The restaurant con

Three men in a restaurant are presented with a bill for 25 pounds. They give the waiter 30 pounds, in 10 pound notes, and he returns with 5 pounds in loose change. The men take 3 pounds and leave a 2 ponds tip.

The men have now each paid out 9 pounds, making 27 pounds in total. The waiter has a 2 pound tip.

27 pounds + 2 pounds = 29 pounds

But the men gave the waiter 30 pounds, so 1 pound is missing. Who is conning whom?

(See end of article for answer)

The famous football con

John Smith was deleting junk email when he spotted one that caught his attention. It was titled “AMAZING FA CUP PREDICTION” and being a football fan, he opened it to find out more. The message read:

Dear Football Fan

We know you will be skeptical, but we have devised a remarkably accurate method of predicting the results of football matches. This afternoon, Coventry City play Sheffield United in the third round of the FA Cup. Our system forecasts that Coventry City will win. We advise you not to bet on this but you might be interested to note the result this afternoon.

Yours truly,

The Cup Predictors

So, as he always did, John watched the match and Coventry won their game. About two weeks later, he got another email.

Dear Football Fan

Do you recall that we accurately predicted the victory of Coventry City in the last round of the FA Cup? Today, Coventry plays Middlesbrough. Our prediction is that it is Middlesbrough who will go through to the fifth round. We strongly advice you not too bet, but please follow our results to see if they are correct.

Yours truly,

The Cup Predictors

John waited the results that afternoon with, as you can imagine, a bit more interest. Result – a 1-1 draw. So it had all been a fluke, but the following Tuesday, Middlesbrough won the replay 2-0. An email from the Cup Predictors soon followed. They forecasted that Tranmere Rovers would defeat Middlesbrough, and they did. In the quarter finals, they predicted that Tranmere were to lose against Tottenham, correct again. The next email read, “We know this is an unusual system, but maybe you are now more convinced that we are on to something. In the semifinal, Arsenal will beat Ipswich”. Arsenal went on to win 2-1. This was incredible, John thought.

The next day, another email arrived:

Dear Football Fan

You have witnessed the results of our amazing football predictor system. Are you convinced? We have made five correct predictions out of five, which you will agree defies the normal chance, especially since a team that won was not always the favourite. As a special deal, we are offering you a chance to subscribe to a trial month without match forecasting service for just 200 pounds. You email us the two teams and we send you the prediction.

We look forward to receiving your order.

Sincerely yours,

The Cup Predictors

Although 200 pounds is a bit steep, John went ahead thinking he would be able to make more money back from the bookmaker. So he used his credit card to make the 200 pound payment.

So, where was the con? Or is there really a con and the writer (me) is actually conning the reader (you) into thinking that their actually is a con. Nope. The con is relatively simple.

Consider this, say 8000 emails were sent out by the Cup Predictors. Instead, unlike John’s first email, Dave who lives down the road, received an email saying that Sheffield would beat Coventry. Of course, 4000 emails would be correct and the incorrect ones, like Dave got, would just be deleted and no more thought given to it. Out of the 4000 people who got the correct email, 2000 were sent saying Middlesbrough would beat Coventry and the other 2000 said Coventry would beat Middlesbrough. After Coventry lost, no more emails would be sent to the people who received the incorrect email which said Coventry would win. So by the time of the final, 250 people had five correct predictions. 50 of them handed over 200 pounds (John being one of them) and had given the organizers a lovely profit. Most scams like this depend on our inclination to think we are special, so that when lucky things happen there must be a reason.

The restaurant con

Remember the three men in the restaurant earlier? Well, unlike the football scam, it is actually the writer conning the reader who believes one pound is really missing. All that was being presented was some misleading accounting.

At the end of the transaction, the men have paid 27 pounds, of which 25 was for the meal and 2 pounds for the tip.

27 pounds – 2 pounds = 25 pounds

This balances out perfectly.

Another way to look at it is that the men had paid 30 pounds, 25 went to the meal, 3 pounds returned change and a 2 pound tip.

The sum 27 pounds plus 2 pounds = 29 pounds is a complete red herring, but because it is so close to 30 pounds it is easy to believe the two numbers are related.