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Harold Hamm is an unlikely billionaire: the 13th child of Oklahoma sharecroppers whose identity as a self-made man could just be his downfall in his impending divorce battle.

Hamm, the founder and CEO of Continental Resources, is the world's 34th-richest person in the world, with a personal fortune of an estimated $20.3 billion.

The oilman is in the second week of a divorce hearing from his wife of 25 years, Sue Ann, and experts say the only way he can avoid paying half of his assets - and possibly losing a controlling share of his company - is to argue that his fortune is the result of sheer dumb luck.

The amount divisible in the divorce settlement is $17 billion.

Legally, if Hamm can prove that the appreciation of the marital assets was passive, rather than an active attempt by him to increase his wealth, then they will remain his property.

'You have a piece of vacant land before you get married, a separate property. If you do nothing about it and by passive acts it increases [in value], for instance they build a railroad next door or a road, fine, it’s passive,' prominent New York divorce attorney Raoul Felder told Yahoo Finance.

'But if you make a victory garden on there or you build a house, it’s now active.'

In essence, for Hamm to keep the $17 billion in question, he would have to contradict the popular image of himself that he has projected for decades as an astute businessman and innovator and instead say he simply got lucky.

The analysis of Kenneth Button, an expert witness hired by Hamm's wife Sue Ann, was laid out in court testimony and in a document provided to Reuters by Oklahoma County Judge Howard Haralson. It is one of the first pieces of financial testimony to be released from the trial, which has been conducted mostly in secrecy.

Unusually for a divorce case, Haralson has barred the public from the courtroom on most days and sealed most of the evidence. He says he is trying to protect shareholders in Hamm's Continental Resources from the release of confidential business information.

Through his 68 percent stake in Continental, a leading driller in North Dakota, Harold Hamm is believed to own the most oil in the ground of any American.

The family also worked to keep word of the divorce from going public. The case was originally titled Jane Doe vs. John Doe when Sue Ann filed the suit in 2012, alleging that her husband was unfaithful. The identity of the parties was only discovered in March of 2013.

The couple was married in 1988 and has two daughters, Jane and Hillary, from the marriage. The family split its time between four homes, including a two-mansion family enclave in Nichols Hills, Oklahoma, with its own combination basketball and tennis court, which the couple bought in 2009. Harold Hamm also has three children from a marriage that ended in divorce in 1987.

Behind closed doors, the case has had its own sensationalistic highlights. Sue Ann went through the trouble of installing surveillance equipment in the home beginning in 2007, according to court documents. One bill alone was to the tune of $9,866.09. Lawyers for Harold are demanding the 'home video or audio recordings' be turned over, in an attempt to show their separation effectively occurred before 2012.

The recently introduced document, a trial exhibit marked 'confidential business information,' is a 122-page report compiled by Button, a PhD economist. Haralson released the report after determining it isn’t subject to the protective order he has placed in the case.

Button's report contends that up to $15 billion of the growth in Continental's market capitalization during the period he studied is 'active' marital capital, or subject to division between the spouses. Button crunched data from the years between the couple’s 1988 wedding and February 2014.

Since then, Continental's value has grown by nearly $4 billion more, adding to the wealth the court may divide, Button said in court earlier in August. About $2.6 billion of that appreciation would accrue to Harold through his 68 per cent stake in Continental.

All told, Button's analysis suggests that the marital capital subject to division could add up to some $17.6 billion.

If Judge Haralson accepts Button's reasoning and awards Sue Ann a significant share of the marital estate, the Hamm split could yield the largest divorce settlement ever. If Hamm has to sell Continental shares to finance a large settlement, his control of the company could be eroded.

Attorneys for Harold Hamm and for Continental didn't respond to questions from Reuters. Harold's witnesses will testify later in the trial, which began last week and is expected to end in October.

What caused Continental's increase in value is critical to the outcome. Under Oklahoma law, any increase in the Hamms' net worth resulting from the active efforts of either spouse during the marriage is considered part of the marital estate.

The dubious distinction of most expensive divorce settlement goes to Russian businessman Dmitry Rybolovlev, who forked over $4.5 billion to his ex-wife Elena after their divorce concluded this year.

The marriage of Elena and Dmitry, both 47, had soured recently, leading into a years-long divorce proceeding.

'He was not very subtle with his infidelities,' Elena's lawyer David Newman told the Daily News of Dmitry.

The business magnate, nicknamed the 'fertilizer king,' was valued around $8.8 billion.

During the divorce, he unloaded cash on various properties, including a share in French soccer club AS Monaco, two islands belonging to Aristotle Onassis and a $88 million apartment overlooking Central Park for his then-college-age daughter.

Rybolovlev also reportedly had the opportunity to save himself some money.

A $1 billion settlement deal was offered by Elena shortly before the court's decision that was nixed by a lawyer for Dmitry's trust.

The divorce was first filed in 2008, when Elena said she had finally had enough with her husband's unfaithfulness. In documents submitted to the court, Elena described wild yacht parties where Dmitry shared 'young conquests with his friends, and other oligarchs.'

Continental's impressive growth itself isn't in dispute. According to Button's report, the Oklahoma-based driller was valued at between $10 million and $50 million when the couple wed in 1988. It is now worth around $27 billion.

Sue Ann Hamm's legal team contends that this growth resulted largely from the active leadership and astute decision-making of Harold. He is widely credited as a pioneer in developing the Bakken Shale formation of North Dakota, America's largest oil discovery in decades.

Harold's attorneys will try to show that Continental's growth resulted mostly from factors beyond his control. They signaled this strategy in their cross-examination of Button, pressing the economist to consider that external forces, such as higher oil prices and new drilling technologies, were decisive factors in Continental’s success.

Button is trying to undercut Harold's position by comparing Continental's spectacular growth with that of rivals. The margin by which Continental's financial returns outpaced those of similar oil and gas companies should be considered Continental's 'active' appreciation, the Button report says.

It compares Continental's financial returns to those of 76 other publicly traded US independent drillers.

Continental and these 'peer companies,' the report says, faced similar risks, opportunities and market conditions - such as fluctuating oil prices, choices among technologies and drilling locations, and methods to raise and deploy capital.

Continental's return on investment was at least 44,271 percent during the Hamm marriage, Button wrote. The average return among peers - extrapolated over the same period - was a relatively modest 691 percent, the report says.

Continental's outsize returns compared to its competitors are 'likely the results of difference over time in the specific operational decisions and actions of the management of these companies.'

Hamm founded Continental in 1967, two decades before his marriage to Sue Ann, a former attorney at the company.

Continental has said the divorce is a private matter that hasn't affected the business and isn't expected to. At the same time, Continental attorneys have submitted hundreds of thousands of pages of documents in the trial in support of Harold. They also have repeatedly persuaded the judge to seal evidence and close the courtroom to avoid damaging Continental's interests.