If someone told you about a prize behind one of three doors, you would have about a 33 per cent chance of guessing the right one. Before you get the answer, you’re told that the door you didn’t pick was a loser. What are your chances now?
Photo by Marc Falardeau.
You might think you now have the same chance, but what you should really do is change your choice. In fact, according to one detailed and helpful rundown of what’s known as the Monty Hall Problem:
So by changing doors you double the probability of winning the prize from 1/3 to 2/3.
If you don’t switch, the probability remains 1/3.
If you are not convinced yet, play the game with a colleague as the host and try 30 times with and 30 times without switching. Then count the number of successes in each condition.
The principal applications of the Monty Hall conundrum — that new information does in fact change what seems like simple odds — are in A/B testing, scientific results and other maths-geek uses. But whenever you’re asked to make a choice at picking the right item, and you can figure out somehow that choices you didn’t pick are losers, keep Let’s Make a Deal and Mr Hall in mind.
The famous Monty Hall problem and what it has to do with A/B testing [The Visual Website Optimizer]
And Behind Door No. 1, a Fatal Flaw [New York Times]
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