The System
The System
TV series
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Derren Brown did this with horse races IIRC for a TV show.
https://derrenbrown.co.uk/shows/the-system/
British illusionist Derren Brown made a documentary about this, called "The System", where he wrote letters to people predicting the outcome of horse races using his secret system, and suggesting they place a bet.
He sent different predictions to different people, some saw his predictions come true, and he sent more letters to all those people. And then repeated that, eventually narrowing it down to one person, who saw week after week correct gambling predictions, and really believed he had a system for winning.
She borrowed family money to bet big - then he revealed that she was the result of survivor bias and he had no system.
http://topdocumentaryfilms.com/derren-brown-the-system/
TL;DW for The System (courtesy of Wikipedia):
The System, a Channel 4 special in which Brown shared his "100 percent guaranteed" method for winning on the horses, was first shown on 1 February 2008.
The show was based around the idea that a system could be developed to "guarantee a winner" of horse races. Cameras followed a member of the public, Khadisha, as Brown anonymously sent her correct predictions of five races in a row, before encouraging her to place as much money as she could on the sixth race. To demonstrate the system to the viewer, Brown tossed a coin showing ten heads in a row to prove it was not impossible, just highly improbable.
After Brown had placed a bet of £4,000 of Khadisha's money on a horse in the final race, he explained that "The System" did not really exist. He had started by contacting 7,776 people and split them into six groups, giving each group a different horse. As each race had taken place 5⁄6 of the people had lost and were dropped from the system. Brown had a different person backing each horse in each race, and one individual, Khadisha, won five times in a row. This was similar to the coin flipping earlier: rather than having a predictive technique, Brown had tossed a coin repeatedly until ten heads had come up in a row, taking over nine hours to produce the required film. Brown expressed the opinion that the principle behind "The System" (essentially confirmation bias or survivorship bias) is what is behind belief in spiritualism or homoeopathic and alternative medicine.
After the selected horse in the final race lost, and Khadisha was convinced that she had lost all her borrowed money, Brown told Khadisha to look again at the betting slip in her hand. The ticket showed the winning horse's name, meaning Khadisha kept her stake and received winnings of £13,000. Brown claimed that he had decided to bet on a different horse when he got to the booth.
At the end of the show, a title card explained that "at each stage of the process, participants who did not make it to the next round were offered a complete refund of any bets they had placed."
This reminds me of Derren Brown's awesome "The System" special:
http://www.youtube.com/watch?v=9R5OWh7luL4
More info for anyone who hasn't had the pleasure of knowing who Derren Brown is:
http://en.wikipedia.org/wiki/Derren_Brown
Derren Brown is a British illusionist, mentalist, trickster, hypnotist, painter, writer, and sceptic. He is known for his appearances in television specials, stage productions, and British television series such as Trick of the Mind and Trick or Treat. Since the first broadcast of his show Derren Brown: Mind Control in 2000, Brown has become increasingly well known for his mind-reading act. He has written books for magicians as well as the general public.
Though his performances of mind-reading and other feats of mentalism may appear to be the result of psychic or paranormal practices, he claims no such abilities and frequently denounces those who do. Brown states at the beginning of his Trick of the Mind programmes that he achieves his results using a combination of "magic, suggestion, psychology, misdirection and showmanship".
The Derren Brown episode he mentions is well worth a watch if you enjoyed this - he doesn't deal so much with the mathematical side, but the idea of using misdirection to show something unlikely happening simply through consistent trial.
Edit: the show is called "The System"