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Author: Raudaskyla Christian College Monty Hall - Problem Introduction In some TV-shows the winner may choose one of three doors. Behind one door there is the top prize, for example a trip or a car. There is nothing behind two other doors. At first player chooses one door. After that the host of this game show opens one of the two doors player has not chosen. Behind this door, there is nothing. Then the host asks: ”Do you want to change the door?” This is the main point of Monty Hall – problem: does it pay off to change? The host knows all the time, where the prize is. Theory This interesting problem is based on probability. Results in theory can easily be shown through a table. Here we assume that player picks the first door at start: Chosen door Door 2 Door 3 Result by changing Prize Empty Empty Empty Prize Empty Empty Empty Prize Lose Win Win Result, if player doesn’t change Win Lose Lose Thus this table shows that if you change the door, the probability to win is 2/3. If you don’t change the door, the probability to win is 1/3. In other words: by changing the door player loses only if he has chosen right at first. Probability of that is 1/3. Therefore probability to win by changing is 2/3. Organization We tested this problem in mathematics lesson at Raudaskylän Lukio. The group consisted of first and second year students. They were divided in small groups (3-4 students/group). Each group had three cups and one ”prize”, for example a rubber. In a group, student took roles as a host and as a player. The roles were changed. They listed their statistics by changing and by staying in first option. Results When each group had finished their job, we got following results (presented at the next page): Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Total Wins 14 16 13 16 15 18 Change Defeats 11 9 12 9 10 7 Wins 12 8 9 7 8 11 No change Defeats 13 17 16 18 17 14 92 58 55 95 When player changed the door, his/her winning percentage was 61,3. Without a change the percentage was 36,7. Conclusion Our experimental game supports the theory. Neverheless, this problem is also psychological and after first phase player may think that chances are now even: two doors and there is a prize behind one or the other. Dare I change? This test and probability theory shows that the change pays off. As we all know ”variety is the spice of life!”