Statistical scam

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An instructive example of how easily people are fooled.

I'm going to write this first from the perspective of a skeptic - who becomes a true believer - then secondly from the perspective of the psychic. You get a letter out of the blue that predicts the outcome (who will win) of eight upcoming football games that are playing on the next weekend - no name on the letter, no return address, nothing. Just eight simple predictions: "Team X will beat Team Y". Every single one of them turns out to be true! You're blown away! How can someone possibly predict eight football games perfectly? He can't be bribing that many players and referees! A few weeks later you get a typewritten note in the mail: "You know I can predict the future - you know I can do it. You If you pay me $10 in cash I'll send you a prediction for the such-and-such versus so-and-so game two weeks from now- you'll have plenty of time to place a bet on it and earn a lot more than $10 - but don't tell anyone! The more people who know the more chance the bookmakers will realise that I can do this!". The return address is a PO box. You decide that $10 isn't much - and this is pretty fascinating stuff - so you send it off and lo and behold, you get another prediction in the mail (as promised) - you bet $20 on predicted winners - and AMAZING! It turns out to be true! This guy really is a psychic! You won money! The letter that comes with the prediction says he'll send you another prediction - but this time it's going to cost you $20...this goes on several times - each time the amount it's going to cost you goes up...but you're making a FORTUNE on your gambling winnings - way more than this is costing you to pay for more predictions! Subsequent letters demand $40, $80, $160, $320...but he nails every single game perfectly just as he promised and you're betting LOTS of money on each game now! Then, finally - he tells you that he's going to send you only one more letter and it's going to cost you $1,000 but it will contain predictions for every single football game for the rest of the season. He says "This is your last chance - then the game is over!". Do send him the money (many people did)?

What happened here? This is a genuine, for real psychic - right? How else could someone predict all of those football games? Why did everything go wrong at the end?

Well, what actually happened was that the "psychic" picked 65,536 people at random from all around the USA. He had a computer program that printed 256 copies of 256 different letters - each different letter predicting one of the 256 possible outcomes of the same eight football games. No matter how the games turn out, one out of every 256 letters will contain the right set of predictions - and the other 255 letters will fail to predict all of the games. The letters are posted off anonymously. After the football games are over - he notes which people got the letters that correctly predicted the outcome of the eight games - there are 256 people. The other 65,300 or so people never hear from him again - they are puzzled - but assume it's some kind of viral marketting thing. Of the 256 people who got good predictions, over 200 of them sent him $10 - more than enough to cover his initial postage costs for the $65,000 initial letters. Now he sends one half of the people a letter saying that team X will win in the big X versus Y game - the other half are told that Y will win. Half of the people are upset that his prediction goes wrong - most of them don't send him any more money - but the half that get a true prediction are elated! ALL of them (about 100 people) send him $20. He sends fifty of them one outcome for the following week - the other fifty get the other outcome. Same deal - next time only 50 people win - but they are hooked! They've found a cash cow! 50 envelopes with $40 in each arrive. Then 25 people, $80 each, 12 people $160 each, 6 people $320 each, 3 people sent him $10,000. When none of them got good predictions, they tried to get the police involved - but he was long gone. Each stage of the game nets him $2000 - the game went through 5 stages ($10,000) and the final stage is icing on the cake - and probably got him another $3,000 - so a total of $13,000 for posting some letters and having a smart idea.