Sunday, 1 April 2001

April

You may have come here,

Seeking the rules,

In which case you’ve fallen,

For Cassini’s April Fool’s

Friday, 2 February 2001

Thirteen Against The Bank by Norman Leigh


Originally published ten years afterwards, this book recounts one man's efforts at training up a team of system roulette players and travelling to Nice in the South of France during the late summer of 1966. Whilst there they applied his system with cast iron discipline, allegedly cleaned out the local casino, were eventually barred and finally obliged to leave France by the French Authorities.

Whilst the main events of the story did indeed take place, despite being a fairly enjoyable read I think it comes closer to an adventure from the Enid Blyton stable than being a "true and detailed account" of what actually happened - some aspects seem suspiciously detailed considering they were written about so much later. The author, who was aged thirty-eight at the time the story takes place, states he was a lifetime roulette obsessive, a heavy drinker, had never applied himself to very much apart from roulette and was "no candidate for canonization". Within the book's foreword he also admits to having been accommodated at Her Majesty's expense for a time, having been found guilty of fraud some two years after the team returned home and disbanded. Thirteen against the Bank is his tale of the last in a succession of visits to the South of France undertaken, over many years and with many others, for the purpose of beating the wheel.

Never having succeeded, he convinced himself of the validity of a theory published in 1923 by the Hon.S.R.Beresford, third son of the third Baron Decies, that the reason people lost so much playing roulette was less about the impact of the house edge and more about the consequence of increasing bets when losing and chasing losses. So if he adopted a system of keeping bets at a constant level when losing, but increased them when winning the additional player exposure risk the house enjoyed when players chased losses, and laid out more and more money, would be reversed and he'd benefit from this "advantage" as the bank played against wagers made with money it had lost - albeit with its mathematical edge remaining unchanged. An instance of turning the tables so to speak.

Following on from this he adopted the Honourable Mr B's suggested "system", which takes the already known Labouchere negative progression system (one where you bet more when losing to recover losses), and simply reverses the staking plan to arrive at the Reverse Labouchere - bets would be progressively increased as successive wins occurred, but remained constant when they didn't. By betting on both opposing sides of an evens-payout option (ie red and black together), barring zero being spun the result would be no loss (lose one, win one) and he could carry this on until a prolonged positive streak occurred and he could ride it whilst increasing bets up to the table limit. Furthermore, by having six players at the table, all covering the six evens-payout options he'd increase the likelihood of one of them hitting such a streak, which he refers to in the book as a "progression" and one of his team members as a "mushroom". All sounds workable? Unfortunately, despite all of this the house edge was always there, and by arranging to cover all of the evens-payout options, instead of just two of them that lay off each other, he was simply increasing the amount wagered, and therefore the amount exposed to it, by a factor of three.

The premise of this unbeatable system seems to be based on the chance that streaks of continuous winning results will occur often enough, and continue for long enough to reach the table limit, to generate sufficient winnings to offset the losses resulting from the zero being spun and the house edge biting. Unfortunately, the fatal flaw in the system, as with all roulette systems, is the inevitability that the variance will average out, and with sufficient volume of play there'll come a point where even a result that's three standard deviations north of the EV will still leave players out of pocket. After that, no amount of favourable results will ever recover the accrued losses sustained. The house edge will have done its job. Within the story there's no mention made of players keeping a tally of the amount they'd wagered during each session, and so presumably nobody was keeping track of the team's EV and the actual results relative to it - a major oversight by the team manager. Or was it?

Some have suggested that perhaps maths may not have been the author's strong point, although I'm not so sure? In his story he contributed none of his own capital to the enterprise and all of his team were required to pay all of their own travel and accommodation expenses, and provide a minimum amount of £250 stake money (the equivalent of £4,200 today) in order to apply his system in France - he carried no financial risk, apart from his own travel and accommodation expenses, and made his money by taking 10% of any winnings. Interesting that the tally of the winnings that took place regularly never seemed to take account of the losses suffered by each player, when their progressions petered out and they had to start the betting sequence again, to arrive at a net profit for those sessions? Nice work if you can get it - take a percentage of the gains, but suffer none of the losses every team member had to take on the chin?

I suppose a question is could the Reverse Labouchere be applied today, on the prospect of just getting lucky? Sure, and you might just be so. But as casinos nowadays have a five or ten times table minimum bet requirement on evens-payout options, and maximums of 500 or 1000 times table minimum, the scope for recouping sustained losses from progressing to the table limit is fairly limited over what it may have been in the past. You could reduce the exposure by betting 6 lines (6 lots of 6 numbers, so all of them bar the zero) at the table minimum with a co-player, which would mean betting 6 units per spin rather than 20 but achieving the same coverage and providing some el-cheapo entertainment into the bargain. It might be fun, but don't be under any illusions that the longer term prospects for this system lead South. Accurate and comprehensive record keeping will expose it's fallibility.

After reading the book, I did wonder what became of Norman Leigh? Half an hour searching the web provided the answer; I came across some postings from someone who knew and had played roulette with him together with two entries on the Amazon review page for Thirteen against the Bank from his niece and his ex-wife, Pauline. Her recollections of the outcome of the trip to France in 1966 contrast starkly with those in the book. Unsurprisingly it seems he never managed to beat the wheel, was declared bankrupt three years after his book was published and lived the latter years of his life impoverished and reliant on state benefits. He was admitted to Queen Alexandra Hospital, Portsmouth, late in 1992 suffering with pneumonia, and whilst there suffered a fatal heart attack resulting from his illness. He died on 4th January 1993, aged just sixty four.
To an outsider it does look as though Norman Leigh was just another in a long line of people whose ruin can be attributed to the "devil's wheel". No doubt there'll be many more in the future. No coincidence that when you add all of the numbers on a roulette wheel together you get 666; there's a message in there somewhere?

Thirteen against the Bank was reprinted in 2006 and remains available from all major book retailers.

November 2014

Postscript

Shortly after I finished reading Thirteen against the Bank I wrote to Pauline, Norman Leigh's ex-wife, and she kindly agreed to meet me and answer some questions . . .

Q. Was the team really made up of an Etonian, a publican, an ex-copper, a glamourous mum, an elderly widow etc? Can you recall the backgrounds of the team members you met?

A. I think the characters portrayed in the book are a fairly accurate reflection of the team's mix. The Etonian, named as "Blake" in the book, who acted as Norman's second, was actually a stockbroker. All of the characters' names have been changed of course, and I think it would be indiscreet of me to name them.

Q. Was the team's barring from the Casino Municipale in Nice carried out in the respectful manner described in the book, or was it simply a case of them being turned away at the door one day with no reason being given? Are you able to elaborate?

A. I don't know as I didn't join the team until after they had been barred from playing at the Casino Municipale in Nice.

Q. At what point did the French police become involved (if at all) and to what extent?

A. Again, I don't know. The team certainly wasn't ejected from the Country, as after I joined them we stayed in France for a further three weeks and returned home voluntarily (and broke).

Q. After the team's members were barred, did you all travel to any other casinos in France to try your luck?

Yes. By the time I joined the team they were already playing at the Casino du Palais de la Mediterranee, which is also in Nice.

Q. Do you know how much money was actually won or lost on the trip - for Norman and the individual team members?

A. No. I became aware that things weren't going too well when the letters Norman had been sending home, that contained French banknotes, dried up and the amount of money we had to pay for our stay in France dwindled; we went from enjoying three meals a day to having just one. Eventually, after three weeks, a meeting of the team was called to decide whether to continue or not. Norman was all for carrying on, but the majority voted not to and to return home. I recall that towards the end of the discussions "Blake" turned to Norman and said, "Mr Leigh, you are a dreamer and your wife is a realist!".

Norman and I travelled back to England, all the way through France, by train on third class rail tickets. Some members of the team, who were staying in better hotels and were not short of funds, opted to stay.

Q. Your father gets a mention in the book, and Norman describes him as "old school" when meeting him for the first time. What was his reaction to the plan to travel to France to break the bank at roulette?

A. If I recall rightly he was calm and uncommitted when I told him of the plan, and said something along the lines of "if that's what you want to do, good luck".

