It should have been a cakewalk. On a Saturday afternoon in 1972 in a seedy hotel conference room in Midtown Manhattan, two men faced off across a chessboard. Well, one of them was a man—Walter Browne, a six-time United States champion regarded as perhaps the best American player not named Bobby Fischer. Facing him was a 14-year-old kid only a few years removed from his very first game. Dark, curly hair curtained his eyes. He was slight and a little over medium height, with a notable lack of physical coordination that belied a singular concentration. He was good, sometimes very good, and many observers considered him a future star. But he wasn’t Walter Browne.

Thirty-seven moves later, it had indeed been a cakewalk. But it was the kid, Peter Winston, who emerged the victor, “blowing up Browne’s position in a way that never happens to a player of his caliber,” as Chess Life magazine explained. Winston crushed the elder player so decisively that their contest would be discussed in chess circles for years, called simply “The Game.”

Winston, some thought, had the chops to be a grandmaster. Instead, a few years later, he would make a move more bewildering than anything he’d done in front of a chessboard.

ON A LATE-JANUARY AFTERNOON in 1978, Charles Hertan—then not quite 18 and visiting with his family in New Jersey—got a strange phone call. It was his friend Peter, insisting that Hertan come see him at the roach-infested Bleecker Street apartment he called home. Peter didn’t sound like himself. His words came out in a rush, like someone in the grips of a manic episode.

Hertan told Peter he couldn’t get back to the city yet, but he returned a week later, once school was back in session. It might have been around January 25, or it might have been a week after that, Mr. Hertan told The Observer in a telephone interview.

Peter shared his apartment with a roommate who kept to himself. The place was in even worse shape than Hertan remembered from the previous semester, when he’d often been among those hanging around till the late hours playing poker or blitz chess for cash. Peter looked terrible, too. He clearly hadn’t slept or bathed. His eyes darted around. He’d gone off his medication.

He was determined to go to the Meadowlands to bet on the harness races. And he wanted Hertan to come along.

“He kept wheedling me to come,” Mr. Hertan recalled. “He didn’t sound very good. I didn’t know how to refuse him.”

Hertan noted that and Peter had spent hours together in the previous months, forming a trio with another friend and competitive chess player, Mike Polowan. When the three weren’t in classes, they hung out in Peter’s apartment, listening to Jefferson Airplane, the Moody Blues and Dylan, or at Mahmoun’s Falafel around the corner, or over in Washington Square Park.

Polowan wasn’t around, though, and Peter wasn’t taking no for an answer.

So off the two boys went, taking the bus from the Port Authority. They sang the Moodies’ “Melancholy Man” together, which struck Hertan as a strangely appropriate song choice. Despite the euphoria and the sarcastic wit that was a hallmark of Peter’s personality, Hertan knew something was very wrong.

For at least an hour (Mr. Hertan’s memory was hazy here) the two gambled at the track—or rather, Peter gambled and lost while Hertan watched. The clock sailed past midnight and Hertan grew tired. But Peter refused to leave. He became angry and suddenly dashed off, disappearing into the throng. Hertan looked around frantically. He was tired and had to get home. Peter was an adult, Hertan thought. He could fend for himself.

But Charles Hertan never saw Peter Winston again.