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The Monty Hall paradox

This paradox is named after Monty Hall, the host of the famous American Television game ‘Let’s make a deal’. This problem is based on the probability theory.

In the original game, the player is asked to stand in front of three sets of doors. There is a prize hidden behind one of them (assigned completely randomly by the computer system, and only the TV host knows where it is).  When the player picks one of the doors, the presenter then opens one of the other two doors highlighting that the prize is not there. Then the player is asked to either stick with their original choice or to switch to the other door. Mueser and Granberg (1999), found that when first presented with the Monty Hall problem, majority of people concluded that it does not matter whether you stick or switch.

According to intuition it does not matter whether the player sticks or switches. However it turns out to be completely different. By choosing to stick with the original choice, the probability of winning is 1/3, however the probability of winning when choosing to switch is 2/3.

This means that it is better to switch the doors, as it doubles your chances of winning. The paradox is a result of a common misunderstanding, and underestimation. The host by opening one of the empty doors tries to trick the players, to think that they have 50/50 chance of winning (since there are only two doors left). The show is cleverly designed, and they know that most of the people will choose to stick with their original choice (in their study, Granberg and Brown, (1995), found that only 13% out of 228 subjects in the study, chose to switch. In the experiment carried out by ’Mythbusters’ (see the video clip attached) all of their 20 participants decided to stick with their original choice), whereas switching doubles your chances of winning.

Another words by opening an ‘empty’ door, the host decreases the number of ‘empty’ doors, and therefore decreases the probability of losing from 2/3 to 1/3. Therefore the ’remaining’ probability of winning needs to be 2/3.

One of the strategies that the host of the show uses is the endowment effect (Kahneman et al., 1991). The idea behind this effect is that people tend to overestimate the probability of winning of the door, they have already chosen. Also because of the ‘status quo bias’ (Samuelson and Zeckhauser, 1988), which states that people are more likely to stick to the choice they have already made. However the research of Morone and Fiore (2007), shows that this bias does not depend on the probability intuition.

Picture taken from: http://en.wikipedia.org/wiki/Monty_Hall_problem

In the popular show ‘Mythbusters’ (see the video clip attached) were asked by the audience to investigate the Monty Hall Paradox. This clip summarizes the problem very well and I believe it is a very good introduction to the topic. Therefore feel free to have a look.

To conclude this is a very interesting topic, which requires people to look at the problem without any sentiments. Clive Thompson (http://www.wired.com/magazine/2010/04/st_thompson_statistics/) suggested that students shouldn’t leave education unless they complete statistics course, and this would not be a bad idea, as it would make people realize that sticking with their original choice has half the winning probability as switching.

Clip By ‘Mythbusters’:


Clip by ‘stedwick’:


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