Q. After returning to the UK, were there any plans for the team to continue playing together in casinos in Britain?

A. No. I'm pretty sure that those members of the team who returned home had all lost money.

Q. Did you and/or Norman ever meet up with any of the team members after the return from France?

A. Just once. Norman and I met up with one couple for dinner, but that was the only time.

Q. Did Norman subsequently continue to play roulette and plan around "beating the wheel"?

A. I'm sure he did. He always had one scheme or another in hand, including selling "winning systems".

Q. In the book's foreword, Norman admits to having been convicted on a fraud charge in 1968 and of serving time as a result (although he doesn't state how long). Is this something that happened whilst you were still together? If so, would you be willing to share the details?

A. I'm afraid I can't recall the circumstances of the case or the charges. Around that time we had to give up our house in Twickenham; I'd foolishly allowed him to use my name on some HP agreements, and shortly after that he was convicted and accommodated by Her Majesty's Prison Service. I know he was sent to prison on more than one occasion and was made bankrupt.

Q. Are you able to provide any details of Norman's fortunes after your separation and divorce?

A. After we separated I returned to the Isle of Wight and Norman was convicted. Our divorce formalities took longer to conclude than they needed to as a result of Norman making difficulties from prison. After he was released, he did contact me and ask if I could help him out with some money, but I declined - during our marriage, all of my savings and a bequest from an Aunt were used up supporting his schemes.

Before we were married, Norman had worked as an Insurance Agent for a short time, but resigned due to a dispute over sales and withheld commissions, and I think that was the last time he ever had a real job. Norman did come and meet our son, Julian, and a vague contact ensued until the time of Norman's death - which Julian found out about through seeing a local press headline on a newsagent's billboard.

Norman's last address was a room at the Catisfield Hotel in Fareham, which to all intents and purposes was a DSS hostel. After his death I was contacted and asked if I would go there and clear out his effects, which I did. He didn't have much and was given a pauper's funeral.

Norman's estate is still managed by an agent, and the TV and film rights to his book are renewed by a production company every two years.

Many thanks to Pauline for indulging my curiosity.

Thursday, 1 February 2001

Ron Pollard

From the Daily Telegraph's Obituary pages, 5 July 2015:

Ron Pollard, who has died aged 89, changed the face of British betting by taking the bookmaking business beyond horse and greyhound racing into the more exotic arenas of beauty contests, politics, book prizes and the arrival of aliens from outer space.

Guided by his principle that “betting should be fun”, Pollard’s genius was to realise that many punters would cheerfully bet on outcomes far less likely than their being struck by lightning. “It was abundantly clear”, he once said, “that the public would gamble on absolutely anything. If it moved, if it was on TV, if it caused an argument in a pub, they wanted to bet on it.”

His aim was always for his firm, Ladbrokes, to be first with anything new, thus raising its profile and encouraging more punters to use it. Having introduced betting on cricket, golf, tennis, darts and snooker, in 1977 Pollard offered odds on the existence of the Loch Ness Monster; in the same year Ladbrokes started to take bets on the arrival of aliens on Earth, giving 500-1 to a group in California run by a woman who claimed to be a reincarnation of the Mona Lisa.

Pollard offered odds of 1,000-1 against Elvis Presley returning from the dead. Although he conceded that this was a “tasteless exercise”, Ladbrokes took so much business that it soon had a £2·5 million liability, and he had to cut the price to 100-1. The safest bet he ever laid was placed by a teenage girl: 5,000-1 against her taking tea with a reincarnated Elvis by the end of 1982.

Although these stunts were not always profitable – Ladbrokes had offered 100-1 against a man walking on the moon in the 1960s – he appreciated that they reaped for his firm “the most precious commodity of all: publicity”.

Pollard did not attribute his success entirely to his own acumen. He was a self-confessed spiritualist who believed that he was guided by a 15th-century bearded Chinaman in a white skull-cap. His interest in this field had been aroused in 1955 when, aged 29, he accompanied his mother-in-law to Kennards, a department store in Croydon, where she consulted a medium.

Although then a sceptic, Pollard also saw the medium, who caressed the young man’s comb before pronouncing: “Goodness gracious, I wish I was going to have your life. You are going to be in all the papers, everyone wants to know what you are saying, and you are going to Buckingham Palace [to] meet members of the Royal Family.” It was she who alerted him to the presence of his Chinaman. Twenty-four years lat er Pollard was honoured as “Spiritualist of the Year”.

His greatest coup came in 1963, when he introduced betting on politics with the “Tory Leadership Stakes”: “For two weeks I did not know if I was a bookmaker or a film star. The telephone did not stop ringing. I was constantly on television and radio. Everyone wanted a quote.” Sir Alec Douglas-Home (the eventual winner, who had initially ruled himself out of the contest) was installed at 16-1; Ladbrokes took £14,000 on the exercise, making a profit of only £1,400. But the company was now known across the world.

At the next general election, in 1964, Ladbrokes opened a book. The hotelier Maxwell Joseph bet £50,000 on a Labour victory, winning £32,272 when Harold Wilson emerged with a five-seat majority. Had the Tories won, the firm would have lost £1·5 million — money it did not have. Pollard was so concerned about this outcome that he resolved to commit suicide in the event of a Conservative victory.

The £640,000 that Ladbrokes took on that election was the record at the time for any single event (including the Derby or the Grand National). In the general election of 1966 the firm took £1.6 million.

Before long, Pollard was being entertained by MPs at the House of Commons. At the time of the Conservative Party’s leadership election of 1975 he was invited to lunch at White’s, where someone inquired what odds he was offering on Margaret Thatcher to win the Tory leadership. Pollard replied: “Fifty to one.” Pollard’s companion confided: “I would be very careful if I were you.” The odds were immediately slashed to 20-1.

Occasionally, Pollard’s political antennae (or his Chinaman) let him down, as in the general election of 1970, which the Conservatives unexpectedly won, costing Ladbrokes around £80,000. Some members of the board wanted Pollard sacked; but the chairman, Cyril Stein, remained loyal, telling his colleagues: “If he goes, I go.” The odds-maker survived.

Ronald James Joseph Pollard was born in London on June 6 1926. His paternal grandfather distributed relief money to the unemployed, and would visit pubs in Southwark disguised as a chimney sweep to see if any of his clients were spending their welfare on beer. Although Ron’s father was the accountant to a mineral water company, the family had little money and his mother worked from home as a glove machinist. At school in Peckham Ron failed to shine academically but enjoyed playing football and cricket. He left with no qualifications.

He got a job as an office boy in a building firm at Peckham, learning bookkeeping. On Saturdays he went greyhound racing at Catford. Then, in 1943, he became a ledger clerk with William Hill at the bookmaker’s office in Park Lane. At first he ran errands, such as paying a jockey who had obligingly finished second on a hot favourite at Goodwood. At this stage Hill’s was operating illegally by handling cash betting, which was then allowed only on the racecourse (transactions off-course had to be on a credit basis).

Although he was called up for the Army, Private Pollard was still at Westcliff-on-Sea on VE Day. He then served on the Gold Coast, where he was promoted to sergeant and won the Gold Coast ping-pong championship two years in succession.

He returned to Britain in 1947, and was demobbed the following year, returning to work for William Hill. He was made a course clerk, recording the bets taken by the Hill’s representative, and occasionally acting as the bookmaker at some of the smaller meetings; he was then appointed manager of the accounts department.

Pollard joined Ladbrokes as credit manager in 1962, the year the firm opened its first betting shops. “These were still the days of credit betting, and you had an account with Ladbrokes at their Burlington Street offices only if you were in Debrett,” he said. “If you were in trade, no matter how prosperous, you had no chance of an account with the firm that had a direct telephone link to Buckingham Palace for the regular royal bets that would be struck, sometimes daily.”

Before long he had been appointed general manager of Ladbrokes, and, in 1964, he was made a director of Town and Country Betting, the Ladbrokes holding company which was to become Ladbroke Racing. In the same year he became the firm’s PR director, remaining there until his retirement in 1989.

Among Pollard’s most famous stunts were his forays into the Miss World contest. These did not endear him to the organisers, Eric and Julia Morley. After Julia Morley accused him, apparently without irony, of “dragging [the contest] into the cattle market”, and banned him from the Miss World rehearsals in a television studio, Pollard disguised himself as a carpenter (complete with overalls, cloth cap and a tool kit) and spent a morning assessing the attributes of the candidates on whom he was to make a book.

