BERD Design and Computational Resources Unit

History of Let's Make a Deal:

"Let's Make a Deal" is an American television game show that originated in the 1960s. It was created and produced by Stefan Hatos and Monty Hall, who also served as the show's host. The show first aired on December 30, 1963, on NBC, and later on ABC, CBS, and in syndication. The basic format involves contestants making deals with the host to trade items or choose between hidden prizes behind doors, boxes, or curtains, often with the possibility of winning big prizes or receiving undesirable "zonk" prizes.

The Monty Hall Problem:

The Monty Hall problem, also known as the Monty Hall paradox, is a probability puzzle based on a scenario that appeared on the show. The classic version of the problem is as follows:

1. A contestant is presented with three doors. Behind one door is a car (the prize), and behind the other two doors are goats.
2. The contestant chooses one door, say Door A.
3. Monty Hall, who knows what's behind each door, opens another door, say Door B, which has a goat.
4. The contestant is then given the option to stick with their original choice (Door A) or switch to the remaining unopened door (Door C).

The puzzle asks: Is it to the contestant's advantage to switch their choice?

Solution to the Paradox:

Mathematically, it is to the contestant's advantage to switch doors. When the contestant first picks a door, there is a 1/3 chance they picked the car and a 2/3 chance they picked a goat. When Monty reveals a goat behind one of the other two doors, the probability of winning by switching is 2/3, whereas the probability of winning by staying with the initial choice is 1/3. This counterintuitive result is often surprising to many people.

Marilyn vos Savant and the Controversy:

The Monty Hall problem gained widespread attention in 1990 when Marilyn vos Savant, who holds the record for the highest IQ, addressed the problem in her "Ask Marilyn" column in Parade magazine. She presented the problem and explained that switching doors increases the contestant's chances of winning.

Response from Mathematicians:

Vos Savant's explanation received thousands of letters, many of them from readers who disagreed with her solution. Among the respondents were numerous mathematicians and professors who argued that her solution was incorrect. This widespread disagreement highlighted how counterintuitive the solution is, even for those well-versed in probability and mathematics. Over time, however, many mathematicians and statisticians verified her explanation and used the problem to illustrate important concepts in probability theory and decision-making.

Impact and Legacy:

The Monty Hall problem remains a popular example in teaching probability and statistics. It illustrates the importance of considering all available information and understanding conditional probabilities. The controversy surrounding vos Savant's column also demonstrates how even experts can struggle with counterintuitive problems, underscoring the value of rigorous mathematical reasoning.