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The Three Doors
I was listening to Quirks and Quarks on CBC radio once and there was a guest who spoke about probability. He mentioned this puzzle that was on the Monty Hall game show. The deal was that there were three doors, a car behind one and goats behind the other two. The contestant chose a door and then the host would open one of the other doors that didn't contain the prize. He would ask the contestant if he wanted to stick with his original guess or change to the other door. So, would it make a difference if you switched or not? Most people would say no - there is a 50/50 chance that the last two unopened doors contain the car. In fact, however, you have a 2/3 chance of winning the game if you switch and a 1/3 chance if you don't. So it is always better to switch. I dug up this webpage that explains the probability of the game. Anyway, I thought it would be cool to see this for myself so I built a program that randomly places the goats and car and then randomly chooses the doors. You can specify how many rounds are played and whether you should always stick with your first guess or switch. At the bottom of all the rounds you can see the winnings. Check it out for yourself - is it better to stick or switch?
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