On another occasion he assumed the character of a waiter, sporting a false grey moustache, to penetrate the dining room at the Dorchester where the finalists were attending a function. Pollard was extremely successful in predicting the outcomes of Miss World, and in 1982 personally won £5,000 when Miss Dominican Republic took the title. His guiding principle was: “The sexy ones never win.”

When it came to fixing odds for the Booker Prize, Pollard would read the first 60 or so pages of a novel; a similar number in the middle; and the final 60.

Pollard himself was not a habitual gambler (betting “only when I thought I knew something”) and did not have a high opinion of those who were: “The reason why people bet has nothing to do with money. They do it because they want to get one up on the other fellow and because they want to be right.”

He was an entertaining man and a fine raconteur who courted, and made many friends among, the press. A lifelong socialist, his greatest regret was that he never became an MP; he claimed to have been offered a seat by all three main parties.

In 1991 he published an autobiography, Odds & Sods: my life in the betting business.

Ron Pollard is survived by his wife, Pat, and three children.

Ron Pollard, born June 6 1926, died June 10 2015

Navinder Singh Sarao – The Hound of Hounslow

It took Navinder Singh Sarao a long time to accept that he might have been scammed out of $50 million. Stuck in London’s Wandsworth prison, wracked with anxiety and unable to sleep, the realization dawned on the man dubbed the “Flash Crash Trader” as slowly as spring turned to summer outside the barred window of his jail cell.

The trauma of the past few weeks had been difficult to process. On April 20, 2015, the slight, doe-eyed 36-year-old had dozed off peacefully in the same suburban bedroom he’d slept in since he was a boy. The next day he was arrested and taken to a police station, where he was charged with 22 counts of fraud and market manipulation carrying a maximum sentence of 380 years.

According to the U.S. government, the British day trader had made tens of millions of dollars using an illegal practice called spoofing, including, fatefully, on the morning of May 6, 2010, when the Dow Jones Industrial Average fell almost 1,000 points in minutes before bouncing back. The extent of Sarao’s culpability for the flash crash is fiercely contested, but the incident exposed the shaky foundations on which the hyper-fast, computer-dominated financial markets now rest.

Sarao’s bail was set at 5.05 million pounds ($6.3 million). It was a hefty sum, but according to the accounts of his company, Nav Sarao Futures Limited, he’d earned 30 million pounds in the previous five years. Newspaper reports, in which Sarao was dubbed “The Hound of Hounslow,” speculated that he’d be back with his family in the shabby West London borough by the weekend. 


Instead, the nightmare got worse.

Where’s the money, Nav, his lawyers wanted to know. Sarao couldn’t make bail, they gradually learned, because the bulk of his wealth was tied up in investments and offshore trusts, each more complicated than the last. Days in Wandsworth prison, a Victorian-era fortress where Sarao was housed with sexual predators and violent offenders, turned into weeks.

After four months of dead ends, his legal team struck a deal with the authorities: If the U.S. Justice Department and the Commodity Futures Trading Commission agreed not to oppose a reduction in bail to 50,000 pounds, the firm would act as a bounty hunter, taking on responsibility for tracking down the missing millions on the condition that its fees be paid if it did.

They were going down a rabbit hole. A review of Sarao’s investments from 2005 to the present day, based on dozens of interviews and thousands of pages of documents, reveals another twist in an already remarkable story. 

Navinder Sarao, the trading savant accused of sabotaging the world’s financial markets from his bedroom, may himself have been the naïve victim of what his lawyers portray as a series of cons that stripped him of almost every cent he earned.

Sarao declined to comment for this article. His lawyer, Roger Burlingame of Kobre & Kim in London, told a U.S. judge in November that all of the defendant’s assets “have been stolen.” Sarao invested in ventures from which he, the law firm and the CFTC had been unable to recover the funds, Burlingame said. “Basically, he has some extraordinary abilities with respect to pattern recognition and certain sorts of mathematical abilities, but he has some fairly severe social limitations.”

Sarao’s trading career started inauspiciously in 2002 at Futex, a fledgling outfit in an unglamorous office an hour from the City of London that housed wannabe traders in exchange for as much as 50 percent of their profit. In a roomful of recent college graduates and drifters, Sarao stood out from the pack.

“Nav was always going to be the kind of person that would be legendary in some way,” Futex Chairman Paolo Rossi said in an interview with Bloomberg TV after Sarao’s arrest. He had “the potential to be remembered as one of the world’s greatest traders.”

It wasn’t until Sarao left Futex in 2008 and struck out on his own that he started to make serious money. Public filings show his assets popped to 14.9 million pounds from 461,000 pounds in the 12 months ending in June 2009, long before he enlisted a programmer to build a system that authorities say was designed to cheat the market.

Former colleagues talk about Sarao’s frugality—his scruffy clothes, his reluctance to spend money on cars and watches, his abstemious eating habits. He learned early at Futex that withdrawing cash ate into his bankroll and reduced the size of trades he could place.

That near-obsessive drive to hold on to as much of his wealth as possible can also be seen in the way he conducted his business affairs. Looking to minimize his tax bill, he was introduced by his accountant to John Dupont, a director at the London arm of an Isle of Man-based financial advisory firm called Montpelier Tax Consultants.

Dupont, then in his mid-30s, was a high-energy salesman whose accent veered from upper class gent to Guy Ritchie cockney depending on who he was speaking with, a former employee recalls. Operating from an office on Cockspur Street in London’s West End, members of his team cold-called contractors, day traders and bankers and tried to enlist them in a range of plans to minimize their tax bills, documents seen by Bloomberg show.

The aim was to identify loopholes before they were closed. One former Montpelier employee said he coaxed wavering customers to sign up by promising to pay their legal bills in the event of a clampdown by Her Majesty’s Revenue and Customs. Everyone at the firm thought he was Alec Baldwin in “Glengarry Glen Ross,” the person said.

Self-employed traders were particularly good prospects because they were predisposed to high levels of risk. And Sarao, an absent-minded dreamer with an unerring gift for making money who would later be diagnosed with Asperger syndrome, would prove to be the ultimate mark.

In 2009, on the advice of Montpelier, Sarao entered into a complicated dividend-stripping scheme that resulted in a major reduction in his tax bill, according to a close adviser to Sarao who spoke on the condition of anonymity. Happy with the result, Sarao went a step further the following year, the person said.

Among Dupont’s crew was Miles MacKinnon, a polished so-called introducer who had left school for a stint as a rugby player before heading to the City of London. For four months in 2010, MacKinnon became the only other director of Sarao’s firm.

Around the same time, Sarao set up two employee benefit trusts in the Caribbean island of Nevis, according to a document filed in Sarao’s case. He plowed his earnings into those trusts, then gave himself interest-free loans to trade with and live on, the adviser said. The arrangement meant Sarao all but avoided paying corporate taxes. One vehicle was named the “NAV Sarao Milking Markets Fund.”

Dupont and MacKinnon said in an e-mail that they “did not introduce or advise” on the Nevis trusts.

Sarao had an uncanny ability to attract controversial characters. He sought advice from tax specialist Andrew Thornhill, who in 2015 would be charged by the British barristers’ industry group with five counts of professional misconduct. And, as the Wall Street Journal reported, one of Sarao’s trusts was, for a period, affiliated with David Cosgrove, the Irish director of Belvedere Management who has been barred by Mauritius authorities from serving as a company officer because of regulatory violations. Thornhill declined to comment. Cosgrove didn’t respond to e-mails.

In 2011, the British government ended the benefit-trust gravy train. Sarao paid back the loans and restructured his business. Montpelier was investigated and dissolved, and about 3,000 of its customers were ordered by a judge to pay 200 million pounds in back taxes. Fraud charges against two directors were later dropped.

MacKinnon and Dupont—along with a third partner, Ryan Morgan—then founded MacKinnon Dupont Morgan, which was later reborn as MD Capital Partners. The firm describes itself on its website as a boutique private equity firm.

They leased an office in Mayfair, home of hedge funds, Michelin-starred restaurants and private members clubs. MacKinnon joined the Worshipful Company of International Bankers and the executive board of the Special Olympics. He and Dupont set up about a dozen companies between them, focusing on industries such as renewable energy.

