This paradox is inspired by the 1960s American TV quiz show *Let’s make a deal*, hosted by host **Monty Hall**. The game consists of three doors, behind each of which there is a prize or non-premium, and the prize is hidden behind a single door. The probability of the prize being behind a given door is the same for all doors and is 1 in 3.

## How to play

The player chooses one of the doors and tells everyone. The handler knows what lies behind each door and must open one of the doors not selected by the player and absolutely one without a prize: if the player has chosen a losing door, the handler will open the other losing door; if, on the other hand, the player has chosen the winning door, the handler will open one of the two remaining doors at will.

After opening the first door, The handler gives the player the option of finding out what is behind the door he or she initially chose or to change. Which strategy is best for the player? Keep the first choice or change?

It would seem a paradox, but it is better to change the initial choice: doing so doubles the probability of winning. How is this possible?

At the beginning there are three possible scenarios, each having probability 1/3:

(1) The player chooses the first non-winning door (number 1), The host shows the other non-winning door, (number 2): by changing the player wins. By not changing he loses.

(2) The player chooses the second non-winning door (number 2). The handler chooses the other non-winning door (number 1): by changing, the player wins. By not changing, he loses.

(3) The player chooses the winning door. The handler shows one of the two losing doors. By changing, the player loses. By not changing, he wins.

In the first two scenarios the player wins only by changing; in the third scenario the changing player does not win: the “changing” strategy leads to victory two out of three times (2/3), while the “not changing” strategy leads to victory in only one out of three cases (1/3).

The resolution of this problem is so counter-intuitive that several academics did not recognize it until it was explained to them in detail. A simple way to understand it is to increase the number of doors, and to simplify you can use playing cards, the figure represents the winning card, the cards represent the doors.

Let’s put this time 4 doors, 3 losers and one winner. The player, as before, chooses one door, the host, however, shows two – losers, as before – and later asks the player if he wants to change or keep his initial choice. Thus there will be 3 out of 4 eventualities in which the player wins only if he changes and 1 out of 4 in which he wins only if he does not change. The result is valid and, indeed, is even clearer the more you increase the number of doors, and with cards it is very easy to increase iul number of doors at will.

## How to build

**EXHIBIT MATERIAL DIN VERSION**

- n. 1 vertical pallet 120×200 cm – with square hole of 60×60 cm
- n. 1 base pallet 120×80 cm
- n. 3 small doors of different shapes
- n. 1 TV template
- n. 3 red MDF circles with numbers
- n. 1 title panel 120×20 cm
- n. 1 printed TV back panel with instructions and pallet attachment system.
- n. 3 wooden panels with holes to insert prizes (wooden shape) // to be placed behind the three small doors
- n. 3 wooden templates, one prize and two sheep

**CLICK AND DOWNLOAD PRINT-READY .PDF FILES:**CARDBOARD PANEL MONTY HALL (retro) 70×60 cm (ITA) CARDBOARD PANEL MONTY HALL (fronte) 70×60 cm (ITA) CARDBOARD PANEL MONTY HALL (retro) 70×60 cm (FRA) CARDBOARD PANEL MONTY HALL (fronte) 70×60 cm (FRA) MONTY HALL PRIZE NUMBERS (rectangle) MONTY HALL PRIZE (round) NO-PRIX CARDBOARD (rectangle) PRIX CARDBOARD (rectangle) PRIX SILOHUETTE NO-PRIX SILOHUETTE