that, while being taken somewhere in a vehicle on the alien planet (on the way to the tournament?), the protagonist is deeply frightened by the experience of being on a highway due to the apparent insanity of the traffic system, which has rules he doesn't understand.
I climbed into Trobt's three-wheeled car as it stopped before me, and the minute I settled into the bucket seat and gripped the bracing handles, Trobt spun the car and it dived into the highway and rushed toward the city. The vehicle seemed unstable, being about the width of a motorbike, with side car in front, and having nothing behind except a metal box that must have housed a powerful battery, and a shaft with the rear wheel that did the steering. It was an arrangement that made possible sudden wrenching turns that were battering to any passenger as unused to it as I. To my conditioning it seemed that the Veldians on the highway drove like madmen, the traffic rules were incomprehensible or nonexistent and all drivers seemed determined to drive only in gull-like sweeping lines, giving no obvious change of course for other such cars, brushing by tricars from the opposite direction with an inch or less of clearance.
He ends up losing the game but comes close enough to winning that it causes a stir, and as a result he is discovered by the local authorities. I think it's revealed that they've known he was an outsider for some time but tolerated him for reasons I can't recall.
He loses the final game against the alien master, but he's found out as an Earthian early in the story, after he beats a strong player at the fair:
Suddenly his eyes widened. His glance swept upward to my face and what he saw there caused his expression to change to one of mingled dismay and astonishment. There was but one move he could make. When he made it his entire left flank would be exposed. He had lost the game.
Abruptly he reached forward, touched his index finger to the tip of my nose and pressed gently.
"After a minute, during which neither of us spoke, I said, "You know?"
He nodded. "Yes," he said. "You're a human."
[. . .]
I suppressed an ineffectual impulse to deny what I was. The time was past for that. "How did you find out?"
"Your game. No one could play like that and not be well known. And now your nose."
"My nose?" I repeated.
"Only one physical difference between a human and a Veldian is apparent on the surface. The nose cartilage. Yours is split—mine is single." He rose to his feet. "Will you come with me, please?"
It was not a request.