Dupont and MacKinnon said in their e-mail to Bloomberg that they “never made, or introduced investments to projects that are purely driven by tax breaks” and that at the time they got involved in renewables there weren’t any tax incentives in place. Morgan, who left the firm, didn’t respond to a request for comment.

By 2011, Sarao had trebled his assets to 42.5 million pounds. He agreed to become an investor in an Isle of Man-based entity called Cranwood Holdings, set up to acquire land in Scotland that would one day house wind farms, according to two advisers to Sarao. Documents on the enterprise filed in the British dependency are light on detail, but the advisers say Sarao put about 12 million pounds in Cranwood—money they say Dupont and MacKinnon could access.

Dupont and MacKinnon said in their e-mail that Sarao conducted “substantial independent due diligence” before investing in Cranwood and that he approved all of its payments. One of their companies, Wind Energy Scotland, is funded by and provides project management services to Cranwood.

The pair also acted as agents for more exotic ventures, such as sending divers to search shipwrecks for sunken treasure. The returns on offer were never less than impressive. Sarao, who told acquaintances he harbored aspirations of becoming a billionaire, invested in several. All were tame compared with what came next.

Sometime in 2012, Sarao was introduced—again through Dupont and MacKinnon—to a squat, intense Mexican named Jesus Alejandro Garcia Alvarez, who was looking for investors for his company IXE Group. Garcia said he was the scion of a family of billionaire landowners and industrial-scale farmers with swaths of land around the world. He had arrived in Zurich from Latin America a few years earlier and had been working hard to build a reputation ever since.

IXE was conceived as a one-stop shop for high-net-worth individuals, offering services ranging from asset management to event planning to advice on private schools. Then, around the time Sarao met Garcia, the company’s website underwent a radical overhaul. Gone were the concierge services. IXE was henceforth a “conglomerate of companies worldwide” involved in “agribusiness, wealth management, commodity trading and venture capital.”

Articles appeared in the Swiss media profiling the mysterious young man making waves among Zurich’s business elite, including pictures of Garcia wearing a poncho over his suit, arm outstretched across Bolivian salt plains he said he owned. One newspaper put him on its annual rich list. Garcia was invited on Bloomberg TV to talk about his family’s quinoa interests, then on CNBC to discuss the “white gold rush” for lithium.

Garcia had all the trappings of a successful entrepreneur: half a dozen sports cars, a small but well-appointed office in the center of Zurich, a glamorous Russian wife. He even joined the Swiss board of the Robert F. Kennedy Center for Justice & Human Rights, an organization whose U.S. directors include Tim Cook and Martin Sheen.

Garcia flew to London and met with Sarao two or three times, according to people with knowledge of the matter. In an interview on IXE’s website, Garcia laid out his pitch to investors: “We are offering alternative investment vehicles that provide constant returns to investors. The investment in real economy makes the advantages obvious—investors are benefiting from constant returns generated from actual transactions with zero speculation and zero volatility.”

Garcia told Sarao he would get an annual 11 percent return, the people said, and assured Sarao that any money he handed over would be used only as collateral, not put at risk. He also introduced Sarao to Swiss banking contacts, they said. The trader was again restructuring his business, this time around an Anguilla-based vehicle called International Guarantee Corporation.

Sarao did some due diligence about IXE, according to one adviser, but he seems to have overlooked a few red flags: The company website is littered with spelling mistakes, and several executives are members of Garcia’s family.

Garcia initially agreed to meet to discuss this story, then opted to respond to questions through a colleague at IXE. The colleague, Dominic Forcucci, wrote in an e-mail that Garcia hadn’t done anything improper and that IXE “properly disclosed the risks of investments” to Sarao. A lawyer representing Garcia, William Wachtel, later said that Garcia described any allegations against him as “baseless and without merit.”

On Aug. 20, 2012, documents show, Sarao agreed to give about $17 million to Garcia and his company—by far his biggest investment and a substantial chunk of his net worth. He later invested an additional $15 million, according to a person with knowledge of the matter. Even though they’d met on only a handful of occasions, he would describe Garcia to associates as a friend.

Sarao may have been particularly trusting, but he wasn’t alone in buying into the IXE miracle. Former employees interviewed by Bloomberg describe Garcia as charming and, on first meeting, impressive. He offered commissions to third-party agents to send prospective investors his way, ensuring a steady stream of business and creating a buzz around the firm.

In 2014, Garcia signed a deal to acquire Banca Arner, a Swiss lender in decline after allegations that it had helped former Italian Prime Minister Silvio Berlusconi hide money. To coincide with the transaction, Arner’s new marketing chief, Garcia’s wife Ekaterina, issued a press release announcing it had appointed a new chairman: Michael Baer, a great grandson of the founder of private bank Julius Baer Group and a respected figure in Swiss banking.

IXE just needed sign-off by Switzerland’s financial regulator, Finma. In order to seal the deal, Finma told Garcia he’d have to come up with 20 million Swiss francs ($18.7 million) in capital and account for where it came from. After heated meetings with the regulator and the owners of Arner, Garcia offered to hand over the money in unmarked gold, according to two people with knowledge of the talks. Without a stamp, the gold was unacceptable to the regulator, and in the end Garcia walked away from the deal, leaving Baer and a raft of other new recruits frustrated and embarrassed, the people said. Baer and a spokesman for Finma declined to comment.

For the time being, though, Sarao had no cause for concern. IXE sent him periodic statements showing the interest accruing in his accounts. As ever, he was happy to let it sit there and grow.

By then, Sarao’s readiness to consider almost any opportunity that offered an attractive rate of return was well-established. After another strong year in 2013, Dupont and MacKinnon introduced him to Damien O’Brien, a physically imposing Irish entrepreneur with aspirations to revolutionize the online-gaming industry.

The unique selling point of O’Brien’s company, Iconic Worldwide Gaming, according to a pitch document seen by Bloomberg, was that it allowed gamblers to bet on movements in currencies and securities using an interface that looked like an online casino, with a roulette wheel and buttons for “higher” and “lower” instead of red and black. The patented software was called MINDGames, short for Market Influenced Number Determination games.

The concept may not have pleased Gamblers Anonymous, but the financial projections were enticing. O’Brien predicted in the pitch document that Iconic would go from a standing start to a cash balance of 110 million pounds by the end of its third year. There were also some reassuring names on the board: Robin Jacob, a U.K. appeals court judge, and David Michels, a former deputy chairman of Marks & Spencer.

In July 2014, documents show, Sarao invested 2.2 million pounds in Iconic. Cranwood Holdings extended loans of an additional 1 million pounds, according to one Sarao adviser. He was, several times over, the largest investor in the company.

Dupont and MacKinnon said in their e-mail that Sarao was an experienced gambler and trader who conducted his own due diligence on the gaming sector before investing. They also said they objected when Sarao told them he planned to lend money to Iconic. O’Brien didn’t respond to requests for comment. Jacob and Michels said they were no longer board members.

In the months following Sarao’s investment, O’Brien went on a campaign to increase Iconic’s profile. The company sponsored World Touring Car Championship driver Rob Huff and filmed a slick advertisement with mixed martial arts superstar Conor McGregor. O’Brien and his employees were photographed ringside or wining and dining clients. In one shot taken in Las Vegas and posted on Twitter, a line of promo girls posed in matching uniforms with Iconic logos emblazoned on their hot pants. In another, O’Brien stood next to a matte-black Rolls-Royce with the license plate DAMI3N.

By the time Sarao was arrested in April 2015, he had about $50 million tied up in investments around the world, according to people with knowledge of the matter who even now aren’t positive it’s all accounted for. It was only as his lawyers tried to recoup the money that he was forced to face up to the possibility that it was gone. Sarao was released that August after his parents put up the family home as collateral against the bail of 50,000 pounds.

In November of last year, following an unsuccessful extradition fight, Sarao flew to Chicago where he pleaded guilty to one count of wire fraud and one of spoofing, which entails placing bids or offers with the intention of canceling them before they’re executed. He was ordered to pay $38.4 million to the CFTC and the Justice Department, which determined that, of the money he made by day trading, only $12.8 million came from cheating the market.

