As the show’s nasty gamesters keep flipping the tables on one another, a touch of hammy acting wouldn’t exactly be out of line, and Jim Petosa’s production seems to goad the performers skyward by the sheer flamboyance of its design. Cristina Tedesco provides a shiny, high-ceilinged English manor with a white floor that gleams like a china plate; when Bob Ari, in a deluxe smoking jacket as Andrew Wyke, the writer, points a remote control, little panels of the floor slide away to reveal hidden treasures.

You can all but taste the payoff that Wyke dangles in front of Milo, the younger man (Jeffries Thaiss). And you can believe certain things that Ari and Thaiss suggest in their performances: Ari moving in great circles around the stage as he embodies Wyke’s entitled arrogance, for instance, and Thaiss narrowing his eyes and slowing down his rhythms as the seemingly outclassed Milo asks suspicious questions.

A certain intellectual relish is missing, though, especially in Ari’s Wyke. “Sleuth” is a game of wits, but you never really hear the gears whirring, or feel the little shivering triumph of single cards well played. The complications seem simplified.

On the other hand, Petosa gently teases a surprising little something out of the drama: that “Sleuth” can be played as a love song to the theater. There are statements about games and role-playing as the very stuff of life, which, of course, for theater people it is. These are notes that Ari and Thaiss sound with clarity and grace.

Petosa is leaving the Olney after running it for nearly two decades. (Round House producing artistic director Blake Robisonis departing, too; are murder mysteries the new sayonara?) Lately the Olney’s programming has moved toward the middle as the troupe recovers from rocky financial times, but Petosa has done his share of challenging audiences on an expanded campus that’s too far a trek into the northern burbs for a lot of D.C. theater buffs to venture. “Sleuth” may be a budget-friendly crowd pleaser, but the production’s heartfelt vows about art and craft make it an intriguing exit.