Mississippi Grind puts a captivating, contemporary and sometimes comic spin on the antebellum allure of a downriver gambling odyssey — soaking in the sights of the trip and soaring on the unexpectedly excellent juju of the odd-couple casting for the two low-rollers at its center.

Ryan Reynolds is Curtis, a motormouth raconteur living on the make, Ben Mendelsohn is Gerry, a poker-playing mope whom Curtis befriends and bankrolls for a trip to New Orleans, and Grind offers career-best work from both men. (The film opens Friday at the Fort Wayne Cinema Center in Fort Wayne and will hit on-demand video systems later this month.)

Often the hard-charging heavy (and usually great at it), Mendelsohn (Animal Kingdom and The Dark Knight Rises) resourcefully retreats from his usual oily menace into a man so mousy and melancholy he can hardly express the malcontented misery he has made for himself. Instead, Gerry pursues preposterous patterns in the ponies he plays and the poker hands he’s dealt. Of course he’s obsessed with rainbows — a pleasant byproduct of nasty storms we wish for but rarely receive. Gerry’s hunches are sometimes good … but that’s any gambler. We initially thrill as Curtis sparks Gerry’s pilot light. But then we see how little control Gerry has over this flame and how much of his life it has consumed. By journey’s end, we sense Gerry has broken down beside this road to “redemption” many, many times.

Playing a man of inherently suspicious charm, Reynolds chips away at the hawkish, haggard hunger behind Curtis’s happy exterior. The actor is still quick with a quip in his rat-a-tat rapier way, but also uncommonly contemplative of Curtis’s swiftly narrowing options. “It’s not losing, it’s entertainment,” Curtis shrugs after a bad night at the tables. He certainly takes games less seriously than Gerry, but the jovial novelty with which Curtis uses this line to inure himself to a long, fruitless stroll is wearing thin. An errant Don Quixote in his own mind, Curtis wears tarnished armor and a battered shield. Reynolds takes lumps for his big-budget flops, but his high-risk choices such as this are almost invariably high-reward. Those who’ve written him off think flip is his default setting, but Reynolds finds sincerity, depth and surprises here.

At best, a talkative poker player is an obvious tell awaiting detection and exploitation. At worst, he’s a nattering annoyance who has a chilling effect on the table. Thus, we immediately assume Curtis is out to undermine Gerry at the Iowa riverboat casino where we meet both men. Gerry orders a cheap house bourbon, Curtis ponies up to get him a Woodford Reserve. Certainly Curtis has played this mind game of pity on plenty of guys like Gerry, whose talk is so small it’s practically Lilliputian.

Instead the duo strikes up a friendship forged by a form of sexless seduction, in which Curtis colorfully conveys his life’s itinerant idiosyncrasies. The outlandish specifics wash over us, but they seep into Gerry’s bones; this, this is the gambler’s holiday he could aspire to if only his life weren’t all if onlys. Gerry’s Realtor job is tenuous. So is a leash on his six-figure debt to a deceptively friendly loan shark (Alfre Woodard). Curtis has certainly backed lamer horses, so he takes Gerry up on his offer: Gerry’s car and Curtis’s cash in a $2,000 stake to build a pot en route to a high-stakes New Orleans poker game.

So begins a Huck-and-Jim tale in a beat-up Subaru, with detours to casinos that dot the drive to the Delta, a touchy reunion with Gerry’s ex-wife (Robin Weigert), and St. Louis rendezvous with prostitutes (Sienna Miller and Analeigh Tipton), neither of whom ticks the easy box of hooker with a heart of gold. With her cartoonishly broad makeup, Tipton is a young woman who hasn’t yet figured out her face let alone her life, and Miller’s Simone — whom Curtis has long failed to pull into his permanent orbit — throws drunk-tank sobriety on his fizzy fantasies of being flush with cash.

Through believable byplay, Reynolds and Mendelsohn explore how these two men inspire, and invert, each other’s good fortune. The script — by Ryan Fleck and Anna Boden (Half Nelson), who also co-direct and edit the film — avoids the usual tells of comeuppance and betrayal or bogging us down in the finer points of table games. Instead, it forces Curtis and Gerry to confront their predictably corrosive tendencies and the unpredictable ways in which they come to complement each other. We keep waiting for one of their sharp-cleated shoes to drop on the other’s neck … but Grind gently trades compassionate character-building for cutthroat suspense at every turn. There is immense pleasure in Grind’s unhurried, unfussed pace — the sort of film that, 40 years ago, might have starred another Reynolds (Burt) alongside, say, John Cazale and been just as accomplished.

As in their baseball film Sugar, Fleck and Boden put a soft touch on the hard truths of life in America’s heartland. The tics and tenors of the cities Curtis and Gerry visit — as well as the casinos that dot their drive down to the Delta — lend Grind a gritty travelogue feel; Fleck and Boden have certainly done their homework on Gerry’s neck of the woods, a river town on the wrong side of boom-and-bust.

Just like their protagonists, though, the filmmakers miss the right time to step away from the table. You’ll know the perfect ending line when you hear it … and cringe when that next cut is not to credits. Setting aside the fine way Mendelsohn and Reynolds trade confidence and desperation in repeating the line “We can’t lose,” the finale feels shuttled in from a more simplified version of the story. Curtis and Gerry’s stories both wrap up neatly but the film walks away poorer for it. In a film as generous and genuine as this, no viewer would confuse a lack of certainty for cheap cynicism.

Until that easy-out ending, Mississippi Grind offers an effective, empathetic study of all its characters, as well as a respective smallness and sincerity you’ve not seen from Mendelsohn and Reynolds. They’re the real winning hand in this drama about the aftermath of frail human hopes battling the cards’ cold logic.