Sarao is scheduled to find out the length of any custodial sentence later this year. In the meantime, he has been allowed to return to Hounslow, where he is banned from trading and, despite pushing 40, placed under the care of his father.

Sarao’s lawyers are no closer to getting their hands on the money beyond about 5 million pounds seized from his trading accounts after his arrest. The CFTC and the Justice Department have joined them in the hunt, according to people close to the situation. The agencies could try to compel banks holding Sarao’s assets to give them up, but that might not be easy because most of the money is outside the U.S. Spokesmen for the CFTC and the Justice Department declined to comment, as did Burlingame, a former Justice Department prosecutor who represents U.K. targets in U.S. investigations.

IXE told Sarao it would return the cash in instalments in 2015 and 2016, according to a person familiar with the matter. The deadlines came and went, but no money has been produced. Garcia is rarely seen driving his sports cars around Zurich anymore, according to former associates. In October, German magazine Brand Eins skewered what it portrayed as his outlandish claims about plots of land in Bolivia and Mexico and linked Garcia to Burton Greenberg, who’s serving eight years in a Florida prison for fraud.

Former IXE employees interviewed by Bloomberg say that Garcia spent whatever he brought in to fund his own lavish lifestyle and that projections he gave in presentations to Sarao, Baer and others were plucked out of thin air. Still, Garcia’s efforts to acquire a bank continue. In August, IXE announced it was buying Private Investment Bank in the Bahamas from Swiss firm Banque Cramer & Cie. The deal is scheduled to be completed this month.

Garcia hasn’t been accused of any wrongdoing. Forcucci, the IXE spokesman, said the company is “working to return the money in a fair and equitable manner to its investors.”

Iconic went into liquidation in January 2016. A company hired to advise it on resale options said O’Brien had underestimated the cost of breaking into the online gaming market by about 10 million pounds.

Sarao’s lawyers have been unable to retrieve his investments in Cranwood despite repeated requests, owing to its convoluted offshore ownership structure, according to a person with knowledge of the situation. Dupont and MacKinnon said in their e-mail that Wind Energy Scotland has been working to get funds to Cranwood.

From their base in Berkeley Square, the pair last year started another company focused on renewable energy, Celtic Asset Management, which offers “access to a substantially higher return profile, with less capital at risk.”

Meanwhile, Sarao is back in his bedroom. The computer that got him into so much trouble is gathering dust in a Washington evidence room. Depending on how much the authorities are able to recoup, he will probably spend the rest of his life paying back the money he owes. If they really want it, they could always lift the trading ban, one associate quips: He’d make it back in no time.

Monday, 1 January 2001

Sharp And Soft Books

From Nikolai Livori - Sportsbook Soft or Sharp

The sports betting industry is fragmented into Sharp and Soft books, and of course a mix in between. But what does this mean? We use a more precise term by referring to them as Asian and European books respectively - with Asian books being sharper than European ones.

Soft bookmakers like the renowned Unibet, Betsson, William Hill etc. make use of a lot of traders within the company that use manual or semi-automatic odds movements to ultimately rely on gut feelings, knowledge and game statistics within the industry. They operate with high margins. They do not welcome sports traders and most of the time limit such customer accounts thus falling into the trap called a “false positive”. What if the person you just limited could have been one of your VIP Casino players? Soft bookmakers like these target mostly punters and gamblers and usually have other products to support their sports book such as Casinos, Poker, Bingo etc.

The Sharp bookmaker model is based mostly on mathematical and highly efficient automatic risk management tools. They do employ traders as well to compile odds, however balancing their book is sharper and done with the help of mathematical models. Most of the time they are able to offer better prices in the industry, due to being faster and sharper than Soft bookmakers. Most of them also do not limit bettors and accept large bet stakes, thus they welcome traders and punters alike. Examples of such books are Pinnacle Sports, ED3688, SBOBet etc. Their profit is derived on smaller margins due to a huge turnover.

Being a Soft bookmaker is becoming very challenging nowadays, considering that the Asian market is expanding at a very quick rate. Why would I place a bet on a Soft book for a much cheaper return (and also risk being erratically limited) when I could place a much larger bet at a much better price through an Asian book?  

Bundeslayga System

In September 2010, I noticed that the strategy of laying home favourites in the German Bundesliga was consistently profitable, making this an ideal system for mitigating Betfair's Premium Charges.

The rules are simple. Selections are those teams priced by Pinnacle at between 1.3 and 2.00.

In the three full seasons of 2012-15, (prior to this there is no Pinnacle price data) backing the home favourite in the top European Leagues is a profitable strategy with an ROI of 3.93% from 434 bets, but laying home favourites in Germany has been profitable in each of those three seasons.

Because the lay option is only available on the Exchanges, and Pinnacle do not offer a 'lay' price, the formula used in my calculations adjusts the home price depending on the Pinnacle over-round.

For example a Home price of 1.51 in a Pinnacle Sports market of 102% is adjusted to 1.5395.

Here are the results (updated to include 2015-16):

** Note that from 2016-17, the range has been adjusted. Please see this New Bundeslayga post for details.

New Bundeslayga

In September 2010, I noticed that the strategy of laying home favourites in the German Bundesliga was consistently profitable, making this an ideal system for mitigating Betfair's Premium Charges.


The basic Bundeslayga System layed teams priced by Pinnacle at between 1.3 and 2.00.

The results for the four seasons 2012-2016 are posted here, but with the addition of Pinnacle's closing prices to Football Data's spreadsheets, I took a fresh look at the approach and decided to tweak it for a couple of reasons. 

One was that the System was losing some of its potency - markets adapt, and my feeling is that much of the value of laying home odds-on selections was now gone (possibly in part my own fault for publicising this system).

A second reason was to determine whether the 1.3 to 2.0 range was still optimal. Eliminating shorties and odds-against selections made it a simple system, but reviewing the closing price data shows that the implied profitability range of 40% to 75% is more profitable.

The table below shows the results of the Traditional Bundslayga and for the New Bundeslayga, using Pinnacle's Closing prices.
I've left the original returns using the early scrape Pinnacle prices on this post which shows the difference that price movements can have on a system.
  
Note that because the lay option is only available on the Exchanges, and Pinnacle do not offer a 'lay' price, the formula used in my calculations adjusts the home price depending on the Pinnacle over-round.

For example a Home price of 1.51 in a Pinnacle Sports market of 102% is adjusted to 1.5395. 

1 / [( 1 / 1.02 ) * ( 1 / 1.51 )]  

UMPO System

UMPO is an acronym for Underdogs MLB Play-Off and is a simple strategy which backs odds-against underdogs in the Major League Baseball Play-offs.

Since 2004, (the first year for which I have data) it has been a steady winning strategy, and the following returns from a US site can generally be beaten on the exchanges making this an ideal strategy for mitigating Betfair's Premium Charges.

** Last Updated 9/30/18 to end of 2017 season.

I'm also retracting the above comment that this is "an ideal strategy for mitigating Betfair's Premium Charges" because the 30 games a year this system generates is a drop in the ocean.  

BLUnders System

BLUnders (Big Line Unders) is a neat little system that I came up with in the Summer of 2015 when I was asked my opinion on NBA Totals betting in games where one side was heavily favoured.


My gut response was that Unders was more likely to offer value, my thinking being that a team with a comfortable lead has a tendency to psychologically ease up, rest starters, and in addition the often crucial extra points from the fouling towards the end of a close contest are absent.

I looked at the data for the last twenty seasons to see if this idea had any merit, and found that while the older data from 1995-2004 showed more equity between Overs (474) and Unders (480), the numbers since 2005 showed more of a bias (54.8%) towards Unders (487 - 402) and since 2010, even more of a bias at 56.5% (247 - 190).

The number of qualifiers is a little under 100 per season, a very manageable number for a part-timer, although the 2015-16 season has seen an increase with the dominance of the Golden State Warriors and San Antonio Spurs having an effect.

One additional note here is that the system is even more profitable in the play-offs. In the 20 completed seasons since 1994, the Unders has a 15 - 10 advantage.

