Monty Hall Problem
I am an avid puzzle solver, and I would like to share this really interesting one that I read about many years ago. This puzzle is famously known as the Monty Hall problem, based on the name of the host of a game showin the United States.
What happens during the show is this: A contestant is shown 3 doors. He then decides on a door to open, and behind 1 door will be the grand prize of a car (the other 2 doors reveals a goat). After the contestant decides on a door, the host, who has prior knowledge of where the car is, will open 1 of the door that the contestant did not choose, to reveal a goat. This leaves 2 remaining doors unopened, one of which will reveal the car. The host then proceeds to pose a simple question to the contestant: Do you want to change your choice?
The solution to this puzzle is counter-intuitive. By changing one's choice, the contestant actually increases his original chance of winning from 1/3 to 2/3. Many people, including some famous mathematicians who challenged this proposition when it was first suggested, thought that the probability is 50-50 and it did not matter whether you change your choice or now. But they were wrong. By changing his choice, the contestant improved his chance of winning from 1/3 to 2/3.
The thing I like about puzzles is that they sometimes reveal the biases or tendencies that people generally have. It helps you understand what these biases are, and you can avoid them when making day-to-day decisions. After all, life is about making decisions. Knowing the odds well always improve your chances.
In the long-run, the person who makes the most of his choices is likely to fare way better than his peers. Call it compound consequences if you like. They stack up slowly, and by themselves look insignificant, but put together will become consequential.
What happens during the show is this: A contestant is shown 3 doors. He then decides on a door to open, and behind 1 door will be the grand prize of a car (the other 2 doors reveals a goat). After the contestant decides on a door, the host, who has prior knowledge of where the car is, will open 1 of the door that the contestant did not choose, to reveal a goat. This leaves 2 remaining doors unopened, one of which will reveal the car. The host then proceeds to pose a simple question to the contestant: Do you want to change your choice?
The solution to this puzzle is counter-intuitive. By changing one's choice, the contestant actually increases his original chance of winning from 1/3 to 2/3. Many people, including some famous mathematicians who challenged this proposition when it was first suggested, thought that the probability is 50-50 and it did not matter whether you change your choice or now. But they were wrong. By changing his choice, the contestant improved his chance of winning from 1/3 to 2/3.
The thing I like about puzzles is that they sometimes reveal the biases or tendencies that people generally have. It helps you understand what these biases are, and you can avoid them when making day-to-day decisions. After all, life is about making decisions. Knowing the odds well always improve your chances.
In the long-run, the person who makes the most of his choices is likely to fare way better than his peers. Call it compound consequences if you like. They stack up slowly, and by themselves look insignificant, but put together will become consequential.
posted by Jeremy at 10:34 AM
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