Everybody has secrets. But Tom, the protagonist of Suzanne Bradbeer’s invigorating “The God Game,” doesn’t have many. No sex tapes, no history of electroshock therapy, no unfortunate Internet indiscretions. Unfortunately, Tom, whom a presidential candidate is considering as his running mate, harbors the doubt that dare not speak its name in American politics: He doesn’t quite, exactly, really believe in God. And people would like him to keep quiet about that.  “The God Game,” Hudson Stage’s first offering of the season, is an unusual play in several ways. It takes the point of view that the Republican Party can be saved from itself. And although the play clearly argues for freedom of religion — in this case, the freedom to have none — its one churchgoing, Bible-verse-quoting character is also the only one who seems determined to stick to her principles.  One of the joys of Ms. Bradbeer’s script is that although it seems awfully familiar (Robert Redford in “The Candidate,” from 42 years ago, may be the prototype), the audience can never be sure what’s going to happen next, even in the very last seconds. The script’s other strength is its wonderfully on-target contemporary use of language. “Sprinkle around a few ‘I love Jesuses,’ ” one character suggests. Another, after a discussion of Apollo 11, shakes his head and says, “I don’t know how people can be so blasé about the moon.”  The action takes place on Tom and Lisa’s wedding anniversary, which they traditionally celebrate by taking the day off. Tom (Robert Farrior) is a junior United States senator with high approval ratings. Lisa (Yvonne Perry) is the perfect political wife, who also runs a shelter for abused women and girls. Their daughter is away at an arts camp in Michigan, so they have their lovely Virginia home to themselves, until their old friend Matt (Michael Frederic) drops by for what appears to be a surprise visit.  These three have major shared history. Matt was involved in a long-term romantic relationship with Tom’s brother, Jay, who died in a car accident shortly after the two broke up. Guilt, blame and past flirtations, going back as far as college days and transcending sexual orientation, provide plenty of material for verbal battle. But Matt’s visit is strictly business. He’s working for the current Republican presidential candidate and is on a mission from the top. Matt swears that the candidate is a great guy, even though the man once referred to homosexuality as an abomination. (“Ten years ago,” Matt says in the man’s defense.)  The Hudson Stage casting seems flawless. Seated at a big mahogany desk, concentrating on his MacBook screen, Mr. Farrior looks a little like Superman in a suit — as if Clark Kent had decided to reveal his cool confidence and secret superpowers without bothering to change out of Clark Kent’s clothes. Mr. Frederic is excellent (and very funny), establishing once and for all that no actor has to “play gay” in terms of physicality.  Ms. Perry looks the part, from her salon-perfect blondness to her toned upper arms and calves, and she seems completely at ease when her character talks the way Matt wishes Tom talked. When a young girl from the shelter makes a gesture that touches her heart, Ms. Perry’s Lisa expresses her happiness by commenting that just when things seem darkest, “the good Lord shines a light.” When the subject of climate change comes up (and both Tom and Matt are in favor of fighting it aggressively), Lisa agrees, saying, “It’s right there in Scripture.”  At some points, though, Ms. Perry seems oddly uncomfortable with the characters’ back-and-forth, as if she has just time-traveled forward a few decades and doesn’t quite understand the way people talk and joke these days. It’s as if the director, Giovanna Sardelli, and the playwright see the characters as different people. Most of the time, Ms. Sardelli’s direction is sophisticated and visibly imaginative.  David Arsenault’s scenic design, the senator’s book-lined home office, is tastefully elegant. The books themselves are the only off note, all multivolume sets, all a little too shiny and new, which is funny, since Hudson Stage’s handsome new theater (this is the company’s first production there) is inside a library.  “The God Game,” by Suzanne Bradbeer, is at the Whippoorwill Hall Theater, North Castle Library, Kent Place, Armonk, through Oct. 25. Information: 914-271-2811 or hudsonstage.com.  A version of this review appears in print on October 19, 2014, on page WE10 of the New York edition with the headline: The Tension of Politics and No Religion. Order Reprints|Today's Paper|Subscribe
“The God Game,” produced by Hudson Stage, considers whether answering a call to higher public office means betraying private beliefs.