** Update after 2015-16 season. 

For the fifth consecutive season, the system returned a profit, albeit lower than the previous four seasons.
Most qualifying matches are, as might be expected, home games, but on the rare occasions (less rare over the past two seasons) when it is the Away team favoured, the results are:
The second system I play alongside the BLUnders mentioned previously meant that the combined totals for the season ended up as below:

Not the sexiest of profits perhaps, but as I have said before, their value lies in the churn volume and the ease with which selections are determined.

Spoofing

While the basic concept is easy to grasp and it sounds very easy to do, in fact trading has developed into quite a complex and tricky art, because people have designed bots and software to take advantage of the most obvious situations where trading should give you a profit. In addition there are people out there who manipulate the markets using “spoof” money, large sums which appear suddenly in an attempt to move the market in a particular direction. 

These can disappear as fast as they appear, but it is often not easy to tell the difference between spoof money and real money until it is too late. When trading you are swimming in shark-infested waters and you need to have your wits about you or you will get eaten alive.

[Courtesy of Juicestorm]

Cross-Matching

Idiot's guide to Betfair cross-matching and how it might affect your pursuit of the pennies


Byline: Alex Hankin

In the middle of February, without warning, Betfair fundamentally changed the way they matched bets. Did you notice at the time? Me neither, and while the ensuing storm of controversy has been hard to miss, the impact on your experience of using the exchange is likely to remain fairly minimal, in the short term at least.

But betting exchanges are eco-systems. Some specialist users are very unhappy. So what's it all about? As a fully licensed and accredited idiot, I can offer you this idiot's guide.

What have Betfair done?

Introduced cross-matching into their system for handling unmatched bets on sports markets.

What is cross-matching?

Take a tennis match as the most simple example. There are just two possible outcomes, so any back bet on Player A is in effect a lay bet on Player B at the reverse price, e.g. backing A for pounds 10 at 2-1 is the same as laying a bet of pounds 20 on B at 1-2.

Previously, if you wanted your tenner on A but no-one had offered to lay at that 2-1 or better, your bet would be left unmatched. After the February changes, the system would now attempt to cross-match, i.e. resolve your request with any appropriate unmatched back request on B. Betfair said "customer bet requests would stand a greater chance of being matched", and they were right.

What's the problem?

No problem - it's just fine for simple souls who use BF in broadly the same way that they use a bookmaker, i.e. one bet at a time, sweet Jesus.

So who cares?

For traders - include anyone who factors into their strategy the unmatched bets on view - this unheralded change in the system is more problematic.

At its most extreme, if you concern yourself with the pursuit of 'the pennies' - typically chasing under-rounds across whole markets or arbing individual outcomes - it looks like Betfair has just shot your fox.

And BF were upfront about that.

Retrospectively upfront, that is. "The motivation . . . is to reduce the load on the site by making it pointless for customers who use automated tools to bombard the site with traffic looking for arbitrage opportunities 'the pennies'."

What are these 'pennies'?

Risk-free money. Backing every outcome in a 99 per cent book; laying every outcome in a 101 per cent book; buying low, selling high. All that stuff.

The pursuit of these pennies has driven the explosion in trading software, bludgeoning BF's systems with a massive volume of usage that yields relatively little by way of commission.

As far as cross-matching goes, the pennies might appear in our tennis match example if there were unmatched back requests, e.g. player A pounds 1,000 at 2.02 and B pounds 1,500 at 1.98.

Those two prices combined make a 100.01 per cent book - so you could lay them both to appropriate stakes and produce a tiny profit for yourself whichever wins. In this example, there's just over pounds 20 going begging (minus commission).

Who's getting those pennies now?

Betfair - or at least they said they might have "theoretically" got them for a bit. So far, a series of announcements has not done as much as it might to clear this matter up.

Having initially failed to mention that they were cross-matching, Betfair then admitted to now potentially being in a position to trouser any spare money arising.

That didn't go down well, so BF shelved the cross-matching process, for in-play markets at least, while they searched for a way to pass the controversial pennies on to customers through advanced 'best-price' execution in the new system. That is proving a tough technical nut to crack.

Last Thursday, Betfair announced the reintroduction of cross-matching for in-play markets.

They were quick to reassure customers that now "typically" cross-matching would only occur when there was no theoretical arb involved. Unfortunately, they also gave an example of such a no-arb situation: a 2.02/1.98 tennis match (see above).

Does this cross-matching affect horse racing?

No. Not yet anyway, and the non-runner issue looks hard to resolve, although there's always in-running.

I'm a simple backer or layer - am I somehow getting stiffed by new sinister forces beyond my control?

No.

Are Betfair interfering in the market, and is that fair?

You say potato, but they say potato (slightly differently). Betfair have certainly altered the mechanism of the market and hence its behaviour - the rest is complicated.

And what's 'fair' got to do with it?

Betfair aren't some happy-clappy club for punters - they are a fully licensed bookmaker, who define their own terms and conditions under the umbrella of existing legislation, with one objective.

In the end, it's as simple as that, and only an idiot could expect otherwise.

P-value

The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event.

The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

A smaller p-value means that there is stronger evidence in favour of the alternative hypothesis.

Read more: P-Value Definition | Investopedia http://www.investopedia.com/terms/p/p-value.asp#ixzz4VXPCIrKw

Benford's Law

Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. 

For example, in sets which obey the law, the number 1 appears as the most significant digit about 30% of the time, while 9 appears as the most significant digit less than 5% of the time. 

By contrast, if the digits were distributed uniformly, they would each occur about 11.1% of the time. 

Benford's law also makes (different) predictions about the distribution of second digits, third digits, digit combinations, and so on.

It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants,and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881.

The Gambler's Fallacy And Law Of Large Numbers

The Gambler's Fallacy & law of large numbers by Mirio Mella


The Law of Large Numbers was established in the 17th century by Jacob Bernoulli showing that the larger the sample of an event - like a coin toss - the more likely it is to represent its true probability. Bettors still struggle with this idea 400 years on which is why it has become known as the Gambler’s Fallacy. Find out why this mistake can be so costly.

The Law of Large Numbers

Using a fair coin toss as an example (where the chance of hitting heads and tails has an equal 50% chance), Bernoulli calculated that as the number of coin tosses gets larger, the percentage of heads or tails results gets closer to 50%, while the difference between the actual number of heads or tails thrown also gets larger.

It’s the second part of Bernoulli’s theorem that people have a problem understanding – which has led to it being coined the “Gambler’s Fallacy”. If you tell someone that a coin has been flipped nine times, landing on heads each time, their prediction for the next flip tends to be tails.

This is incorrect, however, as a coin has no memory, so each time it is tossed the probability of heads or tails is the same: 0.5 (a 50% chance).

Bernoulli’s discovery showed that as a sample of fair coin-tosses gets really big – e.g. a million – the distribution of heads or tails would even out to around 50%. Because the sample is so large, however, the expected deviation from an equal 50/50 split can be as large as 500.

This equation for calculating the statistical standard deviation gives us an idea what we should expect:

0.5 × √ (1,000,000) = 500

While the expected deviation is observable for this many tosses, the nine-toss example mentioned earlier isn’t a large enough sample for this to apply.

Therefore the nine tosses are like an extract from the million-toss sequence – the sample is too small to even-out like Bernoulli suggests will happen over a sample of a million tosses, and instead can form a sequence by pure chance.
Applying Distribution in betting

There are some clear applications for expected deviation in relation to betting. The most obvious application is for casino games like Roulette, where a misplaced belief that sequences of red or black or odd or even will even out during a single session of play can leave you out of pocket. That’s why the Gambler’s Fallacy is also known as the Monte Carlo fallacy.

In 1913, a roulette table in a Monte Carlo casino saw black come up 26 times in a row. After the 15th black, bettors were piling onto red, assuming the chances of yet another black number were becoming astronomical, thereby illustrating an irrational belief that one spin somehow influences the next.

Another example could be a slot machine, which is in effect a random number generator with a set RTP (Return to Player). You can often witness players who have pumped considerable sums into a machine without success embargoing other players from their machine, convinced that a big win must logically follow their losing run.

Of course, for this tactic to be viable, the bettor would have to have played an impractically large number of times to reach the RTP.

When he established his law, Jacob Bernouilli asserted that even the stupidest man understands that the larger the sample, the more likely it is to represent the true probability of the observed event. He may have been a little harsh in his assessment by once you have an understanding of the Law of Large Numbers, and the law (or flaw) of averages is consigned to the rubbish bin, you won’t be one of Bernouilli’s ‘stupid men’.

