On a rainy afternoon at the Rikers Island Jail Complex in New York City this week, five men and one woman wearing tan uniforms sat in front of chess boards surrounded by an audience of correction officers and fellow inmates.

Maurice Ashley, a 2003 U.S. Chess Federation grandmaster of the year walked from one board to the next, simultaneously playing six games. One by one, he eliminated the inmates—except for Camilo Arcelay, 37 years old, who used his king to take Mr. Ashley’s last pawn. That left Mr. Arcelay and Mr. Ashley...