Experiment 1: Three doors in the classroom

Before you play the game on a computer, you play it together at the front of the classroom: with three doors, a host who knows where the car is, and a different person in every game who gets to guess. The rest of the room votes, watches and keeps the record. After ten games or more you have a first small data set and a feeling for what actually happens in a game. What the game looked like on television is shown in Geh aufs Ganze: the game on television.

What you need

• three doors that can stand side by side and be opened one at a time, marked 1, 2 and 3 in large print: three large envelopes, three upturned boxes or three sheets held to the board with magnets
• three cards that fit behind the doors: one with a car, two with a goat
• a die and a coin
• a screen behind which the cards are placed, such as the lectern or an open flip chart
• the board or a computer on the projector for the record; the table from What should we measure? works well for this

Setup

At the front the three doors stand side by side on a table, their numbers facing the room. The host stands behind the table: before every game he places the cards and is the only one who knows where the car is. In front of the table stands the person who guesses, someone different from the room in every game. Another person keeps the record at the board, and everyone else is the audience.

For the experiment to be worth anything, chance decides, not the host. The die decides where the car goes: on 1 or 2 behind door 1, on 3 or 4 behind door 2, on 5 or 6 behind door 3. If both doors he may open hide goats, he tosses the coin: on heads he opens the one with the lower number. A host who likes to put the car behind door 2, or an audience that watches the cards being placed, spoils the games.

Before: your expectation

Before the first game begins, the whole room votes by show of hands: do you win more often if you stay with your door, if you switch, or does it make no difference? The record keeps the three numbers.

How a game goes

1. Hide. Behind the screen the host rolls the die, puts the car behind the door it shows and the goats behind the other two. Then he sets up the closed doors.
2. Choose. The person at the front points to a door, which stays closed for now.
3. Open. The host opens one of the other two doors, always one with a goat. If he has two to choose from, the coin decides.
4. Decide. The host asks: "Do you stay, or do you switch?" The audience may first show by hand what it would do, but the decision is made by the person at the front alone.
5. Reveal. All doors open, and the record notes the game.

Then the next person comes to the front. Play ten games or more: the more there are, the less the result depends on the luck of single games. Make sure that staying and switching happen about equally often. If one of the two decisions is clearly rarer, decide beforehand for the last games what the person at the front will do.

Record

Every game gets one row. The first three could look like this:

Whether these six columns hold everything you will want to know later, and whether one of them already follows from the others, you discuss in What should we measure?.

Analysis

• How often did the people who stayed win, and how often those who switched, each as a proportion? Does that fit your vote before the first game?
• How often was the first choice already right? What proportion would you have expected?
• In which games did the host have to toss the coin, and in which did he have no choice at all? What did he know in those games that the person at the front did not?
• Would you say after your games which decision is the better one? How many games would you need to be sure?

On your own you then go on in the three-door game, and in phase 4 you let R play so many games that the last question answers itself.