Law Of Small Numbers

The Law Of Small Numbers By Joseph Buchdahl 


The law of small numbers is a cognitive bias where people show a tendency to believe that a relatively small number of observations will closely reflect the general population. Read on to test your logical powers with the hospital quiz and find out how graphs can be misleading and what you can do to avoid losses when using stats to place your bets.

The Hospital Quiz

In 1974 two psychologists, Daniel Kahneman and Amos Tversky, presented their experimental subjects with the following scenario, accompanied by a question. A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day and in the smaller hospital about 15 babies are born each day.

As we know, about 50% of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50%, sometimes lower. For a period of one year, each hospital recorded the days on which more than 60% of the babies born were boys. Which hospital do you think recorded more such days?

The larger hospital
The smaller hospital
About the same (within 5% of each other)

According to binomial theory, the number of days where boys born outnumber girls by at least six to four will be nearly three times greater in the smaller hospital compared to the larger one, simply on account of the larger volatility in birth ratios. A larger sample is less likely to stray very far from 50%. Yet only 22% of respondents gave the correct answer.

What are heuristics?

Kahneman and Tversky described this error as a belief in the law of small numbers. More generally, judgements made from small samples are often inappropriately perceived to be representative of the wider population. For example, a small sample, which appears randomly distributed, would reinforce the belief that the wider population from which the sample is selected will also be randomly distributed.

Conversely, a small sample demonstrating an apparently meaningful pattern – such as nine heads from 10 coin tosses – will cause the observer to believe that the population will display the same meaningful pattern. In this case the assumption would be that the coin is biased. The experience of perceiving patterns in random or meaningless data is called apophenia.

A belief in the law of small numbers is part of a wider group of mental short cuts that people take when making judgements under uncertainty. Kahneman and Tversky called these short cuts heuristics. Making generalisations from small samples is an example of a representativeness heuristic, where people assess the probability of a particular event based solely on the generalisation of previous similar events that comes easily to mind.

Another example of the representativeness heuristic is the expression of the gambler’s fallacy. Indeed, such a bias arises out of the belief in the law of small numbers. As Kahneman and Tversky say:

The heart of the gambler's fallacy is a misconception of the fairness of the laws of chance. The gambler feels that the fairness of the coin entitles him to expect that any deviation in one direction will soon be cancelled by a corresponding deviation in the other. Subjects act as if every segment of the random sequence must reflect thetrue proportion; if the sequence has strayed from the population proportion, a corrective bias in the other direction is expected.

Reading graphs of unequal sample sizes

Sports bettors can be particularly prone to faulty pattern recognition through a misplaced belief in the law of small numbers. Misinterpreting profitability from small samples of wagers as representative of a departure from randomness and evidence of predictive skill can have unpleasant financial consequences over the longer term. Consider the hypothetical profitability chart of 100 wagers on NFL point spreads below. Each bet is struck at a price of 1.95. Impressive, isn’t it?



What if I told you this record comes from a well-known US sports handicapper? With a decent growth trend and a yield of 15% you might be forgiven for believing me. Of course, I’m lying. In fact, the next chart of 1,000 wagers reveals the bigger picture.



Really there was no long term profitability to be had at all. The reason: this was merely produced by a random number generator which assumed a 50% chance of an individual win and a profit expectation of -2.5%. The first chart simply represents the initial 100 wagers of the second.

Yet even in the second longer time series a healthy profitability was maintained for several hundred wagers. Furthermore, despite showing an overall loss, the pattern of the time series looks anything but random, with a fairly consistent wave-like pattern to it.

However, as Kahneman and Tversky recognised, we are far more likely to perceive sequences of similar outcomes as being non-random even if there is no underlying mechanism behind them. Of the two binary sequences below, which looks random and which not?

0, 0, 0, 0 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1

0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1

The majority of people would pick the second sequence. In fact, the first was generated randomly in Excel and I made up the second purposely with shorter sequences of 1s and 0s. When asked to create random sequences like this many of us will switch from 1 to 0 or vice versa if we feel that one of them is happening too often.

Now take a look at the following 1,000-wager charts. They were all randomly generated. The large range of possible outcomes should provide you with a flavour of just how easy it is to be fooled by apparently meaningful patterns.


Remember, these are not series of 100 wagers, but 1,000. Take a look at the middle one. It has all the hallmarks of an expert tipster or bettor with a 5% yield and solid profit growth throughout the entire sequence of betting, the sort of performance the best handicappers are capable of long term. And yet it happened just by chance.

Using the binomial distribution we can work out the probability of still being in profit after a period of betting despite having an expectation of -2.5%.

Number of Wagers (odds 1.95, 50% win probability) / Minimum number of wins needed / Probability of being in profit

100 52 38.22%
250 129 32.90%
500 257 28.05%
1000 513 21.46%
2500 1283 9.68%
5000 2565 3.40%
10000 5129 0.51%

After 1,000 wagers we still have over a 1-in-5 chance of being in the black despite our betting being nothing more than random. If we placed one handicap bet on every NFL game played, this would take us nearly four seasons. That’s a long time to believe we have anything other than luck on our side.

How small is small?

The law of small numbers is a cognitive bias where people show a tendency to believe that a relatively small number of observations will closely reflect the general population. Furthermore, as this exercise has shown, small can sometimes be quite large. It exists because people favour certainty over doubt, explanation over ignorance, causation over association, patterns over randomness and skill (particularly self-serving skill) over chance. For sports bettors, failure to truly appreciate its significance can be costly.

MLB: T-Bone System

The T-Bone System (named after the person who came up with the original idea) is a baseball (MLB) system backing road favourites (-140 or hotter) coming off a loss, and introduced in 2016.

Here are the results over the past five seasons, updated to the end of 2016.

2016 was the best recent season overall, with all three bet categories (Money Line, Run Line and Overs) in profit. 

Expected Value (EV)

Expected value (EV)

In probability theory, the expected value (EV) of a random variable is the weighted average of all possible values a random variable can take on.

The expected value may be intuitively understood by the law of large numbers: It can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll).

Example: If you roll a dice, the possible outcomes are 1, 2, 3, 4, 5 or 6 – all with equal probability of 1/6. The expected value of a dice roll is 3.5.

This example shows that the "expected value" is not a result that may be "expected" in the ordinary sense. Rolling a 3.5 with a dice (or having 2.5 children) is impossible.

In trading, we can speak of EV as the estimated value of an investment with unknown return.

A simple example on EV in trading

We can buy an apple for $10. We expect the following (based on analysis or on our experience):
A likelihood of 50% that we can sell the apple for $16.
A likelihood of 25% that we can sell the apple for $12.
A likelihood of 25% that we will not be able to sell the apple and it goes bad.

The expected revenue of the "apple deal" would be:

(50% x $16) + (25% x $12) + (25% x $0) = $8 + $3 + $0 = $11.

Thus, the expected value of the transaction would be $11 minus the $10 that we spend for the apple. The resulting EV of $1 is positive, indicating that doing the deal would be profitable, or "+EV".

The return on investment in this scenario would be +10%.

In many situations, the expected value of an investment can be estimated with thorough analysis.

Positive result versus positive expected value

Differentiating between a positive result and a positive expected result is a key skill needed for every trader.

A trade that made you profit might in fact have had a negative expected value. And a trade that made you a loss might in fact have had a positive expected value.

Coming back to the dice example: you bet $100 on the result of a single dice roll being larger than 2. Obviously, this is a good bet. Still, the result might be a 1 – and you lose the bet.

EV and money management

It also is obvious that you should not bet your life on the dice roll, even if your bet has a positive expected value. The potential loss simply is far too big. This is a good example that shows that you should not take any trade or bet, even if you have a positive expected value.

This is one of the fundamental ideas behind money management. Do trades with a positive expected value, but do not invest more than 1-2% into a single trade. Otherwise, the risk of going broke despite making the right decisions simply is too large.

Lay Last Loser

The Lay Last Loser System is used in the top five English Football Leagues, and lays the last team to lose in each division until they win again. The idea was found on a post on the Betfair Forum and suggested excluding the Premier League and laying teams in their next two games. I have modified this to include the English Premier League and to keep laying teams until they win again.

