Let's Make a Deal: why you should always switch doors.

Let's Make a Deal, an American television game show, takes centre stage in our story #10. The programme was created and produced by Stefan Hatos and Monty Hall, the latter serving as its host for nearly 30 years.

The focus of our story

The Monty Hall problem was introduced in 1975 by an American statistician as a test study in probability, inspired by the show. It is also called the Monty Hall paradox: a veridical paradox, because the result appears impossible but is demonstrably true. The problem examines the counterintuitive effect of switching one's choice of doors, one of which hides a prize. It has been analysed many times, in books, articles and online.

The game

A guest on the show has to choose among three doors, behind one of which is a prize. The guest states a choice, and the host opens one of the two remaining closed doors — always being careful that it is one with no prize behind it.

Should the guest switch to the remaining closed door? Most people choose to stay with their original choice, which is wrong — switching increases the chance of winning from 1/3 to 2/3. There is a 1/3 chance that the original pick was correct, and that does not change when a door is opened.

Even after playing the game many times — which would give ample opportunity to observe that switching doubles the chances of winning — most people in one study switched only two-thirds of the time. Pigeons did better. After a few tries, the pigeons learned to switch every time.

The problem was also used in the movie 21. And many have observed that it is mathematically identical to a problem proposed by the French mathematician Joseph Bertrand in 1889, and to the three-prisoner problem that Martin Gardner introduced in 1959.