Karen Abbott is the author, most recently, of “Liar Temptress Solider Spy: Four Women Undercover in the Civil War.”

At the heart of every true-crime story is one inevitable fact: Someone is lying. In most cases, the lie pertains to innocence vs. guilt, a clear showdown between the prosecution and the defense — or, in recent trends, between musty boxes of long-forgotten evidence and documentary filmmakers seeking the errors contained within, on a quest to solve a mystery or correct a possible miscarriage of justice. But seldom does the alternative scenario arise: when doubt hovers not over guilt but over motivation — and, even more confounding, when there appears to be no motivation at all. This is the captivating question at the center of "Ranger Games," Ben Blum's singular true-crime tale about his cousin, Alex Blum, that at once upends and expands the genre. The book offers no shocking, whispered confession (a la "The Jinx") nor a heartfelt attempt at exoneration ("Making a Murderer"). Instead, it is a riveting exploration of the malleability of memory and the stories we choose to tell — to others and to ourselves.

The facts of the crime are clear: Late on the afternoon of Aug. 7, 2006, a silver Audi A4 pulled up to a Bank of America branch in an industrial section of Tacoma, Wash. Four men, wearing ski masks and body armor, entered the bank and overtook it with terrifying efficiency, wielding an arsenal of AK-47 assault rifles, pistols and duffel bags to hold their loot. The gang’s leader — distinguished by striking blue eyes peering through the slit of his mask — launched himself ninja-style over a glass partition and made specific demands: fifties and hundreds, no dye packs, no bait money, no serialized bills. Obey or be killed. He would later be identified as Spec. Luke Elliott Sommer, a highly respected and battle-tested U.S. Army Ranger.

Two minutes later, hauling a bounty of $54,000, the men retreated and met up with their getaway driver, Alex Blum, a cocky, goofy 19-year-old wearing flip-flops and board shorts. After his arrest, everyone who knew Alex was seized by one question: How had he allowed such a reckless, futile scheme to ruin his carefully plotted life?

“Ranger Games,” by Ben Blum (Doubleday )

It was inexplicable. This was Alex, who since childhood had been obsessed with one specific goal: become a U.S. Army Ranger and serve his country abroad. At the very moment he participated in the armed robbery, he was supposed to be on a plane home to Colorado, so he could say a brief goodbye to his family and girlfriend before deploying to Iraq. No mere soldier, Alex was a DICK — Dedicated Infantry Combat Killer — who had endured a notoriously brutal training program. “The Rangers did not need soldiers,” Ben Blum writes. “They genuinely wanted cadets to quit. At times they actually seemed to want to kill them.”

As Alex awaited his fate in a federal detention center, he proposed an explanation about his detour into criminality. His indoctrination into the Rangers was disturbingly akin to that of a cult, a process not unlike the brainwashing of the Manson family or Patty Hearst, during which his mind was systematically emptied of everything he’d ever known about himself and the world around him. In a 23,000-word memo titled “Breaking Point: Teaching America’s Youth to Kill,” he recounted the experience in harrowing detail. Highlights included pouring Tabasco sauce in his eyes to stay awake, asking fellow recruits to urinate on him for warmth, and helping a friend remove socks from feet so raw and bloodied that their soles peeled clean away. So thoroughly had this ordeal rewired his mind, Alex concluded, that he believed the bank robbery wasn’t a crime at all; rather, it was an elaborate training exercise planned by his Rangers superior, Sommer, the blue-eyed thief who’d scaled the bulletproof wall. Sommer gave an order and, robbed of the capacity for critical thought and free will, Alex blindly obeyed. “I was unable to think or question,” he wrote. “I was a model Ranger.” He distributed this manifesto to his family.

Alex’s first cousin Ben Blum, meanwhile, was experiencing a crisis of his own. A math prodigy — by age 13, he was studying physics and calculus at the University of Colorado — he had grown disillusioned with analyzing algorithms and abstractions, fearing that his prodigious talents ran “perpendicular or worse to the real meaning of life.” Alex’s predicament presented a different type of puzzle to solve, twisted and dark and untidy with the quirks of the human mind.

Blum instinctively applies scientific principles in an attempt to garner clues. As a child, he played a game of phrenology, studying the distinct curves and gradations of relatives’ heads for insights into their personalities. Investigating Alex’s case, he constructs a model of his cousin’s brain to discern how it had gone terribly, tragically wrong. Realizing that calculations alone won’t provide the answer, he analyzes differences that “were no longer just geometric,” taking stock of the endless accumulation of moments, large and small, that create an enduring family dynamic. But these “emotional truths,” as Blum calls them, come with their own limitations: How does one reconcile a dynamic rife with embellishments and omissions? And to what extent do the lies of the dead imprint upon the minds of the living?

As Blum delves deeper into the mystery, math and logic remain his secret weapons. Despite his growing affection for his cousin, he is able to acknowledge that some of Alex’s statements do not add up. To get closer to the truth he needs distance, and Blum acquires it in the most expedient way possible — striking up a correspondence, and something approaching a friendship, with Sommer, the alleged mastermind of the operation. The 20-year-old Sommer offers an equally strange explanation for his behavior: He wished to expose war crimes committed by U.S. troops in Iraq and Afghanistan. In a serendipitous coincidence, Sommer — a charismatic, beguiling character reminiscent of a less bloodthirsty Hannibal Lecter — is also unusually skilled at math. Both men use the connection to assess each other’s intelligence and intentions, a game Blum eventually wins. Having abandoned math to launch his crusade, he must harness its power to fit the final piece into place.

Blum is as gifted with language as he is with numbers, and “Ranger Games” is an extraordinary book, a thrilling, bumpy journey into the complexities of the mind, with its capacity to protect and betray — often within the very same moment. His investigation into his cousin’s downfall spurs his own tumultuous but ultimately triumphant resuscitation, a shedding of his dangerous habits and destructive thoughts. In the book’s surprisingly poignant conclusion, the cousins are wholly liberated from old restraints, both internal and external. All of the lies have been identified and filed away, on their way to becoming history. Neither man, finally, has anything left to prove.

Ranger Games

By Ben Blum

Doubleday. 412 pp. $28.95