The reasoning appears to be that once a team loses, the market rates them higher than the team might rate themselves! Confidence is powerful, and a loss can quickly make a serious dent in it.

The system is complete for the 2015-16 season, with the final summary as below:

The 2016-17 season saw this system take a small loss:

Lay System Running Totals 2009-10

League : Bets - Wins ROI%

Bundeliga: 10 - 9 +43.46

.Ligue 1 : 9 - 10 -1.8

.....EPL : 16 - 12 +53.8


Last Updated: 18.Sep.2010

The Smart Money: How the World's Best Sports Bettors Beat the Bookies Out of Millions

A Book of Gambling Secrets, but Some Are Easily Spilled
By EDWARD WYATT

Published: November 11, 2004

In the world of gambling, secrets do not last long, and it is not always easy to tell when someone is bluffing.

Those two maxims could weigh on the minds of editors at Simon & Schuster over the next year as it prepares to publish "The Smart Money: How the World's Best Sports Bettors Beat the Bookies Out of Millions."

The book is said to be the true story of the Brain Trust, a group of professional gamblers that legally wagers hundreds of thousands of dollars in Las Vegas each week on college and professional football games, making it one of the most influential forces in the gambling world.

The book's author was a participant in the group for seven years, first as a courier betting the syndicate's money, then as the operator of his own, smaller gambling ring affiliated with the Brain Trust. The proposal identifies him only as 44, an identity adopted, the author said, to protect the privacy of some of the participants in the gambling ring.

Books about gambling have been hugely popular in recent years, and the proposal for "The Smart Money" reads like an edge-of-the-seat thriller, one made all the more intriguing by the likelihood that it is true. David Rosenthal, the publisher of Simon & Schuster's flagship imprint, and Marysue Rucci, a senior editor there, agreed two weeks ago to buy the book for an advance of roughly $500,000. Publication is scheduled for October.

Simon & Schuster hopes to add an extra element of suspense by having the author wager some of his advance on the number of copies of the book sold in the first year: exceeding a certain number wins 44 a bonus, while falling short of the mark means the author has to return some of his advance.

But both the publisher and the author face several potential pitfalls. While all gamblers lie sometimes, changing the identifying details in a purportedly nonfiction book leaves readers in the uncomfortable position of not knowing which parts are really true. And it turns out that the supposedly anonymous players in this gambling drama are, in fact, very well known. A few hours of Googling and database searching by a reporter led to the real identities of 44, the Brain Trust and its principal character. The author is Michael Konik, a freelance writer who worked for several years for Bill Walters, a Las Vegas developer who is one of the country's biggest sports bettors.

The book proposal identifies the leader of the gambling ring as Rick Matthews, describing him as "the kingpin of American sports betting," a philanthropist, restaurateur and Southerner who, by dint of being "one of the greatest golf hustlers of all time," is "a millionaire several times over."

Those descriptions make it relatively easy to determine that Rick Matthews is actually Mr. Walters, a Kentucky native who now spends much of his time developing golf courses in Las Vegas. In a telephone interview, Mr. Walters, whose gambling history has been explored many times in magazine and newspaper profiles, confirmed that he is Rick Matthews.

For years Mr. Walters has run the Computer Group, a betting syndicate that uses computers to analyze reams of information on sports teams and players, placing enormous bets when it determines the point spread in Las Vegas books is out of line with its own calculation. Mr. Walters has been indicted at least three times in federal or Nevada state courts on charges of illegal gambling, but the indictments have been dismissed each time; he has never been convicted of any gambling charge. In 1999 The Las Vegas Review-Journal named him as one of the 10 most influential nonparticipant figures in sports.

Mr. Walters and others also said 44 was Mr. Konik, a television commentator on poker matches for Fox Sports who has written extensively about gambling and golf. Among his several books is "The Man With the $100,000 Breasts and Other Gambling Stories" (Huntington Press, 1999), which includes a profile of a high-stakes golf hustler who is a thinly disguised Mr. Walters.

Mr. Konik, reached at his home in Los Angeles, declined to discuss whether he was 44. Mr. Rosenthal, the publisher, also said he had no comment about Mr. Konik's relationship to 44.

In an earlier telephone interview, arranged by his literary agent, Jennifer Joel of International Creative Management, the anonymous 44 sounded much like Mr. Konik. In the interview, the author said all the events to be described in the book were true and were based on an extensive journal kept during his tenure at the gambling group, from 1996 to 2003. According to the proposal, the author recorded in the journal his gambling wins and losses, brushes with the law and "the stunning sensation of actually holding $1 million worth of cash in my hands."

But the author said he believed that he needed to change identifying details of people in the book because many of the participants in the gambling ring, as well as the peripheral characters in the casinos and elsewhere, are not public figures. As such, their abilities to sue successfully for libel or defamation are greater than they would be if they intentionally sought publicity.

The author also said that while all of his gambling activities were legal, not everyone who knows him is aware of his gambling venture, and he would rather keep it that way. The details revealed in the book proposal, however, seem unlikely to allow that to happen. The proposal details the author's start-up of his own gambling circle, which he calls "the Hollywood boys" and which includes some well-known but as-yet-unidentified celebrities.

Mr. Rosenthal, the publisher, said he did not think that the book needed an anonymous author to succeed. But so far, at least, he said he was willing to honor the author's desire to remain unknown. "He's not a C.I.A. station chief, but he has some specific reasons for wanting to keep his identity under wraps," Mr. Rosenthal said. "It's important to him, which I respect. But I think I could do it either way."


Michael Konik went along for a gut-crunching ride as Big Daddy beat the bookies

Reviewed by Jeff Ostrowski
December 31, 2006

Anybody who has played the office football pool knows how easy it is to fancy yourself an expert handicapper, and just how hard it is to outsmart the Las Vegas line. The matchups sit there like ripe fruit to be plucked. How can the unbeaten Bears be mere 10-point favorites against the lowly Dolphins? Then Rex Grossman throws three interceptions, the Bears lose three fumbles, and the Dolphins win easily.

Add in the bookies' 10 percent commission – which means you have to be right more than half the time just to break even – and you get an idea why casinos are so profitable.

Michael Konik knows these gut-wrenching ups and downs all too well. The magazine writer spent four football seasons as part of a gambling syndicate, an experience that taught him two lessons: Yes, you can outsmart the bookies. And no, it's not worth it.

Not unless you possess ironclad nerves and a bottomless well of patience. You had also better know a programmer who can whip up an algorithm to pick the winners, because opinions and hunches make for sucker bets.

Konik's introduction to this clandestine world came in 1997, when he met Rick “Big Daddy” Matthews. The legendary sports gambler recruited the scribe to work as one of the dupes who placed bets on behalf of Matthews' Brain Trust.

Matthews needed the help because every bookie in Las Vegas had refused his business. So Konik showed up at Caesar's Palace and concocted a story painting him as a high roller who'd cashed a big advance for a screenplay. In fact, he was simply moving Matthews' money.

But there was no such person as Rick “Big Daddy” Matthews, no such syndicate as the Brain Trust; both are names Konik made up. The New York Times and Las Vegas Review-Journal have reported that Konik's boss actually was Las Vegas developer and gambler Billy Walters, and the syndicate was known as the Computer Group.

Konik floats through the first-season honeymoon in which he is entrusted with briefcases full of cash, gets a front-row seat on the action and enjoys the high-roller treatment at Vegas' poshest casinos. The money isn't bad, either. As one of Big Daddy's operatives, Konik keeps 10 percent of the winnings but risks none of the losses.

But he operates under a constant cloud of suspicion: The bookies suspect that he works for Matthews, and any time he launches a winning streak, they limit his bets or close his account. Konik's girlfriend, tired of his gambling obsession, moves out.

By 1999, with offshore casinos booking millions through the Internet, Konik moves his money online, but he finds that the bookies in Costa Rica and Antigua are even slipperier than his pals in Vegas.

Konik deftly builds suspense throughout his fast-paced account, and it's not giving away too much to say that he finally decides that he's just not cut out to be another Big Daddy.

“All the time and psychic energy I devote to wagering on sports surely could be better spent on something else,” he writes in an uncharacteristic bout of introspection. “Anything else.”

© Cox News Service