# Should you Stick or Switch?

When taking a multiple-choice test, it often seems one answer is correct initially, however, on further reflection you think a different answer is correct. In this situation, is it better to switch or stick with your first answer?

Most people believe you should avoid changing your answer, but research has shown that most answers are changed from incorrect to correct, resulting in test scores improving when students change their answers (Kruger, Wirtz & Miller, 2005). But why do most of us still believe that we should stick with our first choice?

“The vast majority of over 70 years of research on answer changing, however, has questioned seriously the validity of this belief and the utility of the “always stick with your first instinct” test-taking strategy. The majority of answer changes are from incorrect to correct, and most people who change their answers usually improve their test scores.”(Kruger, Wirtz & Miller, 2005 p.725).

Counterfactual thinking is the frustrating feeling that follows after the change of a right answer to a wrong answer (Kruger, Wirtz & Miller, 2005). As humans losing carries more impact than winning. This is because when we are disappointed by something it has a longer lasting impression. For example, most people will write a negative review on TripAdvisor over a positive review because the negative experience has made a greater impact. What you focus on is how you will feel, focus on the negative you will feel negative.

“changing an answer when one should have stuck with one’s original answer leads to more “if only…” (Kruger, Wirtz & Miller, 2005)

By looking at the classic thought experiment in probability called ‘The Monty Hall problem’ we can understand the fundamental math’s used. The Monty Hall Problem is a counter-intuitive mathematical puzzle: There are 3 doors, behind which are two goats and a car. The player picks a door (call it door A). The player is hoping for the star prize, a car! The Game show host knows what is behind each door and will always pick the door with a goat behind it to show to the player.

Here’s the question: Do you stick with your original guess Door A or switch to the other unopened door? What are the consequences?

Surprisingly, the odds are not 50-50 which most people might believe, including myself when I was first introduced to the idea. However this is not correct, you actually have twice as much chance of winning if you switch your answer. Below is a diagram I have created to explain this baffling concept.

I tested the strategy by using the “pick and switch” approach. I repeated this 20 times and won 14 and lost 6. This is more than double!

Give it a go yourself:

https://betterexplained.com/articles/understanding-the-monty-hall-problem/

So the answer is you should always swap, as this gives twice the chance of winning the car. But why?

Probability = the likelihood of the event happening/ number of possible outcomes (wikihow.com)

If you chose ‘not to swap’ you have a probability of 1/3 or about 33% chance in not picking the car because there are three doors and only one car. Since there are three doors and 2 goats the probability of you picking a goat is 2/3 or about 66%. So by ‘swapping’ you have a 66% chance of winning the car and a 33% chance of winning a goat.

The trick of the game show is making it appear like the player has a 50-50 chance of winning the car just like the chances of landing on a tail when tossing a coin which sounds sensible but it not correct. So by using your mathematical knowledge of probability will you consider changing your answer the next time you are unsure? Because I certainly will!

References:

Kruger, J., Wirtz, D., & Miller, D. T. (2005). Counterfactual Thinking and the First Instinct Fallacy. Journal of Personality and Social Psychology, 88(5), 725-735. http://dx.doi.org.libezproxy.dundee.ac.uk/10.1037/0022-3514.88.5.725

Wikihow.com: https://www.wikihow.com/Calculate-Probability

Betterexplained.com:https://betterexplained.com/articles/understanding-the-monty